Solar Radiation Pressure

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Description

This module computes the forces and torques on a Spacecraft object based on solar radiation pressure. The computed forces/torques are then applied as external effectors to the spacecraft object. These values may be computed in one of the following modes:

• Fixed: Constant force (based on the solar flux at the spacecraft’s position) aligned with the anti-parallel sun-pointing vector. No torques are generated.
• Lookup Table: Forces and torques are evaluated using a simple nearest-neighbor lookup table that searches for the sun-pointing vector entry most closely aligned with the simulation.

This will use the Solar Model models for the calculations of the forces.

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Example Use Cases

• Solar Sail Analysis: Apply the lookup table method to study the impact of solar sail deployment on orbital dynamics.

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Module Implementation

Fixed

In this mode, the module computes the solar radiation pressure on a body in the body frame $\mathcal{B}$. Given the inertial distance between the spacecraft and the sun ${}^{\mathcal{N}}{\mathbf{s}}_{BS}={\mathbf{r}}_{SN}-{\mathbf{r}}_{BN}$, the force on the body in the inertial frame can be written as,

$${}^{\mathcal{N}}{\mathbf{F}}_{BN}=-C_{R}A{\rho }_{AU}ϵ\frac{r_{AU}^2}{s_{BS}^{3}c}{\hat{\mathbf{s}}}_{BS}$$

Where $C_R$ is the coefficient reflection, $A$ is the projected area of the body ${\rho }_{\mathrm{AU}}$ is the solar flux at 1 AU, $r_{AU}$ is an AU, $c$ is the speed of light in a vacuum and $ϵ$ is an eclipse factor between 0 and 1. Effectively, the first equation computes the solar radiation pressure of a spherical object at 1 AU and then computes a scale factor based on the position of the body and the degree to which it’s in eclipse. Nobody’s torques are computed.

Lookup Table

In this mode, the module accepts a look-up table in .csv format where entries are defined as follows:

${}^{\mathcal{N}}{\hat{\mathbf{r}}}_{BS}$	${}^{\mathcal{B}}{\mathbf{F}}_{BN}$	${}^{\mathcal{B}}{\tau }_{BN}$
Sun pointing unit vector in the inertia frame	Body force in the body frame	Torque in the body frame

The mode will then perform a nearest-neighbors lookup where the entry that minimizes the error between the actual sun pointing vector is selected i.e.

$$\mathrm{index}=\min {(}^{\mathcal{N}}{\mathbf{r}}_{BS}\cdot {}^{\mathcal{N}}{\mathbf{r}}_{\mathrm{lookup},BS}[\mathrm{index}])$$

The mode then follows the same method in the Fixed mode, without the frame transformation step as results are already pre-computed in the body frame.

NOTE

The assumption is that force and torque values in the lookup table have been computed using a solar flux at 1 AU.

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Assumptions/Limitations

• Fixed: Contributions for aerodynamic lift and sideslip are not computed. By convention, these are assumed to be negligible but this is not always true depending on spacecraft geometry and area-to-mass ratio.
• Lookup: The lookup method in this mode becomes computationally intensive for tables with a large number of entries. Consider optimization strategies if needed e.g. gradient search and linear interpolation. As with the Fixed method, lift and sideslip contributions are not accounted for.
• Lookup: The provided lookup table force and torque values are assumed to have been computed using a solar flux value at 1 AU.