API Documentation

KeplerianElements( a, # semi-major axis [AU] e, # eccentricity i, # inclination [rad] ω, # argument of periapsis [rad] Ω, # longitude of ascending node [rad] τ, # epoch of periastron passage at MJD=0 M, # mass of primary [M⊙] plx, # parallax [mas]; defines the distance to the primary )

Represents the Keplerian elements of a secondary body orbiting a primary. Values can be specified by keyword argument or named tuple for convenience.

See also KeplerianElementsDeg for a convenience constructor accepting units of degrees instead of radians for i, ω, and Ω.

astuple(elements)

Return the parameters of a KeplerianElements value as a tuple.

KeplerianElementsDeg(a, e, i, ω, Ω, τ, M, plx)

A convenience function for constructing KeplerianElements where i, ω, and Ω are provided in units of degrees instead of radians.

orbitsolve(elements, t)

Given a set of orbital elements with a time t in days, get the position and velocity of the secondary body (e.g. planet around a star).

This will output an AbstractOrbitSolution struct with the following properties:

• x: δ right ascension [mas]
• y: δ declination [mas]
• ẋ: right ascension proper motion anomaly [mas/year]
• ẏ: declination proper motion anomaly [mas/year]
• ż: radial velocity of the secondary [m/s]
• ẍ: right ascension acceleration [mas/year^2]
• ÿ: declination acceleration [mas/year^2]

You can access the properties by name .x. There are helper functions to calculate each of these properties individually, but if you need more than one it is most efficient to calculate them in one go.

radvel can optionally accept the mass of the primary to calculate the impact of the secondary body on radial velocity of the primary, instead of the radial velocity of the secondary body itself.

Note: these calculations use the small angle approximation, so are only accurate when the star is much further way from the observer than the secondary is from the primary.

See also: orbitsolve_ν, projectedseparation, raoff, decoff, radvel, propmotionanom.

orbitsolve_ν(elem, ν)

Solve a keplerian orbit from a given true anomaly [rad]. See orbitsolve for the same function accepting a given time.

orbitsolve_ν(elem, ν)

Solve a keplerian orbit from a given true anomaly [rad]. See orbitsolve for the same function accepting a given time.

period(elem)

Period of an orbit [days].

distance(elem)

Distance to the system [pc].

meanmotion(elem)

Mean motion [rad/year].

periastron(elements, tref=58849)

Compute the MJD of periastron passage most recently after the reference epoch tref. N.B. mjd of 58849 = 2020-01-01

raoff(elem, t)

Get the offset [mas] from the primary body in Right Ascension at the time t [days].

raoff(o)

Get the offset [mas] from the primary body in Right Ascension from an instance of AbstractOrbitSolution.

decoff(elem, t)

Get the offset [mas] from the primary body in Declination at the time t [days].

decoff(elem, t)

Get the offset [mas] from the primary body in Declination from an instance of AbstractOrbitSolution.

posangle(elem, t)

Calculate the position angle [rad] of the secondary about its primary from our perspective at the time t [days].

posangle(o)

Calculate the position angle [rad] of the secondary about its primary from our perspective from an instance of AbstractOrbitSolution.

projectedseparation(elem, t)

Calculate the projected separation [mas] of the secondary from its primary at the time t [days].

projectedseparation(o)

Calculate the projected separation [mas] of the secondary from its primary from an instance of AbstractOrbitSolution.

propmotionanom(elem, t)

Get the instantaneous proper motion anomaly [mas/year] of the secondary at the time t [days].

propmotionanom(o)

Get the instantaneous proper motion anomaly [mas/year] of the secondary from an instance of AbstractOrbitSolution.

propmotionanom(elem, t, M_planet)

Get the instantaneous proper motion anomaly [mas/year] of the primary in at the time t [days]. The units of M_planet and elem.M must match.

radvel(elem, t)

Get the radial velocity [m/s] of the secondary along the line of sight at the time t [days].

radvel(o)

Get the radial velocity [m/s] of the secondary along the line of sight from an instance of AbstractOrbitSolution.

acceleration(elem, t)

Get the instantaneous acceleration [mas/year^2] of the secondary at the time t [days].

acceleration(o)

Get the instantaneous acceleration [mas/year^2] of the secondary from an instance of AbstractOrbitSolution.

acceleration(elem, t, M_planet)

Get the instantaneous acceleration [mas/year^2] of the primary in at the time t [days]. The units of M_planet and elem.M must match.

acceleration(o)

Get the instantaneous acceleration [mas/year^2] of the primary from an instance of AbstractOrbitSolution. The units of M_planet and elem.M must match.