-
(5.11) \[\begin{align}
+
+(5.11) \[\begin{align}
x_1(t) &= B_1^+ e^{+i\omega_1 t} + B_1^- e^{-i\omega_1 t} + B_2^+ e^{+i\omega_2 t} + B_2^- e^{-i\omega_2 t}, \\
x_2(t) &= -B_1^+ e^{+i\omega_1 t} - B_1^- e^{-i\omega_1 t} + B_2^+ e^{+i\omega_2 t} + B_2^- e^{-i\omega_2 t}.
\end{align}\]
-
Depending on initial and boundary conditions, Euler’s equation could be used to transform the above into a linear combination of \(\sin\) and \(\cos\) functions. For more details, see the lecture by Matthew Schwartz at Harvard or libretexts by Tom Weideman at UC Davis, or lectures on YouTube from Jeffery Chasnov (see below).
+
Depending on initial and boundary conditions, Euler’s equation could be used to transform the above into a linear combination of \(\sin\) and \(\cos\) functions. For more details, see the lecture by Matthew Schwartz at Harvard or libretexts by Tom Weideman at UC Davis, or lectures on YouTube from Jeffery Chasnov (see below). There is also a guide for the generalized method from Lagrangian dynamics provided by the University of Rochester that may be helpful.
VIDEO5. Free and Forced Eccentricity", "1. Introduction to the \u03b1 Centauri System", "7. Basic Climate Modeling", "8. GPU-accelerated planet formation", "2. N-body Simulations", "6. Obliquity Evolution", "4. Planet Packing", "3. Three-body Stability", "Exoplanets within Binary Systems"], "terms": {"attribut": [0, 1, 3, 12], "4": [0, 1, 3, 4, 5, 8, 10, 11, 12], "0": [0, 1, 3, 4, 5, 8, 10, 11, 12], "intern": [0, 1, 3, 12], "creativ": [0, 1, 3, 12], "common": [0, 1, 3, 5, 12], "corpor": 0, "law": [0, 4, 5, 10], "firm": 0, "doe": [0, 5, 10, 11], "provid": [0, 5, 10], "legal": 0, "servic": 0, "advic": [0, 10], "distribut": 0, "public": 0, "licens": [0, 1, 3, 12], "creat": [0, 5, 8, 10, 11], "lawyer": 0, "client": 0, "other": [0, 4, 5, 8, 10, 11], "relationship": 0, "make": [0, 5, 8, 10], "its": [0, 2, 4, 5, 8, 10, 11], "relat": [0, 10], "inform": [0, 3, 8, 12], "avail": [0, 2, 11], "an": [0, 2, 3, 4, 8, 10, 11, 12], "basi": 0, "give": [0, 1, 8, 11], "warranti": 0, "regard": 0, "ani": [0, 3, 5, 10, 12], "materi": [0, 2, 3, 12], "under": [0, 1, 3, 11, 12], "term": [0, 5, 10, 11], "condit": [0, 1, 4, 11], "disclaim": 0, "all": [0, 2, 5, 10, 11], "liabil": 0, "damag": 0, "result": [0, 4, 5, 8, 10, 11], "from": [0, 2, 4, 8, 11], "us": [0, 1, 2, 3, 4, 8, 11, 12], "fullest": 0, "extent": [0, 10], "possibl": [0, 10, 11], "standard": [0, 5, 10], "set": [0, 4, 5, 8], "creator": 0, "right": [0, 4, 5, 8, 10, 11], "holder": 0, "mai": [0, 5, 8, 10], "share": [0, 1, 5], "origin": [0, 1, 5, 10, 11], "work": [0, 3, 5, 8, 10, 11, 12], "authorship": 0, "subject": [0, 5], "copyright": 0, "certain": 0, "specifi": [0, 8], "below": [0, 2, 4, 5, 8, 10, 11], "The": [0, 1, 2, 4, 8, 11], "follow": [0, 4, 5, 8, 10, 11], "consider": 0, "ar": [0, 1, 4, 5, 8, 10, 11], "purpos": 0, "onli": [0, 5, 8, 10, 11], "exhaust": 0, "do": [0, 10, 11], "form": [0, 4, 5], "part": [0, 4, 8, 11], "our": [0, 4, 5, 8, 10, 11], "licensor": 0, "intend": 0, "those": [0, 8, 11], "author": [0, 1, 10], "permiss": [0, 1], "wai": [0, 5, 8, 10, 11], "otherwis": [0, 5, 8, 10], "restrict": [0, 10, 11], "irrevoc": 0, "should": [0, 2, 4, 5, 8, 10], "read": [0, 8], "understand": [0, 11], "thei": [0, 5, 10, 11], "choos": [0, 5, 10], "befor": [0, 5], "appli": [0, 4, 5, 10, 11], "also": [0, 2, 5, 8, 10, 11], "secur": 0, "necessari": [0, 5, 8, 10], "so": [0, 5, 8, 10, 11], "can": [0, 2, 4, 5, 8, 10, 11], "reus": 0, "expect": [0, 4, 8, 10, 11], "clearli": [0, 5], "mark": [0, 10, 11], "thi": [0, 2, 3, 4, 5, 8, 10, 11, 12], "includ": [0, 3, 5, 8, 10, 12], "cc": [0, 1], "except": 0, "limit": [0, 10, 11], "more": [0, 4, 5, 8, 10, 11], "wiki": 0, "creativecommon": 0, "org": 0, "considerations_for_licensor": 0, "By": [0, 8], "one": [0, 4, 5, 8, 10, 11], "grant": 0, "If": [0, 3, 4, 5, 8, 10, 11, 12], "s": [0, 4, 5, 8, 10, 11], "reason": [0, 5, 8], "exampl": [0, 3, 5, 10, 11, 12], "becaus": [0, 4, 5, 10, 11], "applic": [0, 10], "regul": 0, "ha": [0, 2, 4, 5, 8, 10, 11], "still": [0, 10], "have": [0, 2, 4, 5, 8, 10, 11], "A": [0, 5], "special": [0, 10], "request": 0, "ask": [0, 11], "chang": [0, 5, 8, 10, 11], "describ": [0, 4, 5, 10, 11], "although": [0, 10, 11], "requir": [0, 2, 5, 8, 10, 11], "you": [0, 1, 2, 3, 5, 8, 10, 12], "encourag": 0, "respect": [0, 1, 4, 5, 8, 10], "where": [0, 2, 4, 5, 8, 10, 11], "more_consider": 0, "considerations_for_license": 0, "exercis": 0, "defin": [0, 5, 8, 10, 11], "accept": 0, "agre": [0, 10], "bound": [0, 5, 10, 11], "To": [0, 4, 5, 8, 10, 11], "interpret": [0, 10], "contract": 0, "your": [0, 2, 5, 8], "benefit": 0, "receiv": [0, 4, 10], "section": [0, 1, 3, 4, 8, 10, 12], "1": [0, 4, 5, 10, 11], "definit": [0, 5, 10], "adapt": [0, 1, 8], "mean": [0, 1, 5, 8, 10, 11], "similar": [0, 4, 5, 8, 10, 11], "deriv": [0, 5, 10], "base": [0, 3, 4, 12], "upon": [0, 4, 8], "which": [0, 4, 5, 8, 10, 11], "translat": [0, 5], "alter": 0, "arrang": [0, 10], "transform": [0, 4, 5, 10], "modifi": [0, 2, 5], "manner": 0, "held": 0, "For": [0, 4, 5, 8, 10, 11], "music": 0, "perform": [0, 5, 10, 11], "sound": 0, "record": [0, 5], "alwai": [0, 5, 10], "produc": [0, 5], "synch": 0, "time": [0, 4, 5, 8, 10, 11], "move": [0, 5], "imag": [0, 5], "b": [0, 5, 8, 10, 11], "contribut": 0, "accord": [0, 4], "c": [0, 5, 8, 10, 11], "close": [0, 5, 10, 11], "without": [0, 8, 10], "broadcast": 0, "sui": 0, "generi": 0, "databas": 0, "how": [0, 5, 8, 10, 11], "label": [0, 8, 10], "categor": 0, "2": [0, 4, 5, 10, 11], "d": [0, 5, 8], "effect": [0, 5, 10], "technolog": 0, "measur": [0, 5, 8, 10], "absenc": [0, 11], "proper": 0, "circumv": 0, "fulfil": 0, "oblig": 0, "articl": 0, "11": [0, 5, 11], "wipo": 0, "treati": 0, "adopt": 0, "decemb": 0, "20": [0, 5, 8, 10, 11], "1996": [0, 10], "agreement": 0, "e": [0, 2, 4, 5, 8, 10, 11], "fair": 0, "deal": 0, "f": [0, 4, 5, 8, 10, 11], "artist": 0, "literari": 0, "g": [0, 2, 4, 5, 8, 10, 11], "h": [0, 5, 8, 10], "individu": 0, "entiti": 0, "i": [0, 4, 5, 8, 10, 11], "process": [0, 5, 10], "reproduct": 0, "displai": [0, 5], "dissemin": 0, "commun": [0, 11], "import": [0, 2, 5, 8, 10, 11], "member": 0, "access": [0, 8], "place": 0, "chosen": [0, 5], "them": [0, 5], "j": [0, 5, 10], "than": [0, 5, 10, 11], "direct": [0, 4, 5, 10, 11], "96": 0, "9": [0, 5, 8, 10, 11], "ec": 0, "european": 0, "parliament": 0, "council": 0, "march": 0, "protect": 0, "amend": 0, "succeed": 0, "well": [0, 10, 11], "essenti": 0, "equival": 0, "anywher": 0, "world": 0, "k": [0, 4, 5, 8, 10, 11], "correspond": [0, 5, 10], "scope": 0, "herebi": 0, "worldwid": 0, "royalti": 0, "free": [0, 1, 5, 10, 11], "non": [0, 4, 5, 8, 10, 11], "sublicens": 0, "exclus": 0, "reproduc": [0, 11], "whole": [0, 5, 10], "avoid": [0, 10], "doubt": 0, "need": [0, 5, 8, 10, 11], "compli": 0, "3": [0, 5, 8, 10, 11], "6": [0, 5, 8, 10, 11], "media": 0, "format": [0, 2, 10], "technic": 0, "modif": [0, 8], "allow": [0, 2, 5, 8, 11], "whether": [0, 8], "now": [0, 5, 11], "known": [0, 5, 8, 10, 11], "hereaft": 0, "waiv": 0, "assert": 0, "forbid": 0, "simpli": [0, 5, 10], "never": 0, "5": [0, 5, 8, 10, 11], "downstream": 0, "recipi": 0, "offer": 0, "everi": [0, 10], "automat": 0, "No": 0, "impos": 0, "addit": [0, 10], "differ": [0, 5, 8, 10, 11], "endors": 0, "noth": 0, "constitut": 0, "constru": 0, "impli": [0, 5, 10, 11], "connect": [0, 4, 5], "sponsor": 0, "offici": 0, "statu": 0, "design": [0, 8], "moral": 0, "integr": [0, 5, 8, 10, 11], "nor": 0, "privaci": 0, "person": 0, "howev": [0, 5, 8, 10, 11], "patent": 0, "trademark": 0, "collect": [0, 5], "directli": [0, 5, 10], "through": [0, 2, 5, 8, 10, 11], "societi": 0, "voluntari": 0, "waivabl": 0, "statutori": 0, "compulsori": 0, "scheme": [0, 8, 10], "In": [0, 5, 8, 10, 11], "case": [0, 5, 11], "expressli": 0, "reserv": 0, "made": 0, "must": [0, 5, 10, 11], "retain": [0, 5], "suppli": 0, "identif": 0, "pseudonym": 0, "ii": [0, 11], "notic": [0, 4, 5], "iii": 0, "refer": [0, 1, 3, 4, 12], "iv": 0, "v": [0, 5, 10], "uri": 0, "hyperlink": 0, "practic": [0, 10, 11], "indic": [0, 8, 10, 11], "previou": [0, 8, 10], "text": [0, 2, 4, 5, 10], "satisfi": 0, "medium": [0, 5], "context": 0, "resourc": 0, "remov": 0, "prevent": [0, 8], "extract": [0, 11], "substanti": [0, 10], "portion": 0, "content": [0, 2], "supplement": 0, "replac": [0, 5, 8, 10], "unless": [0, 8], "separ": [0, 4, 8, 10, 11], "undertaken": 0, "BY": [0, 1], "THE": 0, "TO": 0, "AS": 0, "IS": 0, "AND": 0, "NO": 0, "represent": [0, 5], "OR": 0, "OF": 0, "kind": [0, 11], "concern": [0, 4, 8], "express": [0, 5, 10], "titl": 0, "merchant": 0, "fit": [0, 11], "FOR": 0, "particular": [0, 5, 8, 11], "infring": 0, "latent": 0, "defect": 0, "accuraci": [0, 8], "presenc": [0, 10], "error": 0, "NOT": 0, "discover": 0, "IN": 0, "full": [0, 5, 8, 10, 11], "event": [0, 10], "WILL": 0, "BE": 0, "liabl": 0, "ON": 0, "theori": 0, "neglig": [0, 5], "indirect": 0, "incident": 0, "consequenti": 0, "punit": 0, "exemplari": 0, "loss": 0, "cost": [0, 11], "expens": 0, "aris": [0, 10], "out": [0, 4, 5, 8, 10], "even": [0, 4, 8, 10], "IF": 0, "been": [0, 5, 11], "advis": 0, "SUCH": 0, "abov": [0, 4, 5, 8, 10, 11], "shall": 0, "most": [0, 4, 5, 10, 11], "approxim": [0, 10, 11], "absolut": 0, "waiver": 0, "termin": [0, 11], "here": [0, 5, 8, 10, 11], "fail": 0, "reinstat": 0, "date": [0, 5, 8], "violat": 0, "cure": 0, "within": [0, 5, 8, 10, 11], "30": [0, 5], "dai": [0, 8], "discoveri": [0, 11], "affect": [0, 8], "seek": [0, 10], "remedi": 0, "stop": 0, "7": [0, 5, 8, 10, 11], "8": [0, 5, 10], "surviv": [0, 11], "state": [0, 4, 10, 11], "herein": 0, "independ": 0, "reduc": [0, 11], "could": [0, 4, 5, 8, 10, 11], "lawfulli": 0, "provis": 0, "deem": [0, 10], "unenforc": 0, "reform": 0, "minimum": 0, "enforc": 0, "cannot": 0, "sever": [0, 11], "remain": [0, 5, 10, 11], "failur": 0, "consent": 0, "privileg": 0, "immun": 0, "jurisdict": 0, "parti": 0, "notwithstand": 0, "elect": 0, "publish": 0, "instanc": [0, 8], "consid": [0, 4, 8, 10, 11], "dedic": [0, 8], "domain": 0, "cc0": 0, "permit": [0, 4], "polici": 0, "logo": 0, "prior": [0, 4, 5], "written": [0, 2, 5, 10], "unauthor": 0, "paragraph": 0, "contact": 0, "repositori": [2, 3, 12], "jupyterbook": [3, 5, 12], "serv": [3, 12], "introduct": [3, 8, 12], "variou": [3, 12], "topic": [3, 12], "my": [3, 12], "research": [2, 3, 10, 11, 12], "shield": [3, 