Keplerian Elements¶

Functions for working with Keplerian orbital elements and computing orbital properties.

Orbital Properties¶

semimajor_axis `builtin` ¶

semimajor_axis(n: float, angle_format: AngleFormat) -> float

Computes the semi-major axis of an astronomical object from Earth given the object's mean motion.

Parameters:

Name	Type	Description	Default
`n`	`float`	The mean motion of the astronomical object in radians or degrees.	required
`angle_format`	`AngleFormat`	Interpret mean motion as AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	The semi-major axis of the astronomical object in meters.

semimajor_axis_general `builtin` ¶

semimajor_axis_general(n: float, gm: float, angle_format: AngleFormat) -> float

Computes the semi-major axis of an astronomical object from a general body given the object's mean motion.

Parameters:

Name	Type	Description	Default
`n`	`float`	The mean motion of the astronomical object in radians or degrees.	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required
`angle_format`	`AngleFormat`	Interpret mean motion as AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	The semi-major axis of the astronomical object in meters.

semimajor_axis_from_orbital_period `builtin` ¶

semimajor_axis_from_orbital_period(period: float) -> float

Computes the semi-major axis from orbital period around Earth.

Parameters:

Name	Type	Description	Default
`period`	`float`	The orbital period in seconds.	required

Returns:

Name	Type	Description
`float`	`float`	The semi-major axis in meters.

semimajor_axis_from_orbital_period_general `builtin` ¶

semimajor_axis_from_orbital_period_general(period: float, gm: float) -> float

Computes the semi-major axis from orbital period for a general body.

Parameters:

Name	Type	Description	Default
`period`	`float`	The orbital period in seconds.	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required

Returns:

Name	Type	Description
`float`	`float`	The semi-major axis in meters.

mean_motion `builtin` ¶

mean_motion(a: float, angle_format: AngleFormat) -> float

Computes the mean motion of an astronomical object around Earth.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`angle_format`	`AngleFormat`	Return output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	The mean motion of the astronomical object in radians or degrees.

mean_motion_general `builtin` ¶

mean_motion_general(a: float, gm: float, angle_format: AngleFormat) -> float

Computes the mean motion of an astronomical object around a general body given a semi-major axis.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required
`angle_format`	`AngleFormat`	Return output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	The mean motion of the astronomical object in radians or degrees.

orbital_period `builtin` ¶

orbital_period(a: float) -> float

Computes the orbital period of an object around Earth.

Uses rastro.constants.GM_EARTH as the standard gravitational parameter for the calculation.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required

Returns:

Type	Description
`float`	The orbital period of the astronomical object in seconds.

orbital_period_general `builtin` ¶

orbital_period_general(a: float, gm: float) -> float

Computes the orbital period of an astronomical object around a general body.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required

Returns:

Name	Type	Description
`float`	`float`	The orbital period of the astronomical object in seconds.

periapsis_distance `builtin` ¶

periapsis_distance(a: float, e: float) -> float

Calculate the distance of an object at its periapsis.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required

Returns:

Name	Type	Description
`float`	`float`	The distance of the object at periapsis in meters.

apoapsis_distance `builtin` ¶

apoapsis_distance(a: float, e: float) -> float

Calculate the distance of an object at its apoapsis.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required

Returns:

Name	Type	Description
`float`	`float`	The distance of the object at apoapsis in meters.

periapsis_velocity `builtin` ¶

periapsis_velocity(a: float, e: float, gm: float) -> float

Computes the periapsis velocity of an astronomical object around a general body.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required

Returns:

Name	Type	Description
`float`	`float`	The magnitude of velocity of the object at periapsis in m/s.

apoapsis_velocity `builtin` ¶

apoapsis_velocity(a: float, e: float, gm: float) -> float

Computes the apoapsis velocity of an astronomical object around a general body.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`gm`	`float`	The standard gravitational parameter of primary body in m³/s².	required

Returns:

Name	Type	Description
`float`	`float`	The magnitude of velocity of the object at apoapsis in m/s.

perigee_velocity `builtin` ¶

perigee_velocity(a: float, e: float) -> float

Computes the perigee velocity of an astronomical object around Earth.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required

Returns:

Name	Type	Description
`float`	`float`	The magnitude of velocity of the object at perigee in m/s.

apogee_velocity `builtin` ¶

apogee_velocity(a: float, e: float) -> float

Computes the apogee velocity of an astronomical object around Earth.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required

Returns:

Name	Type	Description
`float`	`float`	The magnitude of velocity of the object at apogee in m/s.

sun_synchronous_inclination `builtin` ¶

sun_synchronous_inclination(a: float, e: float, angle_format: AngleFormat) -> float

Computes the inclination for a Sun-synchronous orbit around Earth based on the J2 gravitational perturbation.

