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Orbital Elements

Uli Scheuss edited this page Dec 26, 2024 · 17 revisions

Orbital Element Flexibility in CurveSimulator

CurveSimulator offers versatile input options for defining celestial body orbits:

  • Multiple Element Sets: The software can process various combinations of orbital elements.
  • Mixed Definitions: Different orbits within the same simulation can be described using distinct subsets of orbital elements.
  • State Vector Alternative: If the initial position and velocity (state vector) are known, orbital elements become optional.

Primary Star Configuration

The first body listed in the configuration file is designated as the system's primary star.

  • No orbital parameters are required for this body.
  • Its initial position is set to the origin (0, 0, 0).
  • The primary star's velocity vector is derived from the masses and velocity vectors of all other bodies in the system.

Orbital Element Notation

For each orbital element, the following information is provided in parentheses:

  • Abbreviation used in the software
  • A typical value for a transiting planet

Orbital Elements

Mandatory parameters:

  • semi-major axis (a)
  • eccentricity (e = 0, circular orbit)
  • inclination (i = 90, creates an observable transit)

Two of the following three parameters have to be provided:

  • longitude of ascending node (Ω = 0)
  • longitude of periapsis (ϖ = 0)
  • argument of periapsis (ω = 0)

One of the following five parameters has to be provided in order to specify the initial position on the orbit.

  • mean longitude (L = 0 at periapsis) or mean anomaly (ma = 0 at periapsis)
  • true anomaly (nu = 0 at periapsis, nu = 90 at time of primary transit, nu = 270 at time of secondary transit)
  • eccentric anomaly (ea = 0 at periapsis)
  • time of periapsis (T = 0 at periapsis)

There is also an optional parameter t, if you wish to specify an additional time difference, by which the initial position is moved.

Effect of the individual parameters

Coordinate_system

In each of the following figures, the used values of the orbital elements are shown in the upper part. Elements of interest in the particular figure are colored red. As in CurveSimulator's videos, the left part of each figure is typically an overhead view and the right part shows an edge-on view.

L

nu

ea

ma

T

little_omega

angles_nu

big_omega