12], "three": [5, 8, 10], "star": [5, 10, 11], "sim": [5, 8, 10, 11], "rm": [4, 5, 8, 10, 11], "ly": [5, 10], "awai": [5, 11], "sun": [5, 10, 11], "two": [4, 5, 8, 10, 11], "sunlik": [5, 8], "mass": [4, 5, 8, 10, 11], "luminos": 5, "third": [5, 10], "proxima": 5, "much": [5, 10, 11], "cooler": 5, "smaller": [5, 10, 11], "physic": [2, 4, 5, 10, 11], "radiu": [5, 11], "solar": [5, 8, 10], "unit": [5, 8, 10, 11], "given": [3, 5, 8, 10, 11, 12], "tabl": [5, 10, 11], "m_": [5, 10, 11], "odot": [5, 10, 11], "105": 5, "pm": [4, 5], "0070": 5, "934": 5, "0061": 5, "l_": 5, "519": 5, "018": 5, "5002": 5, "016": 5, "r_": [5, 10], "231": [5, 11], "0036": 5, "868": 5, "0052": 5, "while": [5, 8, 10, 11], "th\u00e9venin": 5, "et": [5, 10, 11], "al": [5, 10, 11], "2002": 5, "These": [5, 10, 11], "valu": [5, 8, 10, 11], "updat": [5, 8, 10], "recent": 5, "akeson": 5, "2021": [5, 10], "older": 5, "consist": [5, 8, 10], "ignor": 5, "significantli": [5, 10], "less": [5, 10, 11], "massiv": [5, 10, 11], "approach": [5, 10, 11], "periastron": [5, 11], "passag": 5, "gtrsim": [5, 11], "500": [5, 10], "au": [5, 8, 10, 11], "like": [5, 8, 11], "gravit": [5, 10], "inner": [5, 8, 10, 11], "extant": 5, "planet": [4, 5], "either": [5, 8, 10, 11], "observ": [5, 10, 11], "ski": 5, "southern": 5, "hemispher": 5, "appear": [5, 8, 10, 11], "singl": [5, 10, 11], "nake": 5, "ey": 5, "beta": [5, 10], "some": [2, 3, 5, 8, 10, 11, 12], "circ": [5, 8, 10, 11], "west": 5, "sky": [5, 11], "li": [5, 10], "about": [5, 10, 11], "southwest": 5, "recal": 5, "angular": [5, 10, 11], "diamet": 5, "moon": [5, 10, 11], "width": [5, 8, 10, 11], "bright": 5, "left": [4, 5, 10, 11], "both": [5, 8, 10, 11], "faint": 5, "red": [5, 8, 10, 11], "center": [5, 8, 10, 11], "circl": 5, "lower": [5, 10], "point": [5, 8, 11], "between": [5, 8, 10, 11], "intens": 5, "size": [5, 8], "weaker": 5, "distant": [5, 10], "tripl": 5, "main": [5, 10], "pair": [5, 11], "figur": [5, 8, 10, 11], "credit": [1, 5, 11], "wikipedia": 5, "alpha_centauri": 5, "user": 5, "skatebik": 5, "mani": [2, 3, 5, 8, 10, 11, 12], "campaign": 5, "search": [5, 11], "nearbi": [5, 10], "exoplanet": [2, 5, 11], "led": 5, "few": [5, 8, 10, 11], "fals": [5, 10], "posit": [5, 8, 10, 11], "claim": 5, "detect": 5, "turn": [5, 10, 11], "spuriou": 5, "contrast": [4, 5], "too": 5, "appar": 5, "magnitud": [4, 5, 10], "01": [5, 8, 10, 11], "33": [5, 10], "modern": [5, 8, 10, 11], "techniqu": [5, 8, 11], "charg": 5, "coupl": [5, 10, 11], "devic": 5, "ccd": 5, "light": [5, 10], "come": [5, 10], "telescop": 5, "tend": 5, "satur": 5, "overexpos": 5, "veri": [5, 8], "difficult": [5, 8], "fluctuat": 5, "zhao": 5, "2018": [5, 10, 11], "demonstr": [5, 8, 10, 11], "lesssim": 5, "50": [5, 8, 10, 11], "oplu": 5, "earth": [5, 8, 10, 11], "would": [5, 8, 10, 11], "after": [5, 10, 11], "decad": 5, "acut": 5, "good": 5, "thing": [5, 10], "we": [4, 5, 8, 10, 11], "earthlik": 5, "There": [5, 8, 10, 11], "motion": [4, 5, 10, 11], "bodi": [5, 10], "space": [5, 8, 10, 11], "astrometri": 5, "radial": [5, 10], "veloc": [5, 10], "transvers": 5, "occur": [5, 8, 10, 11], "perpendicular": 5, "line": [5, 8, 11], "sight": [5, 11], "draw": 5, "whiteboard": 5, "movement": 5, "marker": [5, 8, 10, 11], "tip": 5, "assum": [5, 10, 11], "mount": 5, "wall": [4, 5, 11], "captur": 5, "along": [4, 5, 8, 10, 11], "board": 5, "neither": 5, "pictur": 5, "thu": 5, "combin": [4, 5, 8, 11], "determin": [4, 5, 10, 11], "ellips": 5, "kepler": [5, 8, 10], "plane": [4, 5, 8, 11], "quantiti": 5, "semimajor": [5, 8, 10, 11], "axi": [5, 8, 10, 11], "eccentr": [5, 8, 10, 11], "argument": [5, 8, 10, 11], "pericent": [5, 8, 11], "omega": [4, 5, 8, 10, 11], "big": [5, 8], "shape": [5, 10, 11], "squash": [5, 10], "togeth": [4, 5, 8], "rotat": [5, 10, 11], "rel": [5, 8, 10, 11], "typic": [5, 10, 11], "distanc": [4, 5, 10], "r": [5, 8, 10, 11], "frac": [4, 5, 10], "co": [4, 5, 10, 11], "true": [5, 8, 10, 11], "anomali": [5, 8, 10, 11], "denot": [5, 8, 11], "closest": 5, "q": [5, 11], "farthest": 5, "apocent": 5, "see": [1, 2, 4, 5, 8, 10, 11], "fig": [5, 8, 10, 11], "mathemat": [4, 5, 10], "begin": [4, 5, 8, 10, 11], "align": [4, 5, 10, 11], "end": [4, 5, 8, 10], "ellipt": [5, 10], "orang": [5, 10], "focu": [5, 11], "major": 5, "dash": 5, "blue": [5, 11], "dot": [5, 8, 10, 11], "tilt": [5, 11], "x": [4, 5, 8, 10, 11], "45": [5, 8, 11], "numpi": [2, 5, 8, 10, 11], "np": [5, 8, 10, 11], "matplotlib": [5, 8, 10, 11], "pyplot": [5, 8, 10, 11], "plt": [5, 8, 10, 11], "rcparam": 5, "myst_nb": 5, "glue": 5, "font": [5, 8], "14": [5, 10, 11], "mathtext": 5, "fontset": 5, "cm": [5, 10, 11], "semi": [5, 10], "ecc": [5, 10], "omg": [5, 10], "radian": [5, 8, 10, 11], "fs": 5, "larg": [5, 10], "def": [5, 10, 11], "function": [4, 5, 8, 10, 11], "unitless": 5, "f_step": 5, "arang": [5, 10, 11], "pi": [5, 8, 10, 11], "return": [5, 10, 11], "arrai": [5, 10, 11], "sin": [4, 5, 10, 11], "y": [5, 8, 10, 11], "figsiz": [5, 8, 10, 11], "dpi": [5, 8, 10, 11], "150": [5, 8, 10, 11], "ax": [5, 8, 10, 11], "add_subplot": [5, 8, 10, 11], "111": [5, 8, 10, 11], "grid": [5, 10, 11], "color": [5, 8, 10, 11], "grai": [5, 10], "25": [5, 10, 11], "set_aspect": [5, 8, 10, 11], "equal": [4, 5, 8, 10, 11], "arrow": 5, "75": [5, 8], "005": 5, "head_width": 5, "05": [5, 8, 10], "length_includes_head": 5, "ell": 5, "peri": 5, "apo": 5, "plot": [5, 10, 11], "lw": [5, 8, 10], "ms": [5, 8, 10, 11], "10": [5, 8, 10, 11], "arc_r": 5, "15": [5, 8, 10], "ang_rng": 5, "arc_x": 5, "arc_i": 5, "06": 5, "horizontalalign": [5, 10], "fontsiz": [5, 8, 10, 11], "set_xlabel": [5, 8, 10, 11], "set_ylabel": [5, 8, 10, 11], "set_xlim": [5, 8, 10, 11], "set_ylim": [5, 8, 10, 11], "tick": 5, "set_xtick": [5, 10, 11], "set_ytick": [5, 10, 11], "xlabel": 5, "ylabel": 5, "rang": [5, 8, 10, 11], "len": [5, 8, 10, 11], "append": [5, 10], "els": [2, 5, 10], "str": 5, "set_xticklabel": 5, "set_yticklabel": 5, "orbit_fig": 5, "far": 5, "ve": 5, "note": [5, 8, 10, 11], "locat": [5, 10], "univers": [5, 11], "face": [5, 11], "But": [4, 5, 10, 11], "appropri": [1, 5, 8], "matrix": [4, 5], "z": [5, 10, 11], "matric": 5, "r_x": 5, "theta": [5, 10], "pmatrix": [4, 5], "r_y": 5, "r_z": 5, "repres": [5, 8, 10, 11], "angl": [5, 11], "hand": [5, 10], "rule": [5, 10], "vec": 5, "prime": 5, "vector": [5, 10, 11], "counter": 5, "clockwis": 5, "curl": 5, "thumb": 5, "side": [5, 11], "toward": [5, 10], "neg": 5, "transit": [5, 11], "show": [5, 10, 11], "get": [4, 5, 10, 11], "call": [5, 8, 10], "inclin": [5, 11], "when": [4, 5, 10, 11], "90": [5, 11], "79": 5, "ll": [5, 8, 10, 11], "illustr": [5, 8, 10, 11], "view": [5, 8, 10, 11], "black": [5, 8, 10], "rotate_x": 5, "rotate_i": 5, "rotate_z": 5, "get_ellips": 5, "rvec": 5, "true_f": 5, "inc": [5, 10, 11], "radii": [5, 10], "constant": [4, 5, 10, 11], "zero": [5, 8, 10, 11], "xp": 5, "incl": 5, "r_vec": 5, "95": 5, "rotate_fig": 5, "around": [5, 8, 10, 11], "node": [5, 11], "cross": [5, 10], "ascend": [5, 11], "descend": 5, "longitud": [5, 10, 11], "former": 5, "latter": 5, "359": 5, "wrap": 5, "rightarrow": [5, 11], "therefor": [5, 8, 10, 11], "similarli": 5, "magenta": 5, "60": [5, 10, 11], "ra": 5, "ra_omg": 5, "print": [5, 8, 10, 11], "m": [4, 5, 8, 10, 11], "rotate_fig_ra": 5, "35355339": 5, "1767767": 5, "30618622": 5, "11835361": 5, "3399168": 5, "34705762": 5, "fulli": [5, 10], "six": 5, "notat": [5, 8, 10], "v_x": 5, "dx": 5, "dt": [5, 8, 10, 11], "next": [5, 10, 11], "normal": [5, 10, 11], "euler": [4, 5, 11], "shown": [2, 5, 11], "sometim": 5, "nu": 5, "instantan": 5, "180": [5, 10, 11], "diagram": [5, 10], "kepler_orbit": 5, "lasunncti": 5, "On": 5, "phase": 5, "central": [5, 10, 11], "problem": [4, 5, 8, 10, 11], "potenti": [5, 10, 11], "ambigu": [5, 8], "multipl": [5, 10], "natur": [2, 4, 5, 8, 10, 11], "easier": [5, 8, 11], "hierarch": [5, 11], "brief": 5, "overview": [5, 8, 10], "domin": [5, 10], "m_0": 5, "m_1": [5, 10, 11], "let": [4, 5, 8, 10], "exist": [5, 10, 11], "m_o": [5, 10], "Then": [5, 8, 10], "scalar": 5, "speed": [5, 8, 10, 11], "momentum": [5, 10, 11], "p": [5, 8, 10, 11], "product": 5, "interest": [2, 5, 11], "specif": [5, 8, 10, 11], "better": [5, 8, 10, 11], "compon": [4, 5, 10, 11], "via": [4, 5], "det": 5, "hat": 5, "vmatrix": 5, "h_x": 5, "h_y": 5, "h_z": 5, "project": 5, "vi": 5, "viva": 5, "equat": [4, 5, 10, 11], "total": [5, 10], "energi": [5, 10, 11], "t": [4, 5, 8, 10, 11], "mathcal": 5, "depend": [4, 5, 10, 11], "newton": [5, 11], "consequ": 5, "find": [3, 5, 8, 10, 12], "solv": [4, 5, 8, 11], "eq": [5, 11], "vr": 5, "sqrt": [4, 5, 8, 10, 11], "2r": 5, "conserv": [5, 10], "pick": 5, "With": 5, "algebra": [5, 10, 11], "input": [5, 11], "advanc": [5, 8], "sequenc": [5, 10], "ident": [4, 5, 11], "mit": 5, "opencoursewar": 5, "detail": [4, 5, 8, 10, 11], "backup": 5, "across": [5, 11], "cdot": [5, 8, 10], "laplac": [5, 10], "rung": 5, "lenz": 5, "decompos": 5, "varpi": 5, "e_x": 5, "e_i": 5, "arcsin": 5, "arcco": [5, 11], "arctan": 5, "earlier": [5, 10], "onc": [5, 10], "quad": [5, 10], "undefin": [5, 10], "coplanar": [5, 8, 11], "ad": [5, 10], "dogleg": 5, "circular": [5, 8, 10, 11], "epoch": 5, "julian": [5, 8], "1955": 5, "66": 5, "addition": [4, 5, 8, 10], "often": [5, 8, 10], "arcsecond": 5, "actual": [5, 10], "version": [2, 5, 8], "long": [5, 8, 10, 11], "enough": [5, 10], "accur": [5, 10, 11], "period": [5, 8, 10, 11], "91": 5, "013": 5, "yr": [5, 8, 10, 11], "tot": 5, "obtain": [5, 10], "23": [5, 8, 11], "78": [5, 8], "usag": [5, 8], "As": [5, 8, 10, 11], "cancel": [4, 5], "formula": [5, 10], "m_tot": [5, 10], "524": [5, 8], "32": 5, "232": [5, 8, 11], "204": [5, 8], "dynamicist": 5, "convent": [5, 8], "orient": [5, 10], "vertic": [5, 10], "cardin": 5, "n": [5, 10], "horizont": [5, 10], "appendix": 5, "deitrick": 5, "2015": [5, 10, 11], "astrometr": [5, 11], "data": [5, 8, 10, 11], "neuforg": 5, "verheek": 5, "noel": 5, "1999": [5, 10, 11], "comparison": 5, "each": [2, 3, 4, 5, 8, 10, 11, 12], "visual": [5, 8, 11], "334": 5, "pc": 5, "27": 5, "38": 5, "26": 5, "small": [4, 5], "21": 5, "40": [5, 10, 11], "alpha_cen_ab": 5, "recast": 5, "astrocentr": [5, 8, 11], "choic": [5, 10], "invari": 5, "galilean": 5, "frame": [5, 10], "contain": [5, 8, 10], "anoth": [4, 5, 10, 11], "x_o": [5, 10], "y_o": 5, "z_o": 5, "prime_x": 5, "v_": 5, "o": [5, 10, 11], "v_o": 5, "construct": 5, "barycent": [5, 10], "_1": [4, 