From ac8a96265e65c9dded9d988fa6a2554eb7683dbd Mon Sep 17 00:00:00 2001 From: Sarah Blunt Date: Tue, 16 Jan 2024 12:39:33 -0800 Subject: [PATCH 01/12] initial commit of manual --- docs/index.rst | 1 + docs/manual.rst | 11 +++++++++++ 2 files changed, 12 insertions(+) create mode 100644 docs/manual.rst diff --git a/docs/index.rst b/docs/index.rst index 1ca2437e..60024e09 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -50,6 +50,7 @@ User Guide: faq contributing api + manual Changelog: ++++++++++ diff --git a/docs/manual.rst b/docs/manual.rst new file mode 100644 index 00000000..06147337 --- /dev/null +++ b/docs/manual.rst @@ -0,0 +1,11 @@ +.. _manual: + +orbitiz! Manual +============== + +Intro to orbitize! ++++++++++++++++++ + +Here is where the intro stuff will go! (written in markdown) + +Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ \ No newline at end of file From 3f72c8c82f13151e567264add0401cbd6cf8199f Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Fri, 26 Jan 2024 16:48:19 -0800 Subject: [PATCH 02/12] Testing equations --- docs/manual.rst | 40 ++++++++++++++++++++++++++++++++++++---- 1 file changed, 36 insertions(+), 4 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 06147337..73e12c29 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -1,11 +1,43 @@ .. _manual: -orbitiz! Manual +orbitize! Manual ============== -Intro to orbitize! +Intro to ``orbitize!`` +++++++++++++++++ +Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ -Here is where the intro stuff will go! (written in markdown) +At its core, ``orbitize!`` turns data into orbits. +This is done when relative kinematic measurements of a primary and secondary body are converted to posteriors over +orbital parameters through Bayesian analysis. -Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ \ No newline at end of file +``orbitize!`` hinges on the two-body problem, which describes the paths of two +bodies gravitationally bound to each other. +The solution of the two-body problem describes the motion of each body as a +function of time, given parameters determining the position and velocity of both objects at a particular epoch. + + + +There are many basis sets (orbital bases) that can be used to describe an orbit, +which can then be solved using Kepler’s equation. + +It is important, then, to be explicit about coordinate systems. + +For an interactive visualization to define and help users understand our coordinate system, +you can check out `this GitHub tutorial `_. + +There is also a `YouTube video `_. +with use and explaination of the coordinate system. + +In its “standard” mode, ``orbitize!`` assumes that the user only has relative astrometric data to fit. +To obtain these measurements, an astronomer takes an image containing two point sources +and measures the position of the planet relative to the star in angular coordinates. +In the ``orbitize!`` coordinate system, relative R.A. and decl. can be expressed as the following functions +of orbital parameters + +$$ \delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] $$ +$$ \delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] $$ + +where 𝑎, 𝑒, 𝜔p, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is +the true anomaly, and E is the eccentric anomaly, which are related to elapsed time +through Kepler’s equation and Kepler’s third law: \ No newline at end of file From f2c9be4bd4b64b15cce237ecd515a97c5c3d66bb Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Fri, 26 Jan 2024 17:04:27 -0800 Subject: [PATCH 03/12] Equation testing --- docs/manual.rst | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 73e12c29..e8128514 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -24,7 +24,7 @@ which can then be solved using Kepler’s equation. It is important, then, to be explicit about coordinate systems. For an interactive visualization to define and help users understand our coordinate system, -you can check out `this GitHub tutorial `_. +you can check out `this GitHub tutorial `_. There is also a `YouTube video `_. with use and explaination of the coordinate system. @@ -35,8 +35,9 @@ and measures the position of the planet relative to the star in angular coordina In the ``orbitize!`` coordinate system, relative R.A. and decl. can be expressed as the following functions of orbital parameters -$$ \delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] $$ -$$ \delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] $$ +.. math:: + \delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] $$ + \delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] $$ where 𝑎, 𝑒, 𝜔p, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is the true anomaly, and E is the eccentric anomaly, which are related to elapsed time From c2653f2d9dad5a4be2a71b7137b0a0f947b89393 Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Mon, 12 Feb 2024 16:54:40 -0800 Subject: [PATCH 04/12] equation checkpoint --- docs/manual.rst | 93 ++++++++++++++++++++++++++++++++++++------------- 1 file changed, 68 insertions(+), 25 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index e8128514..eb041c24 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -5,40 +5,83 @@ orbitize! Manual Intro to ``orbitize!