Third-Body Perturbations¶

Third-body gravitational perturbation accelerations from the Sun, Moon, and planets.

Note

For conceptual explanations and examples, see Third-Body Perturbations in the Learn section.

Analytical Models¶

accel_third_body_sun `builtin` ¶

accel_third_body_sun(epc: Epoch, r_object: ndarray) -> ndarray

Calculate the acceleration due to the Sun on an object using low-precision analytical ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate the Sun's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to the Sun. Units: (m/s²)

Example

import brahe as bh
import numpy as np

epc = bh.Epoch.from_date(2024, 2, 25, bh.TimeSystem.UTC)

# Using position vector
r_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])
a = bh.accel_third_body_sun(epc, r_object)

# Or using state vector directly
x_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0, 0.0, 7500.0, 0.0])
a = bh.accel_third_body_sun(epc, x_object)

accel_third_body_sun_de `builtin` ¶

accel_third_body_sun_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to the Sun on an object using DE high-precision ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate the Sun's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Ephemeris source to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to the Sun. Units: (m/s²)

Example

import brahe as bh
import numpy as np

bh.initialize_ephemeris()
epc = bh.Epoch.from_date(2024, 2, 25, bh.TimeSystem.UTC)
r_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])
a = bh.accel_third_body_sun_de(epc, r_object, bh.EphemerisSource.DE440s)

Moon Perturbations¶

accel_third_body_moon `builtin` ¶

accel_third_body_moon(epc: Epoch, r_object: ndarray) -> ndarray

Calculate the acceleration due to the Moon on an object using low-precision analytical ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate the Moon's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to the Moon. Units: (m/s²)

Example

import brahe as bh
import numpy as np

epc = bh.Epoch.from_date(2024, 2, 25, bh.TimeSystem.UTC)
r_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])
a = bh.accel_third_body_moon(epc, r_object)

accel_third_body_moon_de `builtin` ¶

accel_third_body_moon_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to the Moon on an object using DE high-precision ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate the Moon's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Ephemeris source to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to the Moon. Units: (m/s²)

Example

import brahe as bh
import numpy as np

bh.initialize_ephemeris()
epc = bh.Epoch.from_date(2024, 2, 25, bh.TimeSystem.UTC)
r_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])
a = bh.accel_third_body_moon_de(epc, r_object, bh.EphemerisSource.DE440s)

accel_third_body_sun_de `builtin` ¶

accel_third_body_sun_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to the Sun on an object using DE high-precision ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate the Sun's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Ephemeris source to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to the Sun. Units: (m/s²)

Example

import brahe as bh
import numpy as np

bh.initialize_ephemeris()
epc = bh.Epoch.from_date(2024, 2, 25, bh.TimeSystem.UTC)
r_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])
a = bh.accel_third_body_sun_de(epc, r_object, bh.EphemerisSource.DE440s)

accel_third_body_mercury_de `builtin` ¶

accel_third_body_mercury_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Mercury on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Mercury's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Mercury. Units: (m/s²)

accel_third_body_venus_de `builtin` ¶

accel_third_body_venus_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Venus on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Venus's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Venus. Units: (m/s²)

accel_third_body_mars_de `builtin` ¶

accel_third_body_mars_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Mars on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Mars's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Mars. Units: (m/s²)

accel_third_body_jupiter_de `builtin` ¶

accel_third_body_jupiter_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Jupiter on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Jupiter's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Jupiter. Units: (m/s²)

accel_third_body_saturn_de `builtin` ¶

accel_third_body_saturn_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Saturn on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Saturn's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Saturn. Units: (m/s²)

accel_third_body_uranus_de `builtin` ¶

accel_third_body_uranus_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Uranus on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Uranus's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Uranus. Units: (m/s²)

accel_third_body_neptune_de `builtin` ¶

accel_third_body_neptune_de(epc: Epoch, r_object: ndarray, source: EphemerisSource) -> ndarray

Calculate the acceleration due to Neptune on an object using DE ephemerides.

Accepts either a 3D position vector or a 6D state vector for r_object.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch at which to calculate Neptune's position	required
`r_object`	`ndarray`	Position (length 3) or state (length 6) of the object in the GCRF frame. Units: (m)	required
`source`	`EphemerisSource`	Which ephemeris kernel to use (DE440s or DE440)	required

Returns:

Type	Description
`ndarray`	np.ndarray: Acceleration due to Neptune. Units: (m/s²)

Third-Body Perturbations¶

Analytical Models¶

accel_third_body_sun builtin ¶

accel_third_body_sun_de builtin ¶

Moon Perturbations¶

accel_third_body_moon builtin ¶

accel_third_body_moon_de builtin ¶

accel_third_body_sun_de builtin ¶

accel_third_body_mercury_de builtin ¶

accel_third_body_venus_de builtin ¶

accel_third_body_mars_de builtin ¶

accel_third_body_jupiter_de builtin ¶

accel_third_body_saturn_de builtin ¶

accel_third_body_uranus_de builtin ¶

accel_third_body_neptune_de builtin ¶

See Also¶

accel_third_body_sun `builtin` ¶

accel_third_body_sun_de `builtin` ¶

accel_third_body_moon `builtin` ¶

accel_third_body_moon_de `builtin` ¶

accel_third_body_sun_de `builtin` ¶

accel_third_body_mercury_de `builtin` ¶

accel_third_body_venus_de `builtin` ¶

accel_third_body_mars_de `builtin` ¶

accel_third_body_jupiter_de `builtin` ¶

accel_third_body_saturn_de `builtin` ¶

accel_third_body_uranus_de `builtin` ¶

accel_third_body_neptune_de `builtin` ¶