5], "_2": [4, 5], "m_2": [5, 10, 11], "introduc": [5, 10], "constraint": 5, "_o": 5, "r_1": [5, 10], "r_2": 5, "parameter": 5, "v_1": 5, "v_2": 5, "ratio": [5, 11], "gener": [4, 5, 8, 10, 11], "sum": [5, 10], "sum_": [5, 10], "m_i": 5, "_i": 5, "qquad": [4, 5, 10], "coincid": 5, "get_rvec": 5, "plot_ellips": 5, "col": [5, 10], "133": [5, 8], "972": [5, 8], "r_vec1": 5, "r_vec2": 5, "ax1": [5, 10], "121": 5, "ax2": [5, 10], "122": 5, "ax_list": 5, "13": [5, 11], "17": 5, "18": [5, 11], "16": [5, 8, 10, 11], "alpha_cen_ab_bari": 5, "sens": 5, "hierarchi": 5, "subsystem": 5, "first": [5, 8, 10, 11], "m_3": [5, 10, 11], "final": [5, 8], "m_4": [5, 10], "r_3": 5, "x_1": [4, 5, 10], "x_2": [4, 5, 10], "x_3": 5, "x_4": 5, "jacobi_coordin": 5, "iter": [5, 8, 10, 11], "keep": [5, 10], "track": 5, "current": [5, 10], "inclus": [5, 8], "th": [5, 10], "eta_j": 5, "_": [4, 5], "_j": 5, "eta_": 5, "second": [5, 8], "jacobian": 5, "won": [5, 11], "mathbf": [4, 5, 10], "eta_1": 5, "eta_2": 5, "eta_3": 5, "eta_4": 5, "prime_1": 5, "prime_2": 5, "prime_3": 5, "_3": 5, "prime_4": 5, "_4": 5, "exactli": [5, 8, 11], "One": [5, 10, 11], "method": [5, 8, 10, 11], "_a": 5, "_b": 5, "i_b": 5, "omega_b": 5, "x_a": 5, "y_a": 5, "z_a": 5, "f_b": 5, "x_b": 5, "a_b": 5, "e_b": 5, "r_b": 5, "y_b": 5, "z_b": 5, "take": [5, 8, 10], "2nd": 5, "m_a": [5, 8, 11], "m_b": [5, 8, 11], "na": 5, "re": [1, 5], "add": [5, 8, 10, 11], "mostli": [5, 8], "same": [5, 8, 10, 11], "procedur": [5, 11], "r_p": 5, "a_p": [5, 10, 11], "e_p": [5, 10, 11], "f_p": [5, 11], "host": [5, 8, 10, 11], "x_p": 5, "omega_p": [5, 10, 11], "i_p": [5, 11], "y_p": 5, "z_p": 5, "planetari": [3, 5, 8, 11, 12], "onto": [5, 8], "_p": 5, "n_p": 5, "m_p": [5, 11], "trivial": [4, 5], "becom": [5, 10], "best": [5, 11], "easiest": [5, 10], "setup": [5, 8, 10], "instead": [5, 10, 11], "wasn": 5, "moreov": [5, 11], "easili": [5, 8, 11], "accomplish": [5, 8], "nifti": [], "citat": [], "akeson2021": [], "orbit": [8, 11], "tricki": 8, "busi": 8, "histor": 8, "due": [8, 10, 11], "transcendent": [8, 11], "p\u00e1l": 8, "2009": [8, 10], "analyt": [8, 11], "numer": [8, 10, 11], "number": [8, 10, 11], "list": 8, "packag": [2, 8], "advantag": 8, "low": [8, 10], "memori": 8, "overhead": 8, "gpu": 8, "cpu": 8, "genga": 8, "code": [2, 8, 10, 11], "mercury6": 8, "mercury6_bin": 8, "binari": [2, 8, 10], "swift": 8, "hnbodi": 8, "nbody6": 8, "nbodi": 8, "gadget2": 8, "galaxi": [8, 10], "starlab": 8, "amus": 8, "guid": [8, 11], "up": [8, 10, 11], "googl": [2, 8], "colab": [2, 8], "conveni": [8, 10], "tool": 8, "test": [8, 11], "python": [2, 3, 8, 10, 12], "link": 8, "inspect": 8, "dropdown": [2, 8], "option": 8, "rocketship": 8, "top": [2, 8, 11], "notebook": [2, 8], "load": 8, "commonli": 8, "librari": 8, "modul": [8, 10], "scipi": [2, 8, 11], "extern": 8, "instal": 8, "run": [8, 10, 11], "pip": 8, "cell": [2, 8, 11], "class": 8, "paramet": [8, 10, 11], "timestep": [8, 10], "particl": [8, 10, 11], "adjust": [8, 10], "coordin": [8, 10, 11], "system": 8, "archiv": [8, 10, 11], "trunk": 8, "tree": 8, "branch": 8, "program": 8, "languag": [2, 8], "object": [8, 10, 11], "initi": [4, 8, 11], "store": [8, 11], "referenc": [8, 10, 11], "later": [8, 10], "default": 8, "tell": 8, "ias15": [8, 10, 11], "algorithm": [8, 10], "msun": [8, 10, 11], "001": [8, 10, 11], "exact_finish_tim": 8, "accordingli": 8, "sampl": 8, "ultim": 8, "evalu": [8, 11], "whfast": [8, 10, 11], "effici": [8, 10], "jacobi": [8, 10], "move_to_com": [8, 10, 11], "convert": [8, 10, 11], "barycentr": [8, 11], "step": [8, 10, 11], "inherit": 8, "3e": 8, "interfac": 8, "document": [2, 8], "high": [8, 10, 11], "qualiti": 8, "idea": [8, 10], "down": [8, 10, 11], "inlin": 8, "op": 8, "orbitplot": 8, "evolv": [2, 8], "automatesimulationarch": [8, 10, 11], "file": [8, 11], "name": [8, 10, 11], "frequenc": [8, 10], "overwrit": 8, "boolean": 8, "interv": [8, 10], "reliabl": 8, "integ": [8, 10, 11], "wherea": 8, "float": 8, "might": [8, 10], "encount": 8, "issu": [8, 10, 11], "finit": 8, "precis": 8, "want": [8, 10, 11], "sure": 8, "output": [8, 11], "bin": [8, 10, 11], "deletefil": [8, 10, 11], "per": 8, "1000": 8, "minut": 8, "itself": 8, "simulationarch": [8, 10, 11], "probe": 8, "sa": [8, 10, 11], "variabl": 8, "last": [8, 10], "snapshot": [8, 10, 11], "9000": 8, "1f": 8, "tmin": 8, "tmax": 8, "20001": 8, "walk": 8, "custom": [8, 11], "specifici": 8, "sublibrari": 8, "done": [8, 10], "statement": [2, 8], "path": 8, "outer": [8, 10, 11], "know": 8, "ps": [8, 10, 11], "hold": 8, "count": 8, "index": [8, 10], "skip": 8, "empti": 8, "string": [8, 11], "assign": 8, "loop": 8, "continu": [2, 8, 10, 11], "until": [8, 10, 11], "reach": [4, 8], "w": [5, 8], "height": [4, 8, 10, 11], "inch": 8, "resolut": [8, 11], "creation": 8, "canva": 8, "row": [8, 11], "column": 8, "subplot": 8, "rci": 8, "markers": 8, "curv": [8, 10], "intermedi": [8, 10, 11], "simpifi": 8, "semicolon": 8, "extra": 8, "altogeth": [4, 8, 10], "stellar": [8, 11], "element": [8, 10, 11], "centauri": 8, "77": 8, "mod": [8, 10], "360": [8, 10, 11], "specifii": 8, "start": [8, 10, 11], "ma": 8, "quarl": [1, 8, 10, 11], "lissauer": [8, 10], "2016": [8, 11], "calcul": [8, 10, 11], "jd": 8, "2452276": 8, "209": 8, "6901": 8, "a_bin": [8, 11], "e_bin": [8, 11], "omg_bin": [8, 11], "ma_bin": [8, 11], "t_bin": [8, 11], "year": [8, 10, 11], "alphacen": 8, "xy_bin": 8, "move_to_hel": [8, 10, 11], "shift": [8, 10, 11], "type": [4, 8, 11], "order": 8, "circumbinari": [8, 11], "resolv": 8, "forc": [8, 10, 11], "m_host": 8, "m_pl": 8, "a_pl": 8, "e_pl": 8, "cartesian": [8, 10, 11], "m_sec": 8, "secondari": [8, 11], "primari": [8, 10, 11], "redirect": 8, "action": 8, "a_": [8, 10, 11], "pl": 8, "global": 8, "mpl_toolkit": [8, 10, 11], "axes_grid1": [8, 10, 11], "inset_loc": [8, 10, 11], "inset_ax": [8, 10, 11], "0035e": [8, 10], "alphacen_wpl": 8, "xy_pl": 8, "scale": [8, 11], "child": 8, "parent": 8, "zoom": [8, 10], "inset": [8, 10], "axin": [8, 10, 11], "100": [8, 11], "bbox_to_anchor": [8, 10, 11], "bbox_transform": [8, 10, 11], "transax": [8, 10, 11], "tbp": 11, "http": 11, "en": [], "body_problem": [], "wa": [10, 11], "develop": 11, "studi": 11, "isaac": 11, "hi": 11, "pioneer": 11, "principia": 11, "formul": 11, "solut": [4, 10, 11], "influenc": [10, 11], "graviti": [10, 11], "anyon": [2, 11], "king": 11, "oscar": 11, "commemor": 11, "birthdai": 11, "1889": 11, "contest": 11, "he": 11, "invit": 11, "scholar": 11, "attempt": 11, "It": [3, 4, 10, 11, 12], "french": 11, "mathematician": 11, "henri": 11, "poincar": 11, "pari": 11, "who": 11, "insuffici": 11, "word": 11, "unambigu": 11, "subsum": 11, "numenclatur": [], "configur": [10, 11], "propos": 11, "collinear": [10, 11], "lagrang": 11, "equilater": 11, "triangl": 11, "2013": 11, "physicist": 11, "insitut": [], "belgrad": 11, "discov": 11, "new": [10, 11], "famili": 11, "galleri": 11, "comput": [10, 11], "eleg": 11, "investig": [10, 11], "explor": 11, "wide": [10, 11], "swath": 11, "potenati": [], "parallel": 11, "jupit": [10, 11], "08": 11, "ge": 11, "1982": [10, 11], "rudolf": 11, "dvorak": 11, "trojan": [10, 11], "astronomi": [2, 11], "roen": 11, "kelli": 11, "1980": [10, 11], "2000": 11, "growth": [4, 11], "power": 11, "were": [10, 11], "t_": 11, "excess": 11, "dynam": [3, 11, 12], "chao": 11, "benettin": 11, "lecar": 11, "1992": 11, "smith": [10, 11], "szebeh": 11, "1993": [10, 11], "froeschl": 11, "1997": [10, 11], "identifi": [10, 11], "rout": 11, "unstabl": [10, 11], "1986": [10, 11], "rabl": 11, "1988": 11, "regular": 11, "quasi": 11, "chaotic": 11, "unbound": 11, "overlap": 11, "instabl": [10, 11], "sensit": 11, "slightli": [10, 11], "drastic": 11, "behavior": 11, "degre": [10, 11], "ahead": 11, "behind": 11, "feel": 11, "net": [10, 11], "slight": 11, "slow": [10, 11], "lead": [10, 11], "increas": [4, 10, 11], "pump": 11, "exchang": [10, 11], "scatter": [10, 11], "focus": 11, "assumpt": [10, 11], "rho": [10, 11], "mu": [10, 11], "critic": [10, 11], "a_c": 11, "leq": 11, "omega_": 11, "f_": 11, "apastron": 11, "bad": [10, 11], "knowledg": [4, 11], "dure": 11, "late": 11, "1990": 11, "e_": [10, 11], "02": 11, "eight": 11, "equidist": 11, "315": 11, "increment": 11, "4d": 11, "dimens": [10, 11], "conceptu": 11, "travers": 11, "2d": 11, "abstract": 11, "nest": 11, "interchang": 11, "summar": 11, "rho_": 11, "cr": 11, "boundari": [4, 10, 11], "stabl": [10, 11], "earli": 11, "escap": [10, 11], "stability_grid1": [], "symbol": [10, 11], "stability_grid2": [], "least": 11, "squar": [10, 11], "trial": [4, 11], "c_1": 11, "c_2": 11, "c_3e_": 11, "c_4": 11, "c_5": 11, "c_6": 11, "minim": 11, "chi": 11, "residu": 11, "merit": 11, "easi": 11, "polynomi": 11, "larger": [10, 11], "discrep": 11, "extrapol": 11, "broad": 11, "regim": [10, 11], "ration": [10, 11], "geq": [10, 11], "signific": [10, 11], "misalign": 11, "disk": [10, 11], "monin": 11, "2006": [10, 11], "2020": [10, 11], "address": [10, 11], "expand": [10, 11], "cover": 11, "wider": [10, 11], "panel": [10, 11], "underli": 11, "github": [2, 11], "repo": 11, "saturnaxi": [2, 11], "threebody_st": 11, "interp2d": 11, "interpol": 11, "griddata": 11, "sy": [], "ebin": 11, "github_fil": 11, "raw": 11, "githubusercont": 11, "com": [10, 11], "master": 11, "a_crit_incl": 11, "5b0": [], "5d": [], "txt": 11, "genfromtxt": 11, "delimit": 11, "comment": 11, "xi": [10, 11], "concaten": 11, "999": [10, 11], "yi": [10, 11], "81": [10, 11], "zi": [10, 11], "none": [10, 11], "linear": [4, 11], "fill_valu": 11, "astab": 11, "rho_cr": 11, "2f": 11, "12": [10, 11], "simplifi": [8, 10, 11], "nearli": 11, "cbp_stabil": 11, "2937": 11, "doyl": 11, "2011": [10, 11], "15944": 11, "a_crit": 11, "70": 11, "rebound": [10, 11], "os": 11, "m_j": [10, 11], "54e": [10, 11], "6897": 11, "20255": 11, "22431": 11, "41": 11, "079220": 11, "365": 11, "inc_bin": 11, "30401": 11, "263": 11, "464": 11, "periaps": 11, "ra_bin": 11, "92": 11, "352": 11, "333": 11, "7048": 11, "t_p": [10, 11], "228": 11, "776": 11, "0069": 11, "inc_p": 11, "0322": 11, "omg_p": [10, 11], "318": 11, "ra_p": 11, "003": [10, 11], "ma_p": 11, "106": 11, "51": 11, "tscale": [10, 11], "025": [10, 11], "kepler16": 11, "rot_x": [], "ang": [], "rot": [10, 11], "kx": [4, 10, 11], "xy_coord": [10, 11], "cart": [10, 11], "rot_xi": [10, 11], "alpha": [10, 11], "question": [10, 11], "vari": [10, 11], "variat": 