Keplerian Orbital Elements

kepler

Represent Keplerian element sets and convert between cartesian

Notes: * This class is used to represent Keplerian elements and convert between Cartesian coordinates * The class uses the semi-major axis (a), not the semiparameter * All angle units are radians * All length units are meters * All velocity units are meters / second

mean_motion property

Mean motion, radians / second

true_anomaly property

True anomaly, radians

eccentric_anomaly property writable

Eccentric anomaly, radians

mean_anomaly property writable

Mean anomaly, radians

period property

Orbital period, seconds

a property writable

Semi-major axis, meters

eccen property writable

Eccentricity, unitless

inclination property writable

Inclination, radians

raan property writable

Right ascension of ascending node, radians

nu property writable

True anomaly, radians

w property writable

Argument of perigee, radians

__init__(a, e, i, raan, argp, nu=..., *, true_anomaly=..., mean_anomaly=..., eccentric_anomaly=...)

Create Keplerian element set object from input elements

Parameters:

Name	Type	Description	Default
a	float	Semi-major axis, meters	required
e	float	Eccentricity, unitless	required
i	float	Inclination, radians	required
raan	float	Right ascension of ascending node, radians	required
argp	float	Argument of perigee, radians	required
nu	float	True anomaly, radians	...
true_anomaly	float	True anomaly, radians (keyword alternative to nu)	...
mean_anomaly	float	Mean anomaly, radians (keyword alternative to nu)	...
eccentric_anomaly	float	Eccentric anomaly, radians (keyword alternative to nu)	...

Notes

If "nu" is provided (6th argument), it will be used as the true anomaly. Anomaly may also be set via keyword arguments; if so, there should only be 5 positional input arguments.

Example

import math

# Create a ~400 km circular LEO orbit
k = satkit.kepler(
    a=6.781e6,        # semi-major axis, meters
    e=0.001,          # near-circular
    i=math.radians(51.6),
    raan=math.radians(0),
    argp=math.radians(0),
    nu=math.radians(0),
)

to_pv()

Convert Keplerian element set to position and velocity vectors

Returns:

Type	Description
tuple[NDArray[float64], NDArray[float64]]	tuple[npt.ArrayLike[np.float64], npt.ArrayLike[np.float64]]: Tuple with two elements representing the position and velocity vectors

Example

pos, vel = k.to_pv()
print(f"Position: {pos} m")
print(f"Velocity: {vel} m/s")

propagate(dt)

Propagate Keplerian element set by input duration

Parameters:

Name	Type	Description	Default
dt	duration | float	Duration by which to propagate the Keplerian element set If float, value is seconds	required

Returns:

Type	Description
kepler	satkit.kepler: Keplerian element set object after propagation

Example

# Propagate orbit by one orbital period
k2 = k.propagate(k.period)

from_pv(pos, vel) staticmethod

Create Keplerian element set from input position and velocity vectors

Parameters:

Name	Type	Description	Default
pos	NDArray[float64]	3-element array representing position vector	required
vel	NDArray[float64]	3-element array representing velocity vector	required

Returns:

Type	Description
kepler	Keplerian element set object

Example

import numpy as np
pos = np.array([6.781e6, 0, 0])  # meters, GCRF
vel = np.array([0, 7.5e3, 0])    # m/s, GCRF
k = satkit.kepler.from_pv(pos, vel)
print(f"Semi-major axis: {k.a/1e3:.1f} km")
print(f"Eccentricity: {k.e:.6f}")