Parameters:

Name	Type	Description	Default
`a`	`float`	The semi-major axis of the astronomical object in meters.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Return output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	Inclination for a Sun synchronous orbit in degrees or radians.

Anomaly Conversions¶

anomaly_eccentric_to_mean `builtin` ¶

anomaly_eccentric_to_mean(anm_ecc: float, e: float, angle_format: AngleFormat) -> float

Converts eccentric anomaly into mean anomaly.

Parameters:

Name	Type	Description	Default
`anm_ecc`	`float`	Eccentric anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	Mean anomaly in radians or degrees.

anomaly_eccentric_to_true `builtin` ¶

anomaly_eccentric_to_true(anm_ecc: float, e: float, angle_format: AngleFormat) -> float

Converts eccentric anomaly into true anomaly.

Parameters:

Name	Type	Description	Default
`anm_ecc`	`float`	Eccentric anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	True anomaly in radians or degrees.

anomaly_mean_to_eccentric `builtin` ¶

anomaly_mean_to_eccentric(anm_mean: float, e: float, angle_format: AngleFormat) -> float

Converts mean anomaly into eccentric anomaly.

Parameters:

Name	Type	Description	Default
`anm_mean`	`float`	Mean anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	Eccentric anomaly in radians or degrees.

anomaly_mean_to_true `builtin` ¶

anomaly_mean_to_true(anm_mean: float, e: float, angle_format: AngleFormat) -> float

Converts mean anomaly into true anomaly.

Parameters:

Name	Type	Description	Default
`anm_mean`	`float`	Mean anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	True anomaly in radians or degrees.

anomaly_true_to_eccentric `builtin` ¶

anomaly_true_to_eccentric(anm_true: float, e: float, angle_format: AngleFormat) -> float

Converts true anomaly into eccentric anomaly.

Parameters:

Name	Type	Description	Default
`anm_true`	`float`	True anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	Eccentric anomaly in radians or degrees.

anomaly_true_to_mean `builtin` ¶

anomaly_true_to_mean(anm_true: float, e: float, angle_format: AngleFormat) -> float

Converts true anomaly into mean anomaly.

Parameters:

Name	Type	Description	Default
`anm_true`	`float`	True anomaly in radians or degrees.	required
`e`	`float`	The eccentricity of the astronomical object's orbit (dimensionless).	required
`angle_format`	`AngleFormat`	Interprets input and returns output in AngleFormat.DEGREES or AngleFormat.RADIANS.	required

Returns:

Name	Type	Description
`float`	`float`	Mean anomaly in radians or degrees.

Keplerian Elements¶

Orbital Properties¶

semimajor_axis builtin ¶

semimajor_axis_general builtin ¶

semimajor_axis_from_orbital_period builtin ¶

semimajor_axis_from_orbital_period_general builtin ¶

mean_motion builtin ¶

mean_motion_general builtin ¶

orbital_period builtin ¶

orbital_period_general builtin ¶

periapsis_distance builtin ¶

apoapsis_distance builtin ¶

periapsis_velocity builtin ¶

apoapsis_velocity builtin ¶

perigee_velocity builtin ¶

apogee_velocity builtin ¶

sun_synchronous_inclination builtin ¶

Anomaly Conversions¶

anomaly_eccentric_to_mean builtin ¶

anomaly_eccentric_to_true builtin ¶

anomaly_mean_to_eccentric builtin ¶

anomaly_mean_to_true builtin ¶

anomaly_true_to_eccentric builtin ¶

anomaly_true_to_mean builtin ¶

semimajor_axis `builtin` ¶

semimajor_axis_general `builtin` ¶

semimajor_axis_from_orbital_period `builtin` ¶

semimajor_axis_from_orbital_period_general `builtin` ¶

mean_motion `builtin` ¶

mean_motion_general `builtin` ¶

orbital_period `builtin` ¶

orbital_period_general `builtin` ¶

periapsis_distance `builtin` ¶

apoapsis_distance `builtin` ¶

periapsis_velocity `builtin` ¶

apoapsis_velocity `builtin` ¶

perigee_velocity `builtin` ¶

apogee_velocity `builtin` ¶

sun_synchronous_inclination `builtin` ¶

anomaly_eccentric_to_mean `builtin` ¶

anomaly_eccentric_to_true `builtin` ¶

anomaly_mean_to_eccentric `builtin` ¶

anomaly_mean_to_true `builtin` ¶

anomaly_true_to_eccentric `builtin` ¶

anomaly_true_to_mean `builtin` ¶