11, "grow": 11, "secularli": 11, "experi": [4, 10, 11], "paper": [10, 11], "output_bin": [10, 11], "output_step": [10, 11], "wait": 11, "save": [10, 11], "short": [10, 11], "fname": [10, 11], "out_step": [10, 11], "altern": 11, "ang1": 11, "ang2": 11, "rot_omg": 11, "rot_inc": 11, "rot_mat": 11, "cyan": 11, "keplerian": 11, "strongli": 11, "perturb": [4, 10, 11], "jitter": 11, "averag": [4, 10, 11], "caus": [10, 11], "nodal": 11, "precess": 11, "timescal": [10, 11], "oscil": 11, "apsid": 11, "sinc": [10, 11], "fast": 11, "kepler16_long": 11, "200": 11, "again": [10, 11], "understood": 11, "seri": [10, 11], "ax11": 11, "ax12": 11, "ax13": 11, "233": 11, "ax21": 11, "234": 11, "ax22": 11, "235": 11, "ax23": 11, "236": 11, "pl_orb": [10, 11], "del_omega": 11, "mut_incl": 11, "ecosw": 11, "esinw": 11, "icoso": 11, "isino": 11, "e_f": 11, "w_f": 11, "arctan2": 11, "3f": 11, "deg": [10, 11], "subplots_adjust": 11, "wspace": [10, 11], "hspace": [10, 11], "034": 11, "278": 11, "553": 11, "evolut": [10, 11], "over": [4, 10, 11], "wobbl": 11, "plate": 11, "middl": [4, 11], "lie": [10, 11], "fix": [10, 11], "periapsi": [], "omega_f": 11, "polar": 11, "bottom": 11, "tightli": 11, "naiv": [10, 11], "suggest": [10, 11], "indefinit": [10, 11], "mutual": 11, "abil": 11, "temporari": 11, "just": 11, "venu": 11, "mercuri": [10, 11], "broadli": 11, "dub": 11, "martin": 11, "triaud": 11, "2017": [10, 11], "blob": [], "holman": [10, 11], "wiegert": 11, "analysi": [10, 11], "Such": [10, 11], "campbel": 11, "hatz": 11, "2003": 11, "huang": 11, "ji": 11, "2022": 11, "refit": 11, "reffert": 11, "quirrenbach": 11, "cep": 11, "fraction": [10, 11], "shorter": 11, "39": 11, "64": 11, "36": 11, "119": 11, "158": 11, "04": 11, "296": 11, "posterior": 11, "072": [], "173": 11, "48": [], "356": 11, "264": 11, "msini": 11, "0125": 11, "gammacep": 11, "pos_z": 11, "neg_z": 11, "000": 11, "longer": 11, "gammacep_long": 11, "5e4": 11, "t_max": 11, "my_cmap": [10, 11], "colormap": [10, 11], "jet": 11, "norm": [10, 11], "vmin": [10, 11], "vmax": [10, 11], "edgecolor": [10, 11], "cmap": [10, 11], "int": 11, "085": 11, "55": 11, "63": 11, "nomenclatur": 11, "institut": 11, "dark": 11, "anti": 11, "correl": 11, "lidov": 11, "kozai": 11, "mechan": 11, "librat": 11, "270": 11, "naoz": 11, "bode": 11, "flip": [10, 11], "retrograd": [10, 11], "attract": 10, "littl": 10, "involv": 10, "seemingli": 10, "simpl": 10, "four": 10, "sub": 10, "sai": 10, "Is": 10, "Will": 10, "bia": 10, "outcom": 10, "overcom": 10, "goe": 10, "though": 10, "hayashi": 10, "2023": 10, "barn": 10, "greenberg": 10, "transport": 10, "expel": 10, "pleas": [3, 10, 12], "review": 10, "look": 10, "arriv": 10, "judg": 10, "astrophys": [2, 10], "gyr": 10, "g2v": 10, "probabl": 10, "undergo": 10, "laskar": 10, "gastineau": 10, "remaind": 10, "answer": 10, "equilibrium": [4, 10], "found": 10, "1784": 10, "past": 10, "giant": 10, "compact": 10, "kaib": 10, "2019": 10, "nesvorni": 10, "todai": 10, "www": 10, "billyquarl": 10, "latest": 10, "estim": 10, "composit": 10, "hydrogen": 10, "helium": 10, "metal": 10, "chapter": [2, 10], "tau_": 10, "proport": 10, "invers": 10, "cube": 10, "propto": 10, "proportion": 10, "myr": 10, "lectur": [4, 10], "jason": 10, "kendal": 10, "extrema": 10, "vanish": 10, "r1": 10, "r2": [], "u": 10, "xx": 10, "yy": 10, "meshgrid": 10, "l1": 10, "l3": 10, "l4": 10, "aspect": 10, "35": 10, "065": 10, "l_1": 10, "l_2": 10, "l_3": 10, "l_4": 10, "135": 10, "l_5": 10, "mfc": 10, "skyblu": 10, "mec": 10, "darkblu": 10, "legend": 10, "numpoint": 10, "frameon": 10, "off": 10, "jacobi_const": 10, "xo": 10, "yo": 10, "x1": 10, "y1": 10, "ro": 10, "phi": 10, "m_sun": 10, "m_e": 10, "r_h": 10, "x_e": 10, "y_e": 10, "x_": 10, "y_": 10, "r_level": 10, "n_lev": 10, "z_level": 10, "sort": 10, "loc": [], "upper": 2, "borderpad": [], "rx": 10, "bone": [], "contour": 10, "level": [2, 10], "zorder": 10, "linewidth": 10, "five": 10, "topolog": 10, "pseudopotenti": 10, "react": 10, "extend": 10, "r_o": 10, "centrifug": 10, "everyth": 10, "partial": 10, "nabla": 10, "associ": 10, "c_j": 10, "2u": 10, "aren": 10, "why": 10, "bother": 10, "constrain": 10, "zvc": 10, "triangular": 10, "lobe": 10, "cs": 10, "interior": 10, "region": 10, "tug": 10, "war": 10, "delin": 10, "sphere": 10, "isn": 10, "correct": 10, "ellipsoid": 10, "seen": 10, "compar": 10, "set1": 10, "approx": 10, "q_": 10, "set_ov": [], "00000347": 10, "0008897": 10, "00093672": 10, "00095947": 10, "00106035": 10, "00124328": 10, "0012661": 10, "00147675": 10, "00175584": 10, "00240875": 10, "03227121": 10, "69332466": 10, "75659148": 10, "obviou": 10, "fortun": 10, "yellow": 10, "enclos": 10, "a_j": 10, "fill": 10, "area": 10, "forbidden": 10, "complex": 10, "real": 10, "imaginari": 10, "unphys": 10, "henc": 10, "lowest": 10, "asteroid": 10, "pseudo_pot": 10, "sign": 10, "maintain": 10, "calc_zvc": 10, "ck": 10, "0329": 10, "c1": 10, "gnuplot": 10, "get_cmap": 10, "cmmapabl": 10, "scalarmapp": 10, "set_arrai": 10, "set_und": 10, "x_color": 10, "contourf": 10, "linestyl": 10, "solid": 10, "rosario": 10, "franco": 10, "satellit": 10, "decreas": 10, "eqn": 10, "prograd": 10, "crit": 10, "4061": 10, "1257e_p": 10, "668": 10, "236e_p": 10, "scalabl": [], "observation": 10, "photometr": 10, "model": 10, "favor": 10, "edg": 10, "strictli": 10, "gladman": 10, "character": 10, "marchal": 10, "bozi": 10, "literatur": [3, 10, 12], "stem": 10, "everyon": 10, "anywai": 10, "concentr": 10, "a_1": 10, "uniti": 10, "a_2": 10, "differenti": 10, "delta": 10, "gladman_setup": [], "parametr": 10, "f_2": 10, "f_1": 10, "henon": 10, "petit": 10, "delta_h": 10, "straightforward": 10, "clear": 10, "damp": [4, 10], "drag": 10, "protoplanetari": 10, "chamber": 10, "h_": 10, "3m_j": 10, "formal": 10, "priori": 10, "explicitli": 10, "among": 10, "pu": 10, "wu": 10, "explicit": 10, "a_k": 10, "oberta": 10, "recurs": 10, "m_star": 10, "calc_orbit": 10, "get_semi": 10, "y_1": 10, "y_2": 10, "opposit": [4, 10], "complet": 10, "arbitrari": 10, "plai": 10, "interplanetari": 10, "suppos": 10, "proxim": 10, "leverag": 10, "closer": 10, "account": 10, "mitig": 10, "achiev": 10, "conjunct": 10, "half": 10, "stori": 10, "faster": 10, "catch": 10, "repeat": 10, "kick": [4, 10], "random": [4, 10], "reson": 10, "destabil": 10, "video": 10, "refresh": 10, "pattern": 10, "emerg": 10, "plant": 10, "themselv": 10, "maximum": [4, 10], "attent": 10, "pollin": 10, "sunflow": 10, "sunlight": 10, "00": 10, "pine": 10, "cone": 10, "pineappl": 10, "spiral": 10, "arm": 10, "explain": 10, "goal": 10, "irrat": 10, "varphi": 10, "iron": 10, "618033988749": 10, "ldot": 10, "fibonacci": 10, "f_n": [], "oper": 10, "modulo": 10, "f_j": 10, "get_trueanomali": 10, "t_1": 10, "innermost": 10, "mu_1": 10, "ssanalog_test": 10, "gridspec": 10, "gs": 10, "ax3": 10, "billi": 1, "sourc": [1, 2, 3, 12], "jupyt": 2, "undergradu": 2, "introductori": 2, "background": 2, "graduat": 2, "student": 2, "snippet": 2, "familiar": 2, "scientif": 2, "meant": 2, "open": 2, "menu": 2, "rocket": 2, "runtim": 2, "alreadi": 2, "panda": 2, "etc": 2, "execut": 2, "curios": 2, "reveal": 2, "markup": 2, "launch": 2, "button": 2, "screen": 2, "publicli": 2, "local": 2, "copi": 2, "live": 2, "collabor": 2, "welcom": 2, "analog": 10, "e_j": 10, "1345": 10, "a_3": 10, "2871": 10, "a_4": 10, "strong": 10, "quit": 10, "suffici": 10, "hybrid": 10, "wisdom": 10, "map": [4, 10], "1991": 10, "greater": 10, "burlisch": 10, "stoer": 10, "rare": 10, "1345183686262765": 10, "2871316026156066": 10, "usual": 10, "terrestri": 10, "strength": 10, "respond": 10, "neighbor": 10, "descript": [3, 12], "cite": [3, 12], "tutori": [3, 12], "coher": 4, "secular": 4, "reminisc": 4, "harmon": 4, "pendulum": 4, "swing": 4, "back": 4, "forth": 4, "overal": 4, "amplitud": 4, "boost": 4, "randomli": 4, "against": 4, "truli": 4, "concept": 4, "driven": 4, "steadi": 4, "transient": 4, "frictionless": 4, "spring": 4, "hook": 4, "kappa": 4, "attach": 4, "slide": 4, "displac": 4, "bring": 4, "compress": 4, "rightmost": 4, "act": 4, "kx_1": 4, "ddot": 4, "kx_2": 4, "isol": 4, "interact": 4, "furthermor": 4, "rearrang": 4, "bmatrix": 4, "b_1": 4, "b_2": 4, "substitut": 4, "characterist": 4, "2m": 4, "quadrat": 4, "root": 4, "eigenfrequ": 4, "omega_1": 4, "omega_2": 4, "coeffici": 4, "matthew": 4, "schwartz": 4, "harvard": 4, "libretext": 4, "tom": 4, "weideman": 4, "uc": 4, "davi": 4, "youtub": 4, "jefferi": 4, "chasnov": 4}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"exoplanet": [3, 12], "within": [3, 12], "binari": [3, 5, 11, 12], "system": [3, 5, 10, 11, 12], "free": 4, "forc": 4, "eccentr": 4, "A": [4, 6, 7, 8, 9, 10, 11], "review": 4, "coupl": [4, 6, 9], "oscil": 4, "impact": 4, "minim": 4, "sampl": [4, 6, 7, 9, 10, 11], "simul": [4, 6, 7, 8, 9, 10, 11], "introduct": 5, "\u03b1": 5, "centauri": 5, "The": [5, 10], "stellar": [5, 10], "paramet": 5, "alpha": [5, 8], "ab": [5, 8, 11], "orbit": [5, 10], "what": 5, "an": [5, 9], "initi": [5, 10], "condit": 5, "cartesian": 5, "element": 5, "us": [5, 6, 7, 10], "cen": [5, 8], "from": [5, 10], "pourbaix": 5, "boffin": 5, "2016": 5, "coordin": 5, "barycentr": 5, "jacobi": 5, "convert": 5, "refer": [5, 8, 10, 11], "basic": [6, 8], "climat": 6, "model": 6, "zero": 6, "dimension": 6, "latitudin": 6, "energi": 6, "balanc": 6, "togeth": 6, "climlab": 6, "gpu": 7, "acceler": 7, "planet": [7, 8, 10, 11], "format": 7, "genga": 7, "repo": 7, "set": 7, "up": 7, "googl": 7, "colab": 7, "mode": 7, "n": [8, 9], "bodi": [8, 9, 11], "avail": 8, "softwar": 8, "simpl": 8, "1": 8, "star": 8, "2": 8, "structur": 8, "rebound": 8, "save": 8, "plot": 8, "ad": 8, "exampl": 8, "obliqu": 9, "evolut": 9, "defin": 9, "planetari": [9, 10], "spin": 9, "equat": 9, "motion": 9, "pack": 10, "scale": 10, "golden": 10, "ratio": 10, "jacobian": [], "three": 11, "stabil": [10, 11], "histor": 11, "overview": 11, "old": [], "standard": 11, "circumbinari": [], "circumstellar": [], "kepler": 11, "16b": 11, "gamma": 11, "cephei": 11, "holman": [], "wiegert": [], "1999": [], "p": [], "type": [], "s": [], "updat": 11, "formula": 11, "lifetim": 10, "constraint": 10, "hill": 10, "radiu": 10, "debia": 10, "phase": 10, "lagrang": 10, "point": 10, "mutual": 10, "radii": [], "how": 1, "cite": 1, "reus": 1, "thi": 1, "materi": 1, "who": 2, "ar": 2, "note": 2, "interact": 2, "book": 2, "clone": 2}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file
