# Available Acceleration Models

In this page, all the acceleration models available in TudatPy are explained. Regardless of the type of acceleration model, the procedure to link such acceleration model to the bodies exerting and undergoing the acceleration is explained in this page: Acceleration Model Setup. Therefore, this information will not be repeated in this page. Instead, for each model, a reference to the related API documentation entry and the requirements are provided.

Note

In TudatPy, acceleration models are defined through factory functions, which define the properties required of the accelerations, but do not perform any calculations themselves. These properties are stored through instances of the AccelerationSettings class or of its derived classes.

List of available acceleration models

In certain pieces of code, such as when requesting the saving of a single acceleration (see Dependent Variables for saving of dependent variables), you will need to supply an identifier for the type of acceleration you are requesting. See the list of supported identifier types in the API documentation: AvailableAcceleration.

## Gravitational

TudatPy contains a number of different models for gravitational accelerations. In general, the gravitational acceleration exerted by a body B, with associated potential $$U_{B}$$, on a body A can be expressed as follows:

$\mathbf{a}_{_{BA}}=\nabla U_{_{B}}\left(\mathbf{r}_{_{BA}}\right)$

with $$\mathbf{r}_{_{BA}}(=\mathbf{r}_{_{B}}-\mathbf{r}_{_{A}})$$ denoting the relative position vector of body A with respect to Body B.

There are different gravitational models available in TudatPy:

These are explained in more detail below.

### Point Mass Gravity

Description
The point-mass gravity acceleration model can be created through the point_mass_gravity() factory function.
Dependencies
1. Gravity field for body exerting acceleration (see Gravity field models for non-default models).
2. Current state of body exerting acceleration, either from a pre-defined ephemeris model (see Ephemeris models) or from the numerical propagation of the translational dynamics of the body exerting the acceleration.

### Spherical Harmonic Gravity

Description
The spherical harmonic gravity acceleration model can be created through the spherical_harmonic_gravity() factory function.
Dependencies
1. Spherical harmonic gravity field for the body exerting acceleration. See Gravity field models for options on how to define one (if the default gravity field model of the exerting body is not spherical harmonic).
2. Rotation model from the inertial frame to the body-fixed frame, either from a pre-defined rotation model (Rotation models) or from the numerical propagation of the rotational dynamics of the body exerting the acceleration (Earth in the above example).
3. Current state of body exerting acceleration, either from a pre-defined ephemeris model (see Ephemeris models) or from the numerical propagation of the translational dynamics of the body exerting the acceleration (Earth in the above example).

Note

The spherical harmonic acceleration up to degree N and order M includes the point-mass gravity acceleration (which is the degree and order 0 term).

### Mutual Spherical Harmonic Gravity

Description
The mutual spherical harmonic gravity acceleration model can be created through the mutual_spherical_harmonic_gravity() factory function. This model is typically only used for detailed propagation of planetary systems. With additional parameters, it can be used even if the bodies mutually exerting the spherical harmonic gravity acceleration are not the central body.
Dependencies
1. Spherical harmonic gravity field for body exerting acceleration and body undergoing acceleration (see Gravity field models for non-default models).
2. Rotation model from the inertial frame to the body-fixed frame and body undergoing acceleration (see Rotation models for non-default models).
3. Current state of bodies undergoing and exerting acceleration, either from an Ephemeris model or from the numerical propagation (see Ephemeris models).

### Third Body Gravity vs. Central Gravity

Description
In addition to the three models listed above, which define different models for gravitational interactions between two bodies, you can of course define a third-body acceleration. In Tudat, however, you do not specify directly whether an acceleration is a ‘third-body’ acceleration. This is fully defined by what you’ve chosen as your center of propagation (see Translational Dynamics), and the bodies exerting and undergoing the acceleration. Similarly, when calculating the dynamics of a massive body, a correction is required for expressing the gravitational acceleration exerted by the propagation origin (e.g. acceleration exerted by Earth on Moon, with Earth as propagation origin). We term this the ‘central’ acceleration.
Dependencies
The same for each gravitational acceleration type.

For more details: Third-body accelerations.