`` +++++++++++++++++ -Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ - -At its core, ``orbitize!`` turns data into orbits. -This is done when relative kinematic measurements of a primary and secondary body are converted to posteriors over -orbital parameters through Bayesian analysis. ``orbitize!`` hinges on the two-body problem, which describes the paths of two -bodies gravitationally bound to each other. -The solution of the two-body problem describes the motion of each body as a -function of time, given parameters determining the position and velocity of both objects at a particular epoch. +bodies gravitationally bound to each other as a function of time, +given parameters determining the position and velocity of both objects at a particular epoch. +There are many basis sets (orbital bases) that can be used to describe an orbit, +which can then be solved using Kepler’s equation, but first it is important to be explicit about coordinate systems. +.. Note:: + For an interactive visualization to define and help users understand our coordinate system, + you can check out `this GitHub tutorial `_. + There is also a `YouTube video `_ + with use and explaination of the coordinate system. +In its “standard” mode, ``orbitize!`` assumes that the user only has relative astrometric data to fit. +In the ``orbitize!`` coordinate system, relative R.A. and declination can be expressed as the following functions +of orbital parameters -There are many basis sets (orbital bases) that can be used to describe an orbit, -which can then be solved using Kepler’s equation. +.. math:: + \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] -It is important, then, to be explicit about coordinate systems. + \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] -For an interactive visualization to define and help users understand our coordinate system, -you can check out `this GitHub tutorial `_. +where 𝑎, 𝑒, :math:`\omega_p`, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is +the true anomaly, and E is the eccentric anomaly, which are related to elapsed time +through Kepler’s equation and Kepler’s third law: +.. math:: + M = 2\pi ({t\over P}-(\tau -\tau_ref)) -There is also a `YouTube video `_. -with use and explaination of the coordinate system. + ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_tot}) -In its “standard” mode, ``orbitize!`` assumes that the user only has relative astrometric data to fit. -To obtain these measurements, an astronomer takes an image containing two point sources -and measures the position of the planet relative to the star in angular coordinates. -In the ``orbitize!`` coordinate system, relative R.A. and decl. can be expressed as the following functions -of orbital parameters + M =E-esinE + + f = 2tan^-1[\sqrt{{1+e\over 1-e}}tan{E\over 2}] + +``orbitize!`` employs two Kepler solvers to convert between mean +and eccentric anomaly: one that is efficient for the highest eccentricities, and Newton’s method, which in other cases is more efficient for solving for the average +orbit. See `Blunt et al. (2020) `_ for more detail. + + +From scrutinizing the above sets of equations, one may observe +a few important inherent degeneracies. + +First, notice that the individual component masses do not show up anywhere in this equation set. +While it is impossible to measure dynamical masses for either the primary or the secondary using just +relative astrometry, there are methods to constrain the system. +If the mass of the planet can be safely assumed to be negligible compared to the mass of the star, +then the total mass derived from Keplerian analysis can be treated as a constraint on the dynamical mass +of the primary. +In practice, the reverse logic is often employed: an independent constraint +on the mass of the primary (from e.g., spectroscopic analysis) is used as a prior on +the total mass when the planet mass is small and can be ignored. + +A second important degeneracy is between semimajor axis 𝑎, total mass :math:`𝑀_tot`, and +parallax 𝜋. If we just had relative astrometric measurements and no external knowledge of the system parallax, +we would not be able to distinguish between a system +that has larger distance and larger semimajor axis (and therefore larger total mass, +assuming a fixed period) from a system that has smaller distance, smaller semimajor +axis, and smaller total mass. Luckily, we live in an era where parallax measurements +are excellent overall thanks to the Gaia mission, with which strict priors can often be applied to, +breaking the degeneracy and enabling dynamical mass measurements of stars (when planet mass is negligible). +However, this degeneracy is important to take into account when considering