+Search.setIndex({"docnames": ["LICENSE", "Preamble/cite-reuse", "Preamble/who-for", "README", "Tutorials/forced-eccentricity", "Tutorials/intro-alpha-centauri", "Tutorials/intro-climlab", "Tutorials/intro-genga", "Tutorials/nbody-integration", "Tutorials/obliquity-evolution", "Tutorials/planet-packing-stability", "Tutorials/three-body-stability", "home"], "filenames": ["LICENSE.md", "Preamble/cite-reuse.ipynb", "Preamble/who-for.ipynb", "README.md", "Tutorials/forced-eccentricity.ipynb", "Tutorials/intro-alpha-centauri.ipynb", "Tutorials/intro-climlab.ipynb", "Tutorials/intro-genga.ipynb", "Tutorials/nbody-integration.ipynb", "Tutorials/obliquity-evolution.ipynb", "Tutorials/planet-packing-stability.ipynb", "Tutorials/three-body-stability.ipynb", "home.md"], "titles": ["<no title>", "How to cite and reuse this material", "Who are these notes for?", "Exoplanets within Binary Systems", "5. Free and Forced Eccentricity", "1. Introduction to the \u03b1 Centauri System", "7. Basic Climate Modeling", "8. GPU-accelerated planet formation", "2. N-body Simulations", "6. Obliquity Evolution", "4. Planet Packing", "3. Three-body Stability", "Exoplanets within Binary Systems"], "terms": {"attribut": [0, 1, 3, 12], "4": [0, 1, 3, 4, 5, 8, 10, 11, 12], "0": [0, 1, 3, 4, 5, 8, 10, 11, 12], "intern": [0, 1, 3, 12], "creativ": [0, 1, 3, 12], "common": [0, 1, 3, 5, 12], "corpor": 0, "law": [0, 4, 5, 10], "firm": 0, "doe": [0, 5, 10, 11], "provid": [0, 4, 5, 10], "legal": 0, "servic": 0, "advic": [0, 10], "distribut": 0, "public": 0, "licens": [0, 1, 3, 12], "creat": [0, 5, 8, 10, 11], "lawyer": 0, "client": 0, "other": [0, 4, 5, 8, 10, 11], "relationship": 0, "make": [0, 5, 8, 10], "its": [0, 2, 4, 5, 8, 10, 11], "relat": [0, 10], "inform": [0, 3, 8, 12], "avail": [0, 2, 11], "an": [0, 2, 3, 4, 8, 10, 11, 12], "basi": 0, "give": [0, 1, 8, 11], "warranti": 0, "regard": 0, "ani": [0, 3, 5, 10, 12], "materi": [0, 2, 3, 12], "under": [0, 1, 3, 11, 12], "term": [0, 5, 10, 11], "condit": [0, 1, 4, 11], "disclaim": 0, "all": [0, 2, 5, 10, 11], "liabil": 0, "damag": 0, "result": [0, 4, 5, 8, 10, 11], "from": [0, 2, 4, 8, 11], "us": [0, 1, 2, 3, 4, 8, 11, 12], "fullest": 0, "extent": [0, 10], "possibl": [0, 10, 11], "standard": [0, 5, 10], "set": [0, 4, 5, 8], "creator": 0, "right": [0, 4, 5, 8, 10, 11], "holder": 0, "mai": [0, 4, 5, 8, 10], "share": [0, 1, 5], "origin": [0, 1, 5, 10, 11], "work": [0, 3, 5, 8, 10, 11, 12], "authorship": 0, "subject": [0, 5], "copyright": 0, "certain": 0, "specifi": [0, 8], "below": [0, 2, 4, 5, 8, 10, 11], "The": [0, 1, 2, 4, 8, 11], "follow": [0, 4, 5, 8, 10, 11], "consider": 0, "ar": [0, 1, 4, 5, 8, 10, 11], "purpos": 0, "onli": [0, 5, 8, 10, 11], "exhaust": 0, "do": [0, 10, 11], "form": [0, 4, 5], "part": [0, 4, 8, 11], "our": [0, 4, 5, 8, 10, 11], "licensor": 0, "intend": 0, "those": [0, 8, 11], "author": [0, 1, 10], "permiss": [0, 1], "wai": [0, 5, 8, 10, 11], "otherwis": [0, 5, 8, 10], "restrict": [0, 10, 11], "irrevoc": 0, "should": [0, 2, 4, 5, 8, 10], "read": [0, 8], "understand": [0, 11], "thei": [0, 5, 10, 11], "choos": [0, 5, 10], "befor": [0, 5], "appli": [0, 4, 5, 10, 11], "also": [0, 2, 4, 5, 8, 10, 11], "secur": 0, "necessari": [0, 5, 8, 10], "so": [0, 5, 8, 10, 11], "can": [0, 2, 4, 5, 8, 10, 11], "reus": 0, "expect": [0, 4, 8, 10, 11], "clearli": [0, 5], "mark": [0, 10, 11], "thi": [0, 2, 3, 4, 5, 8, 10, 11, 12], "includ": [0, 3, 5, 8, 10, 12], "cc": [0, 1], "except": 0, "limit": [0, 10, 11], "more": [0, 4, 5, 8, 10, 11], "wiki": 0, "creativecommon": 0, "org": 0, "considerations_for_licensor": 0, "By": [0, 8], "one": [0, 4, 5, 8, 10, 11], "grant": 0, "If": [0, 3, 4, 5, 8, 10, 11, 12], "s": [0, 4, 5, 8, 10, 11], "reason": [0, 5, 8], "exampl": [0, 3, 5, 10, 11, 12], "becaus": [0, 4, 5, 10, 11], "applic": [0, 10], "regul": 0, "ha": [0, 2, 4, 5, 8, 10, 11], "still": [0, 10], "have": [0, 2, 4, 5, 8, 10, 11], "A": [0, 5], "special": [0, 10], "request": 0, "ask": [0, 11], "chang": [0, 5, 8, 10, 11], "describ": [0, 4, 5, 10, 11], "although": [0, 10, 11], "requir": [0, 2, 5, 8, 10, 11], "you": [0, 1, 2, 3, 5, 8, 10, 12], "encourag": 0, "respect": [0, 1, 4, 5, 8, 10], "where": [0, 2, 4, 5, 8, 10, 11], "more_consider": 0, "considerations_for_license": 0, "exercis": 0, "defin": [0, 5, 8, 10, 11], "accept": 0, "agre": [0, 10], "bound": [0, 5, 10, 11], "To": [0, 4, 5, 8, 10, 11], "interpret": [0, 10], "contract": 0, "your": [0, 2, 5, 8], "benefit": 0, "receiv": [0, 4, 10], "section": [0, 1, 3, 4, 8, 10, 12], "1": [0, 4, 5, 10, 11], "definit": [0, 5, 10], "adapt": [0, 1, 8], "mean": [0, 1, 5, 8, 10, 11], "similar": [0, 4, 5, 8, 10, 11], "deriv": [0, 5, 10], "base": [0, 3, 4, 12], "upon": [0, 4, 8], "which": [0, 4, 5, 8, 10, 11], "translat": [0, 5], "alter": 0, "arrang": [0, 10], "transform": [0, 4, 5, 10], "modifi": [0, 2, 5], "manner": 0, "held": 0, "For": [0, 4, 5, 8, 10, 11], "music": 0, "perform": [0, 5, 10, 11], "sound": 0, "record": [0, 5], "alwai": [0, 5, 10], "produc": [0, 5], "synch": 0, "time": [0, 4, 5, 8, 10, 11], "move": [0, 5], "imag": [0, 5], "b": [0, 5, 8, 10, 11], "contribut": 0, "accord": [0, 4], "c": [0, 5, 8, 10, 11], "close": [0, 5, 10, 11], "without": [0, 8, 10], "broadcast": 0, "sui": 0, "generi": 0, "databas": 0, "how": [0, 5, 8, 10, 11], "label": [0, 8, 10], "categor": 0, "2": [0, 4, 5, 10, 11], "d": [0, 5, 8], "effect": [0, 5, 10], "technolog": 0, "measur": [0, 5, 8, 10], "absenc": [0, 11], "proper": 0, "circumv": 0, "fulfil": 0, "oblig": 0, "articl": 0, "11": [0, 5, 11], "wipo": 0, "treati": 0, "adopt": 0, "decemb": 0, "20": [0, 5, 8, 10, 11], "1996": [0, 10], "agreement": 0, "e": [0, 2, 4, 5, 8, 10, 11], "fair": 0, "deal": 0, "f": [0, 4, 5, 8, 10, 11], "artist": 0, "literari": 0, "g": [0, 2, 4, 5, 8, 10, 11], "h": [0, 5, 8, 10], "individu": 0, "entiti": 0, "i": [0, 4, 5, 8, 10, 11], "process": [0, 5, 10], "reproduct": 0, "displai": [0, 5], "dissemin": 0, "commun": [0, 11], "import": [0, 2, 5, 8, 10, 11], "member": 0, "access": [0, 8], "place": 0, "chosen": [0, 5], "them": [0, 5], "j": [0, 5, 10], "than": [0, 5, 10, 11], "direct": [0, 4, 5, 10, 11], "96": 0, "9": [0, 5, 8, 10, 11], "ec": 0, "european": 0, "parliament": 0, "council": 0, "march": 0, "protect": 0, "amend": 0, "succeed": 0, "well": [0, 10, 11], "essenti": 0, "equival": 0, "anywher": 0, "world": 0, "k": [0, 4, 5, 8, 10, 11], "correspond": [0, 5, 10], "scope": 0, "herebi": 0, "worldwid": 0, "royalti": 0, "free": [0, 1, 5, 10, 11], "non": [0, 4, 5, 8, 10, 11], "sublicens": 0, "exclus": 0, "reproduc": [0, 11], "whole": [0, 5, 10], "avoid": [0, 10], "doubt": 0, "need": [0, 5, 8, 10, 11], "compli": 0, "3": [0, 5, 8, 10, 11], "6": [0, 5, 8, 10, 11], "media": 0, "format": [0, 2, 10], "technic": 0, "modif": [0, 8], "allow": [0, 2, 5, 8, 11], "whether": [0, 8], "now": [0, 5, 11], "known": [0, 5, 8, 10, 11], "hereaft": 0, "waiv": 0, "assert": 0, "forbid": 0, "simpli": [0, 5, 10], "never": 0, "5": [0, 5, 8, 10, 11], "downstream": 0, "recipi": 0, "offer": 0, "everi": [0, 10], "automat": 0, "No": 0, "impos": 0, "addit": [0, 10], "differ": [0, 5, 8, 10, 11], "endors": 0, "noth": 0, "constitut": 0, "constru": 0, "impli": [0, 5, 10, 11], "connect": [0, 4, 5], "sponsor": 0, "offici": 0, "statu": 0, "design": [0, 8], "moral": 0, "integr": [0, 5, 8, 10, 11], "nor": 0, "privaci": 0, "person": 0, "howev": [0, 5, 8, 10, 11], "patent": 0, "trademark": 0, "collect": [0, 5], "directli": [0, 5, 10], "through": [0, 2, 5, 8, 10, 11], "societi": 0, "voluntari": 0, "waivabl": 0, "statutori": 0, "compulsori": 0, "scheme": [0, 8, 10], "In": [0, 5, 8, 10, 11], "case": [0, 5, 11], "expressli": 0, "reserv": 0, "made": 0, "must": [0, 5, 10, 11], "retain": [0, 5], "suppli": 0, "identif": 0, "pseudonym": 0, "ii": [0, 11], "notic": [0, 4, 5], "iii": 0, "refer": [0, 1, 3, 4, 12], "iv": 0, "v": [0, 5, 10], "uri": 0, "hyperlink": 0, "practic": [0, 10, 11], "indic": [0, 8, 10, 11], "previou": [0, 8, 10], "text": [0, 2, 4, 5, 10], "satisfi": 0, "medium": [0, 5], "context": 0, "resourc": 0, "remov": 0, "prevent": [0, 8], "extract": [0, 11], "substanti": [0, 10], "portion": 0, "content": [0, 2], "supplement": 0, "replac": [0, 5, 8, 10], "unless": [0, 8], "separ": [0, 4, 8, 10, 11], "undertaken": 0, "BY": [0, 1], "THE": 0, "TO": 0, "AS": 0, "IS": 0, "AND": 0, "NO": 0, "represent": [0, 5], "OR": 0, "OF": 0, "kind": [0, 11], "concern": [0, 4, 8], "express": [0, 5, 10], "titl": 0, "merchant": 0, "fit": [0, 11], "FOR": 0, "particular": [0, 5, 8, 11], "infring": 0, "latent": 0, "defect": 0, "accuraci": [0, 8], "presenc": [0, 10], "error": 0, "NOT": 0, "discover": 0, "IN": 0, "full": [0, 5, 8, 10, 11], "event": [0, 10], "WILL": 0, "BE": 0, "liabl": 0, "ON": 0, "theori": 0, "neglig": [0, 5], "indirect": 0, "incident": 0, "consequenti": 0, "punit": 0, "exemplari": 0, "loss": 0, "cost": [0, 11], "expens": 0, "aris": [0, 10], "out": [0, 4, 5, 8, 10], "even": [0, 4, 8, 10], "IF": 0, "been": [0, 5, 11], "advis": 0, "SUCH": 0, "abov": [0, 4, 5, 8, 10, 11], "shall": 0, "most": [0, 4, 5, 10, 11], "approxim": [0, 10, 11], "absolut": 0, "waiver": 0, "termin": [0, 11], "here": [0, 5, 8, 10, 11], "fail": 0, "reinstat": 0, "date": [0, 5, 8], "violat": 0, "cure": 0, "within": [0, 5, 8, 10, 11], "30": [0, 5], "dai": [0, 8], "discoveri": [0, 11], "affect": [0, 8], "seek": [0, 10], "remedi": 0, "stop": 0, "7": [0, 5, 8, 10, 11], "8": [0, 5, 10], "surviv": [0, 11], "state": [0, 4, 10, 11], "herein": 0, "independ": 0, "reduc": [0, 11], "could": [0, 4, 5, 8, 10, 11], "lawfulli": 0, "provis": 0, "deem": [0, 10], "unenforc": 0, "reform": 0, "minimum": 0, "enforc": 0, "cannot": 0, "sever": [0, 11], "remain": [0, 5, 10, 11], "failur": 0, "consent": 0, "privileg": 0, "immun": 0, "jurisdict": 0, "parti": 0, "notwithstand": 0, "elect": 0, "publish": 0, "instanc": [0, 8], "consid": [0, 4, 8, 10, 11], "dedic": [0, 8], "domain": 0, "cc0": 0, "permit": [0, 4], "polici": 0, "logo": 0, "prior": [0, 4, 5], "written": [0, 2, 5, 10], "unauthor": 0, "paragraph": 0, "contact": 0, "repositori": [2, 3, 12], "jupyterbook": [3, 5, 12], "serv": [3, 12], "introduct": [3, 8, 12], "variou": [3, 12], "topic": [3, 12], "my": [3, 12], "research": [2, 3, 10, 11, 12], "shield": [3, 12], "three": [5, 8, 10], "star": [5, 10, 11], "sim": [5, 8, 10, 11], "rm": [4, 5, 8, 10, 11], "ly": [5, 10], "awai": [5, 