lamberthub.utils.kepler#

This module holds the so-called Kepler equations for each one of the particular orbit shapes, that is elliptical, parabolic and hyperbolic.

The required formulas are found to be within Vallado’s[1] manual.

References

[1] Vallado, D. A. (2001). Fundamentals of astrodynamics and applications

(Vol. 12). Springer Science & Business Media.

Module Contents#

Functions#

kepler_elliptic(E, ecc)

Computes the time of flight since perigee passage at particular eccentric

kepler_parabolic(B)

Computes the time of flight since perigee passage at particular eccentric

kepler_hyperbolic(H, ecc)

Computes the time of flight since perigee passage at particular eccentric

kepler_from_nu(nu, ecc)

Compute the mean anomaly depending on the particular orbit shape, that is
lamberthub.utils.kepler.kepler_elliptic(E, ecc)#

Computes the time of flight since perigee passage at particular eccentric anomaly for elliptical orbit.

Parameters:

  • E (float) – Eccentric anomaly.

  • ecc (float) – Eccentricity of the orbit. Must be between (0,1).

Returns:

M – Time since perigee passage.

Return type:

float

lamberthub.utils.kepler.kepler_parabolic(B)#

Computes the time of flight since perigee passage at particular eccentric anomaly for paraboliparabolic orbit.

Parameters:

B (float) – Parabolic anomaly.

Returns:

Mp – Parabolic mean motion

Return type:

float

lamberthub.utils.kepler.kepler_hyperbolic(H, ecc)#

Computes the time of flight since perigee passage at particular eccentric anomaly for hyperbolic orbit.

Parameters:

  • H (float) – Hyperbolic anomaly.

  • ecc – Eccentricity of the orbit.

Returns:

Mh – Hyperbolic mean motion

Return type:

float

lamberthub.utils.kepler.kepler_from_nu(nu, ecc)#

Compute the mean anomaly depending on the particular orbit shape, that is elliptical, parabolic or hyperbolic.

Parameters:

  • nu (float) – True anomaly.

  • ecc (float) – Orbit’s eccentricity.

Returns:

M – Mean anomaly.

Return type:

float