the impact of potential +biases in parallax or stellar mass measurements. + +A final degeneracy I would like to point out concerns the argument of periastron :math:`\omega_p` +and the position angle of nodes Ω. The above defined R.A. and decl. functions are invariant to the transformation: .. math:: - \delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] $$ - \delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] $$ + \omega_p' = \omega_p + \pi + \omega' = \omega - \pi -where 𝑎, 𝑒, 𝜔p, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is -the true anomaly, and E is the eccentric anomaly, which are related to elapsed time -through Kepler’s equation and Kepler’s third law: \ No newline at end of file +which creates a 180◦ degeneracy between particular values of :math:`\omega_p` and Ω, and +a characteristic “double-peaked” structure in marginalized 1D posteriors of these +parameters (see Figure 4.2 for an example). +Physically, this degeneracy comes about +because relative astrometry alone only constrains motion in the plane of the sky; an +orbit tilted toward the observer, with the planet moving away from the observer has +the same projection on the plane of the sky as an orbit tilted away from the observer, +with the planet moving toward the observer. In practice, this degeneracy is handy, +because if the :math:`\omega_p`/Ω posteriors do not appear identical before and after 180◦, +it is generally an indication that the MCMC chains are unconverged. \ No newline at end of file From 6361d77049f1a28d73c4dc3e94972e6de4b7d534 Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Tue, 13 Feb 2024 16:54:25 -0800 Subject: [PATCH 05/12] equation check --- docs/manual.rst | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index eb041c24..02464f40 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -15,8 +15,9 @@ which can then be solved using Kepler’s equation, but first it is important to .. Note:: For an interactive visualization to define and help users understand our coordinate system, you can check out `this GitHub tutorial `_. + There is also a `YouTube video `_ - with use and explaination of the coordinate system. + with use and explanation of the coordinate system. In its “standard” mode, ``orbitize!`` assumes that the user only has relative astrometric data to fit. In the ``orbitize!`` coordinate system, relative R.A. and declination can be expressed as the following functions @@ -29,7 +30,8 @@ of orbital parameters where 𝑎, 𝑒, :math:`\omega_p`, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is the true anomaly, and E is the eccentric anomaly, which are related to elapsed time -through Kepler’s equation and Kepler’s third law: +through Kepler’s equation and Kepler’s third law + .. math:: M = 2\pi ({t\over P}-(\tau -\tau_ref)) @@ -57,7 +59,7 @@ In practice, the reverse logic is often employed: an independent constraint on the mass of the primary (from e.g., spectroscopic analysis) is used as a prior on the total mass when the planet mass is small and can be ignored. -A second important degeneracy is between semimajor axis 𝑎, total mass :math:`𝑀_tot`, and +A second important degeneracy is between semimajor axis 𝑎, total mass :math:`𝑀_{tot}`, and parallax 𝜋. If we just had relative astrometric measurements and no external knowledge of the system parallax, we would not be able to distinguish between a system that has larger distance and larger semimajor axis (and therefore larger total mass, @@ -73,7 +75,8 @@ and the position angle of nodes Ω. The above defined R.A. and decl. functions a .. math:: \omega_p' = \omega_p + \pi - \omega' = \omega - \pi + + \Omega' = \Omega - \pi which creates a 180◦ degeneracy between particular values of :math:`\omega_p` and Ω, and a characteristic “double-peaked” structure in marginalized 1D posteriors of these From 8b19f168fbc0494128b917f36e3be74273d6cb98 Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Thu, 29 Feb 2024 10:45:52 -0800 Subject: [PATCH 06/12] cut down for clarity --- docs/manual.rst | 54 ++++++++++++++++++++----------------------------- 1 file changed, 22 insertions(+), 32 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 02464f40..6d82ab48 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -26,20 +26,23 @@ of orbital parameters .. math:: \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] - \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] + \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)+sin^2{i\over 2}cos(f+\omega_p-\Omega)] where 𝑎, 𝑒, :math:`\omega_p`, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is the true anomaly, and E is the eccentric anomaly, which are related to elapsed time through Kepler’s equation and Kepler’s third law .. math:: - M = 2\pi ({t\over P}-(\tau -\tau_ref)) + M = 2\pi ({t\over P}-(\tau -\tau_{ref})) + + + ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) - ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_tot}) M =E-esinE + - f = 2tan^-1[\sqrt{{1+e\over 1-e}}tan{E\over 2}] + f = 2tan^{-1}[\sqrt{{1+e\over 1-e}}tan{E\over 2}] ``orbitize!