11], "sun": [5, 10, 11], "two": [4, 5, 8, 10, 11], "sunlik": [5, 8], "mass": [4, 5, 8, 10, 11], "luminos": 5, "third": [5, 10], "proxima": 5, "much": [5, 10, 11], "cooler": 5, "smaller": [5, 10, 11], "physic": [2, 4, 5, 10, 11], "radiu": [5, 11], "solar": [5, 8, 10], "unit": [5, 8, 10, 11], "given": [3, 5, 8, 10, 11, 12], "tabl": [5, 10, 11], "m_": [5, 10, 11], "odot": [5, 10, 11], "105": 5, "pm": [4, 5], "0070": 5, "934": 5, "0061": 5, "l_": 5, "519": 5, "018": 5, "5002": 5, "016": 5, "r_": [5, 10], "231": [5, 11], "0036": 5, "868": 5, "0052": 5, "while": [5, 8, 10, 11], "th\u00e9venin": 5, "et": [5, 10, 11], "al": [5, 10, 11], "2002": 5, "These": [5, 10, 11], "valu": [5, 8, 10, 11], "updat": [5, 8, 10], "recent": 5, "akeson": 5, "2021": [5, 10], "older": 5, "consist": [5, 8, 10], "ignor": 5, "significantli": [5, 10], "less": [5, 10, 11], "massiv": [5, 10, 11], "approach": [5, 10, 11], "periastron": [5, 11], "passag": 5, "gtrsim": [5, 11], "500": [5, 10], "au": [5, 8, 10, 11], "like": [5, 8, 11], "gravit": [5, 10], "inner": [5, 8, 10, 11], "extant": 5, "planet": [4, 5], "either": [5, 8, 10, 11], "observ": [5, 10, 11], "ski": 5, "southern": 5, "hemispher": 5, "appear": [5, 8, 10, 11], "singl": [5, 10, 11], "nake": 5, "ey": 5, "beta": [5, 10], "some": [2, 3, 5, 8, 10, 11, 12], "circ": [5, 8, 10, 11], "west": 5, "sky": [5, 11], "li": [5, 10], "about": [5, 10, 11], "southwest": 5, "recal": 5, "angular": [5, 10, 11], "diamet": 5, "moon": [5, 10, 11], "width": [5, 8, 10, 11], "bright": 5, "left": [4, 5, 10, 11], "both": [5, 8, 10, 11], "faint": 5, "red": [5, 8, 10, 11], "center": [5, 8, 10, 11], "circl": 5, "lower": [5, 10], "point": [5, 8, 11], "between": [5, 8, 10, 11], "intens": 5, "size": [5, 8], "weaker": 5, "distant": [5, 10], "tripl": 5, "main": [5, 10], "pair": [5, 11], "figur": [5, 8, 10, 11], "credit": [1, 5, 11], "wikipedia": 5, "alpha_centauri": 5, "user": 5, "skatebik": 5, "mani": [2, 3, 5, 8, 10, 11, 12], "campaign": 5, "search": [5, 11], "nearbi": [5, 10], "exoplanet": [2, 5, 11], "led": 5, "few": [5, 8, 10, 11], "fals": [5, 10], "posit": [5, 8, 10, 11], "claim": 5, "detect": 5, "turn": [5, 10, 11], "spuriou": 5, "contrast": [4, 5], "too": 5, "appar": 5, "magnitud": [4, 5, 10], "01": [5, 8, 10, 11], "33": [5, 10], "modern": [5, 8, 10, 11], "techniqu": [5, 8, 11], "charg": 5, "coupl": [5, 10, 11], "devic": 5, "ccd": 5, "light": [5, 10], "come": [5, 10], "telescop": 5, "tend": 5, "satur": 5, "overexpos": 5, "veri": [5, 8], "difficult": [5, 8], "fluctuat": 5, "zhao": 5, "2018": [5, 10, 11], "demonstr": [5, 8, 10, 11], "lesssim": 5, "50": [5, 8, 10, 11], "oplu": 5, "earth": [5, 8, 10, 11], "would": [5, 8, 10, 11], "after": [5, 10, 11], "decad": 5, "acut": 5, "good": 5, "thing": [5, 10], "we": [4, 5, 8, 10, 11], "earthlik": 5, "There": [4, 5, 8, 10, 11], "motion": [4, 5, 10, 11], "bodi": [5, 10], "space": [5, 8, 10, 11], "astrometri": 5, "radial": [5, 10], "veloc": [5, 10], "transvers": 5, "occur": [5, 8, 10, 11], "perpendicular": 5, "line": [5, 8, 11], "sight": [5, 11], "draw": 5, "whiteboard": 5, "movement": 5, "marker": [5, 8, 10, 11], "tip": 5, "assum": [5, 10, 11], "mount": 5, "wall": [4, 5, 11], "captur": 5, "along": [4, 5, 8, 10, 11], "board": 5, "neither": 5, "pictur": 5, "thu": 5, "combin": [4, 5, 8, 11], "determin": [4, 5, 10, 11], "ellips": 5, "kepler": [5, 8, 10], "plane": [4, 5, 8, 11], "quantiti": 5, "semimajor": [5, 8, 10, 11], "axi": [5, 8, 10, 11], "eccentr": [5, 8, 10, 11], "argument": [5, 8, 10, 11], "pericent": [5, 8, 11], "omega": [4, 5, 8, 10, 11], "big": [5, 8], "shape": [5, 10, 11], "squash": [5, 10], "togeth": [4, 5, 8], "rotat": [5, 10, 11], "rel": [5, 8, 10, 11], "typic": [5, 10, 11], "distanc": [4, 5, 10], "r": [5, 8, 10, 11], "frac": [4, 5, 10], "co": [4, 5, 10, 11], "true": [5, 8, 10, 11], "anomali": [5, 8, 10, 11], "denot": [5, 8, 11], "closest": 5, "q": [5, 11], "farthest": 5, "apocent": 5, "see": [1, 2, 4, 5, 8, 10, 11], "fig": [5, 8, 10, 11], "mathemat": [4, 5, 10], "begin": [4, 5, 8, 10, 11], "align": [4, 5, 10, 11], "end": [4, 5, 8, 10], "ellipt": [5, 10], "orang": [5, 10], "focu": [5, 11], "major": 5, "dash": 5, "blue": [5, 11], "dot": [5, 8, 10, 11], "tilt": [5, 11], "x": [4, 5, 8, 10, 11], "45": [5, 8, 11], "numpi": [2, 5, 8, 10, 11], "np": [5, 8, 10, 11], "matplotlib": [5, 8, 10, 11], "pyplot": [5, 8, 10, 11], "plt": [5, 8, 10, 11], "rcparam": 5, "myst_nb": 5, "glue": 5, "font": [5, 8], "14": [5, 10, 11], "mathtext": 5, "fontset": 5, "cm": [5, 10, 11], "semi": [5, 10], "ecc": [5, 10], "omg": [5, 10], "radian": [5, 8, 10, 11], "fs": 5, "larg": [5, 10], "def": [5, 10, 11], "function": [4, 5, 8, 10, 11], "unitless": 5, "f_step": 5, "arang": [5, 10, 11], "pi": [5, 8, 10, 11], "return": [5, 10, 11], "arrai": [5, 10, 11], "sin": [4, 5, 10, 11], "y": [5, 8, 10, 11], "figsiz": [5, 8, 10, 11], "dpi": [5, 8, 10, 11], "150": [5, 8, 10, 11], "ax": [5, 8, 10, 11], "add_subplot": [5, 8, 10, 11], "111": [5, 8, 10, 11], "grid": [5, 10, 11], "color": [5, 8, 10, 11], "grai": [5, 10], "25": [5, 10, 11], "set_aspect": [5, 8, 10, 11], "equal": [4, 5, 8, 10, 11], "arrow": 5, "75": [5, 8], "005": 5, "head_width": 5, "05": [5, 8, 10], "length_includes_head": 5, "ell": 5, "peri": 5, "apo": 5, "plot": [5, 10, 11], "lw": [5, 8, 10], "ms": [5, 8, 10, 11], "10": [5, 8, 10, 11], "arc_r": 5, "15": [5, 8, 10], "ang_rng": 5, "arc_x": 5, "arc_i": 5, "06": 5, "horizontalalign": [5, 10], "fontsiz": [5, 8, 10, 11], "set_xlabel": [5, 8, 10, 11], "set_ylabel": [5, 8, 10, 11], "set_xlim": [5, 8, 10, 11], "set_ylim": [5, 8, 10, 11], "tick": 5, "set_xtick": [5, 10, 11], "set_ytick": [5, 10, 11], "xlabel": 5, "ylabel": 5, "rang": [5, 8, 10, 11], "len": [5, 8, 10, 11], "append": [5, 10], "els": [2, 5, 10], "str": 5, "set_xticklabel": 5, "set_yticklabel": 5, "orbit_fig": 5, "far": 5, "ve": 5, "note": [5, 8, 10, 11], "locat": [5, 10], "univers": [4, 5, 11], "face": [5, 11], "But": [4, 5, 10, 11], "appropri": [1, 5, 8], "matrix": [4, 5], "z": [5, 10, 11], "matric": 5, "r_x": 5, "theta": [5, 10], "pmatrix": [4, 5], "r_y": 5, "r_z": 5, "repres": [5, 8, 10, 11], "angl": [5, 11], "hand": [5, 10], "rule": [5, 10], "vec": 5, "prime": 5, "vector": [5, 10, 11], "counter": 5, "clockwis": 5, "curl": 5, "thumb": 5, "side": [5, 11], "toward": [5, 10], "neg": 5, "transit": [5, 11], "show": [5, 10, 11], "get": [4, 5, 10, 11], "call": [5, 8, 10], "inclin": [5, 11], "when": [4, 5, 10, 11], "90": [5, 11], "79": 5, "ll": [5, 8, 10, 11], "illustr": [5, 8, 10, 11], "view": [5, 8, 10, 11], "black": [5, 8, 10], "rotate_x": 5, "rotate_i": 5, "rotate_z": 5, "get_ellips": 5, "rvec": 5, "true_f": 5, "inc": [5, 10, 11], "radii": [5, 10], "constant": [4, 5, 10, 11], "zero": [5, 8, 10, 11], "xp": 5, "incl": 5, "r_vec": 5, "95": 5, "rotate_fig": 5, "around": [5, 8, 10, 11], "node": [5, 11], "cross": [5, 10], "ascend": [5, 11], "descend": 5, "longitud": [5, 10, 11], "former": 5, "latter": 5, "359": 5, "wrap": 5, "rightarrow": [5, 11], "therefor": [5, 8, 10, 11], "similarli": 5, "magenta": 5, "60": [5, 10, 11], "ra": 5, "ra_omg": 5, "print": [5, 8, 10, 11], "m": [4, 5, 8, 10, 11], "rotate_fig_ra": 5, "35355339": 5, "1767767": 5, "30618622": 5, "11835361": 5, "3399168": 5, "34705762": 5, "fulli": [5, 10], "six": 5, "notat": [5, 8, 10], "v_x": 5, "dx": 5, "dt": [5, 8, 10, 11], "next": [5, 10, 11], "normal": [5, 10, 11], "euler": [4, 5, 11], "shown": [2, 5, 11], "sometim": 5, "nu": 5, "instantan": 5, "180": [5, 10, 11], "diagram": [5, 10], "kepler_orbit": 5, "lasunncti": 5, "On": 5, "phase": 5, "central": [5, 10, 11], "problem": [4, 5, 8, 10, 11], "potenti": [5, 10, 11], "ambigu": [5, 8], "multipl": [5, 10], "natur": [2, 4, 5, 8, 10, 11], "easier": [5, 8, 11], "hierarch": [5, 11], "brief": 5, "overview": [5, 8, 10], "domin": [5, 10], "m_0": 5, "m_1": [5, 10, 11], "let": [4, 5, 8, 10], "exist": [5, 10, 11], "m_o": [5, 10], "Then": [5, 8, 10], "scalar": 5, "speed": [5, 8, 10, 11], "momentum": [5, 10, 11], "p": [5, 8, 10, 11], "product": 5, "interest": [2, 5, 11], "specif": [5, 8, 10, 11], "better": [5, 8, 10, 11], "compon": [4, 5, 10, 11], "via": [4, 5], "det": 5, "hat": 5, "vmatrix": 5, "h_x": 5, "h_y": 5, "h_z": 5, "project": 5, "vi": 5, "viva": 5, "equat": [4, 5, 10, 11], "total": [5, 10], "energi": [5, 10, 11], "t": [4, 5, 8, 10, 11], "mathcal": 5, "depend": [4, 5, 10, 11], "newton": [5, 11], "consequ": 5, "find": [3, 5, 8, 10, 12], "solv": [4, 5, 8, 11], "eq": [5, 11], "vr": 5, "sqrt": [4, 5, 8, 10, 11], "2r": 5, "conserv": [5, 10], "pick": 5, "With": 5, "algebra": [5, 10, 11], "input": [5, 11], "advanc": [5, 8], "sequenc": [5, 10], "ident": [4, 5, 11], "mit": 5, "opencoursewar": 5, "detail": [4, 5, 8, 10, 11], "backup": 5, "across": [5, 11], "cdot": [5, 8, 10], "laplac": [5, 10], "rung": 5, "lenz": 5, "decompos": 5, "varpi": 5, "e_x": 5, "e_i": 5, "arcsin": 5, "arcco": [5, 11], "arctan": 5, "earlier": [5, 10], "onc": [5, 10], "quad": [5, 10], "undefin": [5, 10], "coplanar": [5, 8, 11], "ad": [5, 10], "dogleg": 5, "circular": [5, 8, 10, 11], "epoch": 5, "julian": [5, 8], "1955": 5, "66": 5, "addition": [4, 5, 8, 10], "often": [5, 8, 10], "arcsecond": 5, "actual": [5, 10], "version": [2, 5, 8], "long": [5, 8, 10, 11], "enough": [5, 10], "accur": [5, 10, 11], "period": [5, 8, 10, 11], "91": 5, "013": 5, "yr": [5, 8, 10, 11], "tot": 5, "obtain": [5, 10], "23": [5, 8, 11], "78": [5, 8], "usag": [5, 8], "As": [5, 8, 10, 11], "cancel": [4, 5], "formula": [5, 10], "m_tot": [5, 10], "524": [5, 8], "32": 5, "232": [5, 8, 11], "204": [5, 8], "dynamicist": 5, "convent": [5, 8], "orient": [5, 10], "vertic": [5, 10], "cardin": 5, "n": [5, 10], "horizont": [5, 10], "appendix": 5, "deitrick": 5, "2015": [5, 10, 11], "astrometr": [5, 11], "data": [5, 8, 10, 11], "neuforg": 5, "verheek": 5, "noel": 5, "1999": [5, 10, 11], "comparison": 5, "each": [2, 3, 4, 5, 8, 10, 11, 12], "visual": [5, 8, 11], "334": 5, "pc": 5, "27": 5, "38": 5, "26": 5, "small": [4, 5], "21": 5, "40": [5, 10, 11], "alpha_cen_ab": 5, "recast": 5, "astrocentr": [5, 8, 11], "choic": [5, 10], "invari": 5, "galilean": 5, "frame": [5, 10], "contain": [5, 8, 10], "anoth": [4, 5, 10, 11], "x_o": [5, 10], "y_o": 5, "z_o": 5, "prime_x": 5, "v_": 5, "o": [5, 10, 11], "v_o": 5, "construct": 5, "barycent": [5, 10], "_1": [4, 5], "_2": [4, 5], "m_2": [5, 10, 11], "introduc": [5, 10], "constraint": 5, "_o": 5, "r_1": [5, 10], "r_2": 