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.. _manual: | ||
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orbitiz! Manual | ||
orbitize! Manual | ||
============== | ||
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Intro to orbitize! | ||
Intro to ``orbitize!`` | ||
+++++++++++++++++ | ||
Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ | ||
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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. | ||
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Start with Section 4.2 of Sarah's thesis: https://thesis.library.caltech.edu/16076/ | ||
``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. | ||
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There are many basis sets (orbital bases) that can be used to describe an orbit, | ||
which can then be solved using Kepler’s equation. | ||
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It is important, then, to be explicit about coordinate systems. | ||
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For an interactive visualization to define and help users understand our coordinate system, | ||
you can check out `this GitHub tutorial <https://github.com/sblunt/orbitize/blob/main/docs/tutorials/show-me-the-orbit.ipynb>`_. | ||
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There is also a `YouTube video <https://www.youtube.com/watch?v=0e24VUhQmbM>`_. | ||
with use and explaination of the coordinate system. | ||
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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 | ||
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$$ \delta R.A. = \pi a(1-ecosE)[cos^2{i\over 2}sin(f+\omega_p+\Omega)-sin^2{i\over 2}sin(f+\omega_p-\Omega)] $$ | ||
$$ \delta decl. = \pi a(1-ecosE)[cos^2{i\over 2}cos(f+\omega_p+\Omega)-sin^2{i\over 2}cos(f+\omega_p-\Omega)] $$ | ||
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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: |