`` employs two Kepler solvers to convert between mean and eccentric anomaly: one that is efficient for the highest eccentricities, and Newton’s method, which in other cases is more efficient for solving for the average @@ -47,31 +50,19 @@ orbit. See `Blunt et al. (2020) Date: Thu, 29 Feb 2024 11:40:00 -0800 Subject: [PATCH 07/12] formatting test --- docs/manual.rst | 49 ++++++++++++++++++++----------------------------- 1 file changed, 20 insertions(+), 29 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 6d82ab48..3e53d60e 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -25,7 +25,7 @@ of orbital parameters .. math:: \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] - + \ \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)+sin^2{i\over 2}cos(f+\omega_p-\Omega)] where 𝑎, 𝑒, :math:`\omega_p`, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is @@ -34,14 +34,11 @@ through Kepler’s equation and Kepler’s third law .. math:: M = 2\pi ({t\over P}-(\tau -\tau_{ref})) - - + \ ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) - - + \ M =E-esinE - - + \ f = 2tan^{-1}[\sqrt{{1+e\over 1-e}}tan{E\over 2}] ``orbitize!`` employs two Kepler solvers to convert between mean @@ -52,29 +49,23 @@ orbit. See `Blunt et al. (2020) Date: Thu, 29 Feb 2024 11:53:45 -0800 Subject: [PATCH 08/12] formatting check --- docs/manual.rst | 50 +++++++++++++++++++++++++------------------------ 1 file changed, 26 insertions(+), 24 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 3e53d60e..352f2cbc 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -24,8 +24,8 @@ In the ``orbitize!`` coordinate system, relative R.A. and declination can be exp of orbital parameters .. math:: - \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] - \ + \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] \\ + \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)+sin^2{i\over 2}cos(f+\omega_p-\Omega)] where 𝑎, 𝑒, :math:`\omega_p`, Ω, and 𝑖 are orbital parameters, and 𝜋 is the system parallax. f is @@ -33,12 +33,12 @@ the true anomaly, and E is the eccentric anomaly, which are related to elapsed t through Kepler’s equation and Kepler’s third law .. math:: - M = 2\pi ({t\over P}-(\tau -\tau_{ref})) - \ - ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) - \ - M =E-esinE - \ + M = 2\pi ({t\over P}-(\tau -\tau_{ref})) \\ + + ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) \\ + + M =E-esinE \\ + f = 2tan^{-1}[\sqrt{{1+e\over 1-e}}tan{E\over 2}] ``orbitize!`` employs two Kepler solvers to convert between mean @@ -49,23 +49,25 @@ orbit. See `Blunt et al. (2020) Date: Thu, 29 Feb 2024 13:09:38 -0800 Subject: [PATCH 09/12] Added RV section --- docs/manual.rst | 70 ++++++++++++++++++++++++++++++++++++++++++------- 1 file changed, 61 insertions(+), 9 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 352f2cbc..75cc8482 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -17,14 +17,14 @@ which can then be solved using Kepler’s equation, but first it is important to you can check out `this GitHub tutorial `_. There is also a `YouTube video `_ - with use and explanation of the coordinate system. + with use and explanation of the coordinate system by Sarah Blunt. In its “standard” mode, ``orbitize!`` assumes that the user only has relative astrometric data to fit. In the ``orbitize!`` coordinate system, relative R.A. and declination can be expressed as the following functions of orbital parameters .. math:: - \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] \\ + \Delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] \Delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)+sin^2{i\over 2}cos(f+\omega_p-\Omega)] @@ -33,11 +33,11 @@ the true anomaly, and E is the eccentric anomaly, which are related to elapsed t through Kepler’s equation and Kepler’s third law .. math:: - M = 2\pi ({t\over P}-(\tau -\tau_{ref})) \\ + M = 2\pi ({t\over P}-(\tau -\tau_{ref})) - ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) \\ + ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) - M =E-esinE \\ + M =E-esinE f = 2tan^{-1}[\sqrt{{1+e\over 1-e}}tan{E\over 2}] @@ -49,19 +49,20 @@ orbit. See `Blunt et al. (2020) `_), +which can then be used to generate random prior samples or compute the prior +probability of a sample orbit. Importantly, this prior preserves covariances between +input parameters, allowing ``orbitize!``to use an accurate representation of the RV +posterior to constrain the fit. This method can be referred to as the “posteriors as priors” +method, since posteriors output from a RV fitting code are, through KDE sampling, +being applied as priors in``orbitize!