5, "parameter": 5, "v_1": 5, "v_2": 5, "ratio": [5, 11], "gener": [4, 5, 8, 10, 11], "sum": [5, 10], "sum_": [5, 10], "m_i": 5, "_i": 5, "qquad": [4, 5, 10], "coincid": 5, "get_rvec": 5, "plot_ellips": 5, "col": [5, 10], "133": [5, 8], "972": [5, 8], "r_vec1": 5, "r_vec2": 5, "ax1": [5, 10], "121": 5, "ax2": [5, 10], "122": 5, "ax_list": 5, "13": [5, 11], "17": 5, "18": [5, 11], "16": [5, 8, 10, 11], "alpha_cen_ab_bari": 5, "sens": 5, "hierarchi": 5, "subsystem": 5, "first": [5, 8, 10, 11], "m_3": [5, 10, 11], "final": [5, 8], "m_4": [5, 10], "r_3": 5, "x_1": [4, 5, 10], "x_2": [4, 5, 10], "x_3": 5, "x_4": 5, "jacobi_coordin": 5, "iter": [5, 8, 10, 11], "keep": [5, 10], "track": 5, "current": [5, 10], "inclus": [5, 8], "th": [5, 10], "eta_j": 5, "_": [4, 5], "_j": 5, "eta_": 5, "second": [5, 8], "jacobian": 5, "won": [5, 11], "mathbf": [4, 5, 10], "eta_1": 5, "eta_2": 5, "eta_3": 5, "eta_4": 5, "prime_1": 5, "prime_2": 5, "prime_3": 5, "_3": 5, "prime_4": 5, "_4": 5, "exactli": [5, 8, 11], "One": [5, 10, 11], "method": [4, 5, 8, 10, 11], "_a": 5, "_b": 5, "i_b": 5, "omega_b": 5, "x_a": 5, "y_a": 5, "z_a": 5, "f_b": 5, "x_b": 5, "a_b": 5, "e_b": 5, "r_b": 5, "y_b": 5, "z_b": 5, "take": [5, 8, 10], "2nd": 5, "m_a": [5, 8, 11], "m_b": [5, 8, 11], "na": 5, "re": [1, 5], "add": [5, 8, 10, 11], "mostli": [5, 8], "same": [5, 8, 10, 11], "procedur": [5, 11], "r_p": 5, "a_p": [5, 10, 11], "e_p": [5, 10, 11], "f_p": [5, 11], "host": [5, 8, 10, 11], "x_p": 5, "omega_p": [5, 10, 11], "i_p": [5, 11], "y_p": 5, "z_p": 5, "planetari": [3, 5, 8, 11, 12], "onto": [5, 8], "_p": 5, "n_p": 5, "m_p": [5, 11], "trivial": [4, 5], "becom": [5, 10], "best": [5, 11], "easiest": [5, 10], "setup": [5, 8, 10], "instead": [5, 10, 11], "wasn": 5, "moreov": [5, 11], "easili": [5, 8, 11], "accomplish": [5, 8], "nifti": [], "citat": [], "akeson2021": [], "orbit": [8, 11], "tricki": 8, "busi": 8, "histor": 8, "due": [8, 10, 11], "transcendent": [8, 11], "p\u00e1l": 8, "2009": [8, 10], "analyt": [8, 11], "numer": [8, 10, 11], "number": [8, 10, 11], "list": 8, "packag": [2, 8], "advantag": 8, "low": [8, 10], "memori": 8, "overhead": 8, "gpu": 8, "cpu": 8, "genga": 8, "code": [2, 8, 10, 11], "mercury6": 8, "mercury6_bin": 8, "binari": [2, 8, 10], "swift": 8, "hnbodi": 8, "nbody6": 8, "nbodi": 8, "gadget2": 8, "galaxi": [8, 10], "starlab": 8, "amus": 8, "guid": [4, 8, 11], "up": [8, 10, 11], "googl": [2, 8], "colab": [2, 8], "conveni": [8, 10], "tool": 8, "test": [8, 11], "python": [2, 3, 8, 10, 12], "link": 8, "inspect": 8, "dropdown": [2, 8], "option": 8, "rocketship": 8, "top": [2, 8, 11], "notebook": [2, 8], "load": 8, "commonli": 8, "librari": 8, "modul": [8, 10], "scipi": [2, 8, 11], "extern": 8, "instal": 8, "run": [8, 10, 11], "pip": 8, "cell": [2, 8, 11], "class": 8, "paramet": [8, 10, 11], "timestep": [8, 10], "particl": [8, 10, 11], "adjust": [8, 10], "coordin": [8, 10, 11], "system": 8, "archiv": [8, 10, 11], "trunk": 8, "tree": 8, "branch": 8, "program": 8, "languag": [2, 8], "object": [8, 10, 11], "initi": [4, 8, 11], "store": [8, 11], "referenc": [8, 10, 11], "later": [8, 10], "default": 8, "tell": 8, "ias15": [8, 10, 11], "algorithm": [8, 10], "msun": [8, 10, 11], "001": [8, 10, 11], "exact_finish_tim": 8, "accordingli": 8, "sampl": 8, "ultim": 8, "evalu": [8, 11], "whfast": [8, 10, 11], "effici": [8, 10], "jacobi": [8, 10], "move_to_com": [8, 10, 11], "convert": [8, 10, 11], "barycentr": [8, 11], "step": [8, 10, 11], "inherit": 8, "3e": 8, "interfac": 8, "document": [2, 8], "high": [8, 10, 11], "qualiti": 8, "idea": [8, 10], "down": [8, 10, 11], "inlin": 8, "op": 8, "orbitplot": 8, "evolv": [2, 8], "automatesimulationarch": [8, 10, 11], "file": [8, 11], "name": [8, 10, 11], "frequenc": [8, 10], "overwrit": 8, "boolean": 8, "interv": [8, 10], "reliabl": 8, "integ": [8, 10, 11], "wherea": 8, "float": 8, "might": [8, 10], "encount": 8, "issu": [8, 10, 11], "finit": 8, "precis": 8, "want": [8, 10, 11], "sure": 8, "output": [8, 11], "bin": [8, 10, 11], "deletefil": [8, 10, 11], "per": 8, "1000": 8, "minut": 8, "itself": 8, "simulationarch": [8, 10, 11], "probe": 8, "sa": [8, 10, 11], "variabl": 8, "last": [8, 10], "snapshot": [8, 10, 11], "9000": 8, "1f": 8, "tmin": 8, "tmax": 8, "20001": 8, "walk": 8, "custom": [8, 11], "specifici": 8, "sublibrari": 8, "done": [8, 10], "statement": [2, 8], "path": 8, "outer": [8, 10, 11], "know": 8, "ps": [8, 10, 11], "hold": 8, "count": 8, "index": [8, 10], "skip": 8, "empti": 8, "string": [8, 11], "assign": 8, "loop": 8, "continu": [2, 8, 10, 11], "until": [8, 10, 11], "reach": [4, 8], "w": [5, 8], "height": [4, 8, 10, 11], "inch": 8, "resolut": [8, 11], "creation": 8, "canva": 8, "row": [8, 11], "column": 8, "subplot": 8, "rci": 8, "markers": 8, "curv": [8, 10], "intermedi": [8, 10, 11], "simpifi": 8, "semicolon": 8, "extra": 8, "altogeth": [4, 8, 10], "stellar": [8, 11], "element": [8, 10, 11], "centauri": 8, "77": 8, "mod": [8, 10], "360": [8, 10, 11], "specifii": 8, "start": [8, 10, 11], "ma": 8, "quarl": [1, 8, 10, 11], "lissauer": [8, 10], "2016": [8, 11], "calcul": [8, 10, 11], "jd": 8, "2452276": 8, "209": 8, "6901": 8, "a_bin": [8, 11], "e_bin": [8, 11], "omg_bin": [8, 11], "ma_bin": [8, 11], "t_bin": [8, 11], "year": [8, 10, 11], "alphacen": 8, "xy_bin": 8, "move_to_hel": [8, 10, 11], "shift": [8, 10, 11], "type": [4, 8, 11], "order": 8, "circumbinari": [8, 11], "resolv": 8, "forc": [8, 10, 11], "m_host": 8, "m_pl": 8, "a_pl": 8, "e_pl": 8, "cartesian": [8, 10, 11], "m_sec": 8, "secondari": [8, 11], "primari": [8, 10, 11], "redirect": 8, "action": 8, "a_": [8, 10, 11], "pl": 8, "global": 8, "mpl_toolkit": [8, 10, 11], "axes_grid1": [8, 10, 11], "inset_loc": [8, 10, 11], "inset_ax": [8, 10, 11], "0035e": [8, 10], "alphacen_wpl": 8, "xy_pl": 8, "scale": [8, 11], "child": 8, "parent": 8, "zoom": [8, 10], "inset": [8, 10], "axin": [8, 10, 11], "100": [8, 11], "bbox_to_anchor": [8, 10, 11], "bbox_transform": [8, 10, 11], "transax": [8, 10, 11], "tbp": 11, "http": 11, "en": [], "body_problem": [], "wa": [10, 11], "develop": 11, "studi": 11, "isaac": 11, "hi": 11, "pioneer": 11, "principia": 11, "formul": 11, "solut": [4, 10, 11], "influenc": [10, 11], "graviti": [10, 11], "anyon": [2, 11], "king": 11, "oscar": 11, "commemor": 11, "birthdai": 11, "1889": 11, "contest": 11, "he": 11, "invit": 11, "scholar": 11, "attempt": 11, "It": [3, 4, 10, 11, 12], "french": 11, "mathematician": 11, "henri": 11, "poincar": 11, "pari": 11, "who": 11, "insuffici": 11, "word": 11, "unambigu": 11, "subsum": 11, "numenclatur": [], "configur": [10, 11], "propos": 11, "collinear": [10, 11], "lagrang": 11, "equilater": 11, "triangl": 11, "2013": 11, "physicist": 11, "insitut": [], "belgrad": 11, "discov": 11, "new": [10, 11], "famili": 11, "galleri": 11, "comput": [10, 11], "eleg": 11, "investig": [10, 11], "explor": 11, "wide": [10, 11], "swath": 11, "potenati": [], "parallel": 11, "jupit": [10, 11], "08": 11, "ge": 11, "1982": [10, 11], "rudolf": 11, "dvorak": 11, "trojan": [10, 11], "astronomi": [2, 11], "roen": 11, "kelli": 11, "1980": [10, 11], "2000": 11, "growth": [4, 11], "power": 11, "were": [10, 11], "t_": 11, "excess": 11, "dynam": [3, 4, 11, 12], "chao": 11, "benettin": 11, "lecar": 11, "1992": 11, "smith": [10, 11], "szebeh": 11, "1993": [10, 11], "froeschl": 11, "1997": [10, 11], "identifi": [10, 11], "rout": 11, "unstabl": [10, 11], "1986": [10, 11], "rabl": 11, "1988": 11, "regular": 11, "quasi": 11, "chaotic": 11, "unbound": 11, "overlap": 11, "instabl": [10, 11], "sensit": 11, "slightli": [10, 11], "drastic": 11, "behavior": 11, "degre": [10, 11], "ahead": 11, "behind": 11, "feel": 11, "net": [10, 11], "slight": 11, "slow": [10, 11], "lead": [10, 11], "increas": [4, 10, 11], "pump": 11, "exchang": [10, 11], "scatter": [10, 11], "focus": 11, "assumpt": [10, 11], "rho": [10, 11], "mu": [10, 11], "critic": [10, 11], "a_c": 11, "leq": 11, "omega_": 11, "f_": 11, "apastron": 11, "bad": [10, 11], "knowledg": [4, 11], "dure": 11, "late": 11, "1990": 11, "e_": [10, 11], "02": 11, "eight": 11, "equidist": 11, "315": 11, "increment": 11, "4d": 11, "dimens": [10, 11], "conceptu": 11, "travers": 11, "2d": 11, "abstract": 11, "nest": 11, "interchang": 11, "summar": 11, "rho_": 11, "cr": 11, "boundari": [4, 10, 11], "stabl": [10, 11], "earli": 11, "escap": [10, 11], "stability_grid1": [], "symbol": [10, 11], "stability_grid2": [], "least": 11, "squar": [10, 11], "trial": [4, 11], "c_1": 11, "c_2": 11, "c_3e_": 11, "c_4": 11, "c_5": 11, "c_6": 11, "minim": 11, "chi": 11, "residu": 11, "merit": 11, "easi": 11, "polynomi": 11, "larger": [10, 11], "discrep": 11, "extrapol": 11, "broad": 11, "regim": [10, 11], "ration": [10, 11], "geq": [10, 11], "signific": [10, 11], "misalign": 11, "disk": [10, 11], "monin": 11, "2006": [10, 11], "2020": [10, 11], "address": [10, 11], "expand": [10, 11], "cover": 11, "wider": [10, 11], "panel": [10, 11], "underli": 11, "github": [2, 11], "repo": 11, "saturnaxi": [2, 11], "threebody_st": 11, "interp2d": 11, "interpol": 11, "griddata": 11, "sy": [], "ebin": 11, "github_fil": 11, "raw": 11, "githubusercont": 11, "com": [10, 11], "master": 11, "a_crit_incl": 11, "5b0": [], "5d": [], "txt": 11, "genfromtxt": 11, "delimit": 11, "comment": 11, "xi": [10, 11], "concaten": 11, "999": [10, 11], "yi": [10, 11], "81": [10, 11], "zi": [10, 11], "none": [10, 11], "linear": [4, 11], "fill_valu": 11, "astab": 11, "rho_cr": 11, "2f": 11, "12": [10, 11], "simplifi": [8, 10, 11], "nearli": 11, "cbp_stabil": 11, "2937": 11, "doyl": 11, "2011": [10, 11], "15944": 11, "a_crit": 11, "70": 11, "rebound": [10, 11], "os": 11, "m_j": [10, 11], "54e": [10, 11], "6897": 11, "20255": 11, "22431": 11, "41": 11, "079220": 11, "365": 11, "inc_bin": 11, "30401": 11, "263": 11, "464": 11, "periaps": 11, "ra_bin": 11, "92": 11, "352": 11, "333": 11, "7048": 11, "t_p": [10, 11], "228": 11, "776": 11, "0069": 11, "inc_p": 11, "0322": 11, "omg_p": [10, 11], "318": 11, "ra_p": 11, "003": [10, 11], "ma_p": 11, "106": 11, "51": 11, "tscale": [10, 11], "025": [10, 11], "kepler16": 11, "rot_x": [], "ang": [], "rot": [10, 11], "kx": [4, 10, 11], "xy_coord": [10, 11], "cart": [10, 11], "rot_xi": [10, 11], "alpha": [10, 11], "question": [10, 11], "vari": [10, 11], "variat": 11, "grow": 11, "secularli": 11, "experi": [4, 10, 11], "paper": [10, 11], "output_bin": [10, 