## Aerodynamic

Description
The aerodynamic acceleration model can be created through the aerodynamic() factory function.
Dependencies
1. Atmosphere model for body exerting acceleration (see Atmosphere models).
2. Aerodynamic coefficient interface for body undergoing acceleration (see Aerodynamic coefficients).
3. Mass model for body undergoing acceleration.
4. Current state of body undergoing acceleration and body with atmosphere.
5. Shape model for the body exerting an acceleration (to allow for the calculation of vehicle altitude)
6. Roation model for the body undergoing an acceleration (or numerical propagation of this body’s rotational dynamics)

Note

The aerodynamic acceleration is calculated in the vehicles body-fixed or aerodynamic frame. Expressing the acceleration in an inertial frame (as required by the propagation) requires the vehicle’s orientation to be defined. For a simple definition, in which the body’s angle of attack, sideslip angle, and bank angle are all set to 0, see aerodynamic_angle_based().

There are two different radiation pressure models available in TudatPy:

The distinction between them lies in the type of radiation pressure interface that is used for the body undergoing acceleration (see below).

Description
The cannonball radiation pressure model can be created through the cannonball_radiation_pressure() factory function.
Dependencies
1. Cannonball radiation pressure model for body undergoing acceleration (from source equal to body exerting acceleration), see Radiation pressure.
2. Current state of body undergoing and body emitting radiation.

Description
The panelled radiation pressure model can be created through the panelled_radiation_pressure() factory function.
Dependencies
1. Panelled radiation pressure model for body undergoing acceleration (from source equal to body exerting acceleration), see Radiation pressure.
2. Current state of body undergoing and body emitting radiation.

## Relativistic Correction

Description
The relativistic correction acceleration model can be created through the relativistic_correction() factory function. This is a first-order (in 1/c^2) correction to the acceleration due to the influence of relativity for a massless body (e.g. spacecraft) orbiting a massive body (e.g. Earth), which in turn orbits a third body (e.g. Sun), consisting of three distinct effects: the Schwarzschild, Lense-Thirring and de Sitter accelerations.
Dependencies
1. Mass of the orbited body and the third body (de Sitter only)
2. Current state of body undergoing acceleration, the orbited body, and the third body (de Sitter only)
• Mass of the orbited body and the third body (de Sitter only)

• Current state of body undergoing acceleration, the orbited body, and the third body (de Sitter only)

## Empirical

Description
The empirical acceleration model can be created through the empirical() factory function. This is constant/once-per-orbit acceleration, expressed in the RSW frame (see for instance inertial_to_rsw_rotation_matrix()), for which the magnitude is determined empirically (typically during an orbit determination process).
Dependencies
1. Gravity field of the central body (for calculation of true anomaly).

## Thrust

Description
The thrust acceleration model can be created through one of the factory functions:

Which differ only in the manner in which the user selects the engine model(s) this is(are) to be used for calculating the thrust. The details of the model used for the thrust is given on a dedicated page

Dependencies
1. One or more engine models for the body under thrust
2. A rotation model for the body under thrust
3. Mass of the body under thrust (if the thrust magnitude model for the engine defines a force, and not an acceleration)

## Tidal effect on natural satellites

Description
The acceleration accounting for the tidal effect on natural satellites can be created through the direct_tidal_dissipation_acceleration() factory function. It is a rather specialist model, which is only relevant for the dynamics of natural satellites themselves. When calculating the dynamics of spacecraft orbiting natural satellites, use gravity field variations instead. Two types of accelerations can be computed: acceleration on the satellite due to tide on the planet, or acceleration on the satellite due to tide on the satellite.
Dependencies
1. Masses of planet and satellite.
2. Current state of planet and satellite.
3. Spherical harmonic gravity field for body on which the tide is raised (planet or satellite)
4. Planet rotation model (only for effect of tide on planet)

## Quasi-Impulsive Shot

Description
The acceleration accounting for the tidal effect on natural satellites can be created through the quasi_impulsive_shots_acceleration() factory function. This is a manner in which to incorporate short bursts of thrust into a numerical propagation. When using this model, ensure that your integration step is sufficiently small to be able to capture the burst of thrust.
Dependencies
None.