``. + More coming soon! \ No newline at end of file From b3e98292fba85456fb3e4caa01859dc34abd73d6 Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Thu, 29 Feb 2024 13:30:36 -0800 Subject: [PATCH 10/12] formatting --- docs/manual.rst | 23 +++++++++++++---------- 1 file changed, 13 insertions(+), 10 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 75cc8482..63690d09 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -35,6 +35,8 @@ through Kepler’s equation and Kepler’s third law .. math:: M = 2\pi ({t\over P}-(\tau -\tau_{ref})) + +.. math:: ({P\over yr})^2 =({a\over au})^3({M_\odot \over M_{tot}}) M =E-esinE @@ -75,8 +77,9 @@ Solutions to breaking degeneracies 1 and 3 can be found in the next section. Using Radial Velocities +++++++++++++++++ -In the ``orbitize!``coordinate system, and relative to the system barycenter, the +In the ``orbitize!`` coordinate system, and relative to the system barycenter, the radial velocity of the planet due to the gravitational influence of the star is: + .. math:: rv_p(f) = [\sqrt{{G\over (1-e**2)}}]M_* sini(M_{tot})^{-1/2}a^{-1/2}(cos(\omega_p+f)+ecos\omega_p) @@ -92,15 +95,15 @@ dynamical mass measurements of the planet itself, but of the star. Radial velocity measurements also break the Ω/𝜔 degeneracy discussed in the previous section, uniquely orienting the orbit in 3D space. -``orbitize!``can perform joint fits of RV and astrometric data in two different +``orbitize!`` can perform joint fits of RV and astrometric data in two different ways, which have complementary applications. -The first method is automatically triggered when an -``orbitize!``user inputs radial velocity data. ``orbitize!``automatically parses -the data, sets up an appropriate model, then runs the user’s Bayesian computation -algorithm of choice to jointly constrain all free parameters in the fit. ``orbitize!`` -can handle both primary and secondary RVs, and fits for the appropriate dynamical -masses when RVs are present; when primary RVs are included, ``orbitize!``fits for +The first method is automatically triggered when an ``orbitize!`` user inputs radial velocity data. +``orbitize!`` automatically parses the data, sets up an appropriate model, +then runs the user’s Bayesian computation +algorithm of choice to jointly constrain all free parameters in the fit. +``orbitize!`` can handle both primary and secondary RVs, and fits for the appropriate dynamical +masses when RVs are present; when primary RVs are included, ``orbitize!`` fits for the dynamical masses of secondary objects, and vice versa. Instrumental nuisance parameters (RV zeropoint offset, 𝛾, and white noise jitter, 𝜎) for each RV instrument are also included as additional free parameters in the fit if the user specifies different @@ -116,10 +119,10 @@ creates a representation of the prior using kernel density estimation (`kernel density estimation `_), which can then be used to generate random prior samples or compute the prior probability of a sample orbit. Importantly, this prior preserves covariances between -input parameters, allowing ``orbitize!``to use an accurate representation of the RV +input parameters, allowing ``orbitize!`` to use an accurate representation of the RV posterior to constrain the fit. This method can be referred to as the “posteriors as priors” method, since posteriors output from a RV fitting code are, through KDE sampling, -being applied as priors in``orbitize!``. +being applied as priors in ``orbitize!`` . More coming soon! \ No newline at end of file From 4062eec814139bbe8888609ac3b7708280a361c9 Mon Sep 17 00:00:00 2001 From: Sofia Covarrubias <44685425+sofiacovarrubias@users.noreply.github.com> Date: Thu, 29 Feb 2024 13:44:04 -0800 Subject: [PATCH 11/12] formatting updates --- docs/manual.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/manual.rst b/docs/manual.rst index 63690d09..7b1c1ef4 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -81,9 +81,9 @@ In the ``orbitize!`` coordinate system, and relative to the system barycenter, t radial velocity of the planet due to the gravitational influence of the star is: .. math:: - rv_p(f) = [\sqrt{{G\over (1-e**2)}}]M_* sini(M_{tot})^{-1/2}a^{-1/2}(cos(\omega_p+f)+ecos\omega_p) + rv_p(f) = \sqrt{{G\over (1-e^2)}}M_* sini(M_{tot})^{-1/2}a^{-1/2}(cos(\omega_p+f)+ecos\omega_p) - rv_*(f) = [\sqrt{{G\over (1-e**2)}}]M_p sini(M_{tot})^{-1/2}a^{-1/2}(cos(\omega_*+f)+ecos\omega_*) + rv_*(f) = \sqrt{{G\over (1-e^2)}}M_p sini(M_{tot})^{-1/2}a^{-1/2}(cos(\omega_*+f)+ecos\omega_*) where 𝜔∗ is the argument of periastron of the star’s orbit, which is equal to 𝜔𝑝 + 180◦. From 7d94208bc71ad687552e157e6a17a736b07e1b5b Mon Sep 17 00:00:00 2001 From: Sarah Blunt Date: Wed, 10 Apr 2024 12:59:29 -0700 Subject: [PATCH 12/12] add orbitize manual to changelog --- docs/index.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/index.rst b/docs/index.rst index 60024e09..ecbca7f5 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -59,6 +59,7 @@ Changelog: - discuss MCMC autocorrelation in MCMC tutorial (@michaelkmpoon) - add time warning if OFTI doesn't accept an orbit in first 60 s (@michaelkmpoon) +- add first parts of orbitize! manual (@sofiacovarrubias/@sblunt) **2.2.2 (2023-06-30)**