Spec_SRPEnvironment.md

Specification for Solar Radiation Pressure Environment

1. Overview

1. Functions

• SolarRadiationPressureEnvironment calculates solar power flux at the spacecraft's position, including the earth's eclipse effect.

2. Related files

• src/environment/local/solar_radiation_pressure_environment.cpp, .hpp
  • SolarRadiationPressureEnvironment class is defined.
• src/environment/local/local_environment.cpp, .hpp
  • SolarRadiationPressureEnvironment class is used here as a member variable of LocalEnvironment class.

3. How to use

• Call UpdateAllStates function to calculates solar power flux and updates the eclipse flag.
• Users can get calculated values by using the following functions:
  • GetPressure_N_m2: Return solar pressure (N/m2) with eclipse effect for SRP disturbance calculation.
  • GetPowerDensity_W_m2: Return solar power density (W/m2) with eclipse effect for Electrical Power System calculation.
  • GetPressureWithoutEclipse_Nm2: Return solar pressure (N/m2) without eclipse effect.
  • GetSolarConstant_W_m2: Return solar constant value 1366 [W/m2]
  • GetShadowCoefficient: Return shadow function $\nu$.
    • When the spacecraft is in umbra, $\nu=0$.
    • When the spacecraft is in sunlight, $\nu=1$.
    • When the spacecraft is in penumbra, $0<\nu<1$.
  • GetIsEclipsed: Return eclipse or not

2. Explanation of Algorithm

1. Pressure calculation in UpdateAllStates function

1. overview

• Solar radiation pressure at the position of the spacecraft is calculated by using the inverse square law.

2. inputs and outputs

• Constants
  • Solar constant: $P_{\odot} = 1366$ W/m2
  • Speed of light: $c = 299792458$ m/s
  • Astronomical Unit: $AU = 149597870700$ m
• Input variables
  • The sun position in the body-fixed frame of the spacecraft: $\boldsymbol{r}_{\odot-sc}$ m
    • Unbold $r_{\odot-sc}$ is the norm of $\boldsymbol{r}_{\odot-sc}$
• Output
• Solar radiation pressure: $P_{sc}$ N/m2

3. algorithm

$$P_{sc}=\frac{P_{sun}}{c}\left(\frac{AU}{r_{\odot-sc}}\right)^{2}$$

4. note

• It is known that the solar constant value varies between 1365 and 1367 W/m2, but it is handled as a constant value in S2E.

2. CalcShadowCoefficient function

1. overview

• This function determines that the spacecraft is inside the eclipse of the earth or not.

2. inputs and outputs

• Constants
  • Radius of the earth: $r_{\oplus}=6378137$ m
  • Radius of the sun: $r_{\odot}=6.96\times10^{8}$ m
• Input variables
  • The sun position in the body-fixed frame of the spacecraft: $\boldsymbol{r}_{\odot-sc}$ m
  • The earth position in the body-fixed frame of the spacecraft: $\boldsymbol{r}_{\oplus-sc}$ m
• Output
  • none

3. algorithm

$$\begin{align} A_{\odot} &= \sin^{-1}\left(\frac{r_{\odot}}{r_{\odot-sc}}\right)\\\ A_{\oplus} &= \sin^{-1}\left(\frac{r_{\oplus}}{r_{\oplus-sc}}\right)\\\ \delta &= \cos^{-1}\left(\frac{r_{\odot-sc}}{r_{\oplus-sc}}\cdot \boldsymbol{r}_{\oplus-sc}\cdot(\boldsymbol{r}_{\odot-sc}-\boldsymbol{r}_{\oplus-sc})\right)\\\ \end{align}$$

4. note

• See the following description of the CalcShadowFunction for the calculation of the shadow function.

3. CalcShadowFunction function

1. overview

• This function calculates the degree of the Sun's occultation by the Earth.
• The base algorithm is referred to Satellite Orbits chapter 3.4.

2. inputs and outputs

• Input
  • The apparent radius of the Sun: $A_{\odot}$
  • The apparent radius of the Earth: $A_{\oplus}$
  • The apparent separation of the centers of the Sun and the Earth: $\delta$
  • The angle between the center of the Sun and the common chord: $x$
  • The length of the common chord of the apparent solar disk and apparent celestial disk: $y$
• Output
  • The shadow function: $\nu$

3. algorithm

• If the occultation is total, then $\nu=0$.
• If the occultation is partial but maximum, then $\nu=1-\left(\frac{A_{\oplus}}{A_{\odot}}\right)^2$
• If the occultation is partial, then $\nu = 1-\frac{S}{\pi A^2_{\odot}}$
  • S is given by the following calculation.

$$S=A_{\odot}^2\arccos\left(\frac{x}{A_{\odot}}\right)+A_{\oplus}^2\arccos\left(\frac{\delta-x}{A_{\oplus}}\right)-\delta\cdot y$$

• In other cases, since it means that no occultation takes place, then $\nu=1$.

3. Results of verifications

1. Verification of pressure calculation in UpdateAllStates function

1. overview

• The pressure calculation above is verified.

2. conditions for the verification

• A test code written in the SRPEnvironment.cpp is used.
• The sun position and the earth position are fixed, and the spacecraft position varies as following values.
  • Sun-spacecraft distance: 149604270700m - 153797870700m
  • Earth-spacecraft distance: 6400000m - 4200000000m

3. results

• The pressure calculation is verified.

2. Verification of calculation in CalcShadowFunction function

1. overview

• The calculation of the shadow function is verified.
• The result of the CalcShadowFunction of S2E is compared with the results of the solar intensity of STK.

2. conditions for the verification

• Orbit

  • The orbit of the ISS was used for verification.
  • The TLE data are as follows.

  1 25544U 98067A   20250.86981481  .00000008  00000-0  82464-5 0  9991
  2 25544  51.6470 304.2415 0002004  86.5035 251.6018 15.49214189244677
  

• Simulation time

  • The simulation time is as follows.

  //Simulation start date，[UTC]
  StartYMDHMS=2020/09/13 12:00:00.0
  //Simulation finish time，[sec]
  EndTimeSec=3600
  

3. Results

• The calculation of the shadow function is verified.

4. References

1. Montenbruck, O., Gill, E., & Lutze, F. (2002). Satellite orbits: models, methods, and applications. Appl. Mech. Rev., 55(2), B27-B28.