9. ThreeBodyGravity#

class ThreeBodyGravity(state_vector: StateArray, pnt_masses: list, base_frame: Frame)#

Bases: DynamicModel

Models the gravitational acceleration from multiple third-body sources in a three-body problem. This class computes the total perturbing acceleration due to external gravitational bodies (e.g., Sun, Moon) and its partial derivatives.

Parameters:

state_vector (StateArray) –

The state vector of the main spacecraft, containing:

  • All dynamic and static parameters considered in the simulation (e.g., position, velocity, estimated parameters).

  • The reference frame in which the state is defined.

  • The origin body relative to which the state is expressed.

  • The epoch corresponding to the state.

pnt_masseslist

A list of third bodies (point masses) whose gravitational effects are considered.

base_frameFrame

Frame of the propagator.

See also

scarabaeus.StateArray

Represents state vectors with origins and reference frames.

scarabaeus.SpiceManager

Retrieves ephemeris data for celestial bodies.

Notes

  • Assumes third bodies follow Keplerian motion and do not undergo additional perturbations.

  • Uses SPICE data for third-body positions relative to the main body.

  • The acceleration formulation follows the standard third-body perturbation model.

References

  • Vallado, D. A. (2013). Fundamentals of Astrodynamics and Applications, 4th Ed.

Attributes

origin_mu

The gravitational parameter of the origin body.

origin_name

The name of the origin body in the system.

pnt_masses

List of third-body masses affecting the system.

ref_frame

The reference frame associated with the three-body system.

Methods

compute_acceleration(position, ...)

Computes the acceleration due to third-body gravitational influences.

compute_partial_by_position(position, ...)

Computes the partial derivatives of the third-body accelerations with respect to position.
compute_acceleration(position: ArrayWUnits, current_state: dict, epoch: float, body) → ArrayWUnits#

Computes the acceleration due to third-body gravitational influences.

Iterates through a set of gravitational point masses (third bodies) and sums their contributions to the total acceleration experienced by the spacecraft.

Parameters:

  • position (ArrayWUnits) – 3x1 position vector of the spacecraft in the reference frame. Expressed in units of kilometers.

  • current_state (dict) – Dictionary containing the current state information.

  • epoch (float) – Epoch at which the transformation is performed.

  • body (CelestialBody) – The celestial body for which third-body accelerations are computed.

Returns:

acc_vec – The 3x1 total acceleration vector due to third-body gravitational effects. Expressed in units of \(\frac{km}{s^2}\).

Return type:

ArrayWUnits

compute_partial_by_position(position: ArrayWUnits, current_state: dict, epoch, body) → array#

Computes the partial derivatives of the third-body accelerations with respect to position.

Determines how the acceleration due to third-body gravity changes with respect to variations in the spacecraft’s position.

Parameters:

  • position (ArrayWUnits) – 3x1 position vector of the spacecraft in the reference frame. Expressed in units of kilometers.

  • current_state (dict) – Dictionary containing the current state information.

  • epoch (float) – Epoch at which the transformation is performed.

  • body (CelestialBody) – The celestial body for which third-body accelerations are computed.

Returns:

jacobian – The 3x3 Jacobian matrix of third-body acceleration with respect to position. Expressed in units of \(\frac{1}{s^2}\).

Return type:

ArrayWUnits

property origin_mu: ArrayWUnits#

The gravitational parameter of the origin body.

property origin_name: str#

The name of the origin body in the system.

property pnt_masses: list[str]#

List of third-body masses affecting the system.

property ref_frame: str#

The reference frame associated with the three-body system.