11], "output_step": [10, 11], "wait": 11, "save": [10, 11], "short": [10, 11], "fname": [10, 11], "out_step": [10, 11], "altern": 11, "ang1": 11, "ang2": 11, "rot_omg": 11, "rot_inc": 11, "rot_mat": 11, "cyan": 11, "keplerian": 11, "strongli": 11, "perturb": [4, 10, 11], "jitter": 11, "averag": [4, 10, 11], "caus": [10, 11], "nodal": 11, "precess": 11, "timescal": [10, 11], "oscil": 11, "apsid": 11, "sinc": [10, 11], "fast": 11, "kepler16_long": 11, "200": 11, "again": [10, 11], "understood": 11, "seri": [10, 11], "ax11": 11, "ax12": 11, "ax13": 11, "233": 11, "ax21": 11, "234": 11, "ax22": 11, "235": 11, "ax23": 11, "236": 11, "pl_orb": [10, 11], "del_omega": 11, "mut_incl": 11, "ecosw": 11, "esinw": 11, "icoso": 11, "isino": 11, "e_f": 11, "w_f": 11, "arctan2": 11, "3f": 11, "deg": [10, 11], "subplots_adjust": 11, "wspace": [10, 11], "hspace": [10, 11], "034": 11, "278": 11, "553": 11, "evolut": [10, 11], "over": [4, 10, 11], "wobbl": 11, "plate": 11, "middl": [4, 11], "lie": [10, 11], "fix": [10, 11], "periapsi": [], "omega_f": 11, "polar": 11, "bottom": 11, "tightli": 11, "naiv": [10, 11], "suggest": [10, 11], "indefinit": [10, 11], "mutual": 11, "abil": 11, "temporari": 11, "just": 11, "venu": 11, "mercuri": [10, 11], "broadli": 11, "dub": 11, "martin": 11, "triaud": 11, "2017": [10, 11], "blob": [], "holman": [10, 11], "wiegert": 11, "analysi": [10, 11], "Such": [10, 11], "campbel": 11, "hatz": 11, "2003": 11, "huang": 11, "ji": 11, "2022": 11, "refit": 11, "reffert": 11, "quirrenbach": 11, "cep": 11, "fraction": [10, 11], "shorter": 11, "39": 11, "64": 11, "36": 11, "119": 11, "158": 11, "04": 11, "296": 11, "posterior": 11, "072": [], "173": 11, "48": [], "356": 11, "264": 11, "msini": 11, "0125": 11, "gammacep": 11, "pos_z": 11, "neg_z": 11, "000": 11, "longer": 11, "gammacep_long": 11, "5e4": 11, "t_max": 11, "my_cmap": [10, 11], "colormap": [10, 11], "jet": 11, "norm": [10, 11], "vmin": [10, 11], "vmax": [10, 11], "edgecolor": [10, 11], "cmap": [10, 11], "int": 11, "085": 11, "55": 11, "63": 11, "nomenclatur": 11, "institut": 11, "dark": 11, "anti": 11, "correl": 11, "lidov": 11, "kozai": 11, "mechan": 11, "librat": 11, "270": 11, "naoz": 11, "bode": 11, "flip": [10, 11], "retrograd": [10, 11], "attract": 10, "littl": 10, "involv": 10, "seemingli": 10, "simpl": 10, "four": 10, "sub": 10, "sai": 10, "Is": 10, "Will": 10, "bia": 10, "outcom": 10, "overcom": 10, "goe": 10, "though": 10, "hayashi": 10, "2023": 10, "barn": 10, "greenberg": 10, "transport": 10, "expel": 10, "pleas": [3, 10, 12], "review": 10, "look": 10, "arriv": 10, "judg": 10, "astrophys": [2, 10], "gyr": 10, "g2v": 10, "probabl": 10, "undergo": 10, "laskar": 10, "gastineau": 10, "remaind": 10, "answer": 10, "equilibrium": [4, 10], "found": 10, "1784": 10, "past": 10, "giant": 10, "compact": 10, "kaib": 10, "2019": 10, "nesvorni": 10, "todai": 10, "www": 10, "billyquarl": 10, "latest": 10, "estim": 10, "composit": 10, "hydrogen": 10, "helium": 10, "metal": 10, "chapter": [2, 10], "tau_": 10, "proport": 10, "invers": 10, "cube": 10, "propto": 10, "proportion": 10, "myr": 10, "lectur": [4, 10], "jason": 10, "kendal": 10, "extrema": 10, "vanish": 10, "r1": 10, "r2": [], "u": 10, "xx": 10, "yy": 10, "meshgrid": 10, "l1": 10, "l3": 10, "l4": 10, "aspect": 10, "35": 10, "065": 10, "l_1": 10, "l_2": 10, "l_3": 10, "l_4": 10, "135": 10, "l_5": 10, "mfc": 10, "skyblu": 10, "mec": 10, "darkblu": 10, "legend": 10, "numpoint": 10, "frameon": 10, "off": 10, "jacobi_const": 10, "xo": 10, "yo": 10, "x1": 10, "y1": 10, "ro": 10, "phi": 10, "m_sun": 10, "m_e": 10, "r_h": 10, "x_e": 10, "y_e": 10, "x_": 10, "y_": 10, "r_level": 10, "n_lev": 10, "z_level": 10, "sort": 10, "loc": [], "upper": 2, "borderpad": [], "rx": 10, "bone": [], "contour": 10, "level": [2, 10], "zorder": 10, "linewidth": 10, "five": 10, "topolog": 10, "pseudopotenti": 10, "react": 10, "extend": 10, "r_o": 10, "centrifug": 10, "everyth": 10, "partial": 10, "nabla": 10, "associ": 10, "c_j": 10, "2u": 10, "aren": 10, "why": 10, "bother": 10, "constrain": 10, "zvc": 10, "triangular": 10, "lobe": 10, "cs": 10, "interior": 10, "region": 10, "tug": 10, "war": 10, "delin": 10, "sphere": 10, "isn": 10, "correct": 10, "ellipsoid": 10, "seen": 10, "compar": 10, "set1": 10, "approx": 10, "q_": 10, "set_ov": [], "00000347": 10, "0008897": 10, "00093672": 10, "00095947": 10, "00106035": 10, "00124328": 10, "0012661": 10, "00147675": 10, "00175584": 10, "00240875": 10, "03227121": 10, "69332466": 10, "75659148": 10, "obviou": 10, "fortun": 10, "yellow": 10, "enclos": 10, "a_j": 10, "fill": 10, "area": 10, "forbidden": 10, "complex": 10, "real": 10, "imaginari": 10, "unphys": 10, "henc": 10, "lowest": 10, "asteroid": 10, "pseudo_pot": 10, "sign": 10, "maintain": 10, "calc_zvc": 10, "ck": 10, "0329": 10, "c1": 10, "gnuplot": 10, "get_cmap": 10, "cmmapabl": 10, "scalarmapp": 10, "set_arrai": 10, "set_und": 10, "x_color": 10, "contourf": 10, "linestyl": 10, "solid": 10, "rosario": 10, "franco": 10, "satellit": 10, "decreas": 10, "eqn": 10, "prograd": 10, "crit": 10, "4061": 10, "1257e_p": 10, "668": 10, "236e_p": 10, "scalabl": [], "observation": 10, "photometr": 10, "model": 10, "favor": 10, "edg": 10, "strictli": 10, "gladman": 10, "character": 10, "marchal": 10, "bozi": 10, "literatur": [3, 10, 12], "stem": 10, "everyon": 10, "anywai": 10, "concentr": 10, "a_1": 10, "uniti": 10, "a_2": 10, "differenti": 10, "delta": 10, "gladman_setup": [], "parametr": 10, "f_2": 10, "f_1": 10, "henon": 10, "petit": 10, "delta_h": 10, "straightforward": 10, "clear": 10, "damp": [4, 10], "drag": 10, "protoplanetari": 10, "chamber": 10, "h_": 10, "3m_j": 10, "formal": 10, "priori": 10, "explicitli": 10, "among": 10, "pu": 10, "wu": 10, "explicit": 10, "a_k": 10, "oberta": 10, "recurs": 10, "m_star": 10, "calc_orbit": 10, "get_semi": 10, "y_1": 10, "y_2": 10, "opposit": [4, 10], "complet": 10, "arbitrari": 10, "plai": 10, "interplanetari": 10, "suppos": 10, "proxim": 10, "leverag": 10, "closer": 10, "account": 10, "mitig": 10, "achiev": 10, "conjunct": 10, "half": 10, "stori": 10, "faster": 10, "catch": 10, "repeat": 10, "kick": [4, 10], "random": [4, 10], "reson": 10, "destabil": 10, "video": 10, "refresh": 10, "pattern": 10, "emerg": 10, "plant": 10, "themselv": 10, "maximum": [4, 10], "attent": 10, "pollin": 10, "sunflow": 10, "sunlight": 10, "00": 10, "pine": 10, "cone": 10, "pineappl": 10, "spiral": 10, "arm": 10, "explain": 10, "goal": 10, "irrat": 10, "varphi": 10, "iron": 10, "618033988749": 10, "ldot": 10, "fibonacci": 10, "f_n": [], "oper": 10, "modulo": 10, "f_j": 10, "get_trueanomali": 10, "t_1": 10, "innermost": 10, "mu_1": 10, "ssanalog_test": 10, "gridspec": 10, "gs": 10, "ax3": 10, "billi": 1, "sourc": [1, 2, 3, 12], "jupyt": 2, "undergradu": 2, "introductori": 2, "background": 2, "graduat": 2, "student": 2, "snippet": 2, "familiar": 2, "scientif": 2, "meant": 2, "open": 2, "menu": 2, "rocket": 2, "runtim": 2, "alreadi": 2, "panda": 2, "etc": 2, "execut": 2, "curios": 2, "reveal": 2, "markup": 2, "launch": 2, "button": 2, "screen": 2, "publicli": 2, "local": 2, "copi": 2, "live": 2, "collabor": 2, "welcom": 2, "analog": 10, "e_j": 10, "1345": 10, "a_3": 10, "2871": 10, "a_4": 10, "strong": 10, "quit": 10, "suffici": 10, "hybrid": 10, "wisdom": 10, "map": [4, 10], "1991": 10, "greater": 10, "burlisch": 10, "stoer": 10, "rare": 10, "1345183686262765": 10, "2871316026156066": 10, "usual": 10, "terrestri": 10, "strength": 10, "respond": 10, "neighbor": 10, "descript": [3, 12], "cite": [3, 12], "tutori": [3, 12], "coher": 4, "secular": 4, "reminisc": 4, "harmon": 4, "pendulum": 4, "swing": 4, "back": 4, "forth": 4, "overal": 4, "amplitud": 4, "boost": 4, "randomli": 4, "against": 4, "truli": 4, "concept": 4, "driven": 4, "steadi": 4, "transient": 4, "frictionless": 4, "spring": 4, "hook": 4, "kappa": 4, "attach": 4, "slide": 4, "displac": 4, "bring": 4, "compress": 4, "rightmost": 4, "act": 4, "kx_1": 4, "ddot": 4, "kx_2": 4, "isol": 4, "interact": 4, "furthermor": 4, "rearrang": 4, "bmatrix": 4, "b_1": 4, "b_2": 4, "substitut": 4, "characterist": 4, "2m": 4, "quadrat": 4, "root": 4, "eigenfrequ": 4, "omega_1": 4, "omega_2": 4, "coeffici": 4, "matthew": 4, "schwartz": 4, "harvard": 4, "libretext": 4, "tom": 4, "weideman": 4, "uc": 4, "davi": 4, "youtub": 4, "jefferi": 4, "chasnov": 4, "lagrangian": 4, "rochest": 4, "help": 4}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"exoplanet": [3, 12], "within": [3, 12], "binari": [3, 5, 11, 12], "system": [3, 5, 10, 11, 12], "free": 4, "forc": 4, "eccentr": 4, "A": [4, 6, 7, 8, 9, 10, 11], "review": 4, "coupl": [4, 6, 9], "oscil": 4, "impact": 4, "minim": 4, "sampl": [4, 6, 7, 9, 10, 11], "simul": [4, 6, 7, 8, 9, 10, 11], "introduct": 5, "\u03b1": 5, "centauri": 5, "The": [5, 10], "stellar": [5, 10], "paramet": 5, "alpha": [5, 8], "ab": [5, 8, 11], "orbit": [5, 10], "what": 5, "an": [5, 9], "initi": [5, 10], "condit": 5, "cartesian": 5, "element": 5, "us": [5, 6, 7, 10], "cen": [5, 8], "from": [5, 10], "pourbaix": 5, "boffin": 5, "2016": 5, "coordin": 5, "barycentr": 5, "jacobi": 5, "convert": 5, "refer": [5, 8, 10, 11], "basic": [6, 8], "climat": 6, "model": 6, "zero": 6, "dimension": 6, "latitudin": 6, "energi": 6, "balanc": 6, "togeth": 6, "climlab": 6, "gpu": 7, "acceler": 7, "planet": [7, 8, 10, 11], "format": 7, "genga": 7, "repo": 7, "set": 7, "up": 7, "googl": 7, "colab": 7, "mode": 7, "n": [8, 9], "bodi": [8, 9, 11], "avail": 8, "softwar": 8, "simpl": 8, "1": 8, "star": 8, "2": 8, "structur": 8, "rebound": 8, "save": 8, "plot": 8, "ad": 8, "exampl": 8, "obliqu": 9, "evolut": 9, "defin": 9, "planetari": [9, 10], "spin": 9, "equat": 9, "motion": 9, "pack": 10, "scale": 10, "golden": 10, "ratio": 10, "jacobian": [], "three": 11, "stabil": [10, 11], "histor": 11, "overview": 11, "old": [], "standard": 11, "circumbinari": [], "circumstellar": [], "kepler": 11, "16b": 11, "gamma": 11, "cephei": 11, "holman": [], "wiegert": [], "1999": [], "p": [], "type": [], "s": [], "updat": 11, "formula": 11, "lifetim": 10, "constraint": 10, "hill": 10, "radiu": 10, "debia": 10, "phase": 10, "lagrang": 10, "point": 10, "mutual": 10, "radii": [], "how": 1, "cite": 1, "reus": 1, "thi": 1, "materi": 1, "who": 2, "ar": 2, "note": 2, "interact": 2, "book": 2, "clone": 2}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file