Kepler Solver and Orbit Types

The heart of this package is being able to take a set of Keplerian elements and output relative positions, velocities, etc. For this, we use PlanetOrbits.jl which adopts the same conventions as Orbitize!.

For a quick summary of the coordinate system and orbital-element conventions ($a$, $e$, $i$, $\omega$, $\Omega$, $t_p$, ...), see What conventions does Octofitter use for orbital elements? in the FAQ.

For full documentation on orbit types, coordinate conventions, and available functions, see the PlanetOrbits.jl documentation:

• Introduction - Getting started with orbit creation and solving
• Coordinate Conventions - Coordinate system and orbital element definitions
• API Reference - Complete function reference

Kepler Solver

The Kepler solver used to go from mean anomaly to eccentric anomaly is a tweaked version copied from AstroLib.jl.

From AstroLib.jl:

Many different numerical methods exist to solve Kepler's equation. This function implements the algorithm proposed in Markley (1995) Celestial Mechanics and Dynamical Astronomy, 63, 101 (DOI:10.1007/BF00691917). This method is not iterative, requires only four transcendental function evaluations, and has been proved to be fast and efficient over the entire range of elliptic motion 0≤e≤10.

On my laptop, this solves for a single eccentric anomaly in just 47 ns. Since it is implemented in pure Julia, there is no overhead from calling into a C or Cython compiled function and no need for vectorization.

Choosing an Orbit Type in Octofitter

When defining a Planet in Octofitter, specify the orbit type via the basis parameter:

For generating synthetic data using PlanetOrbits functions, see the Data Simulation tutorial.