Spherical solar radiation model (GMAT)

Question

I'm using GMAT to analyze the orbits. There is a Spherical model for Solar Radiation Pressure. Which equation does GMAT use to calculate it?

I've already searched in the documentation, however, there is no information/equations.

I wrote a program to calculate the solar pressure, accordingly to Vallado and taking the same values for the variables as in GMAT (area, reflectivity, mass). Due to the slightly different result, I suppose, GMAT uses a different algorithm.

$$ \huge\overset{\rightharpoonup}{F}_{srp}=-p_{srp}c_R A_\bigodot \frac{\overset{\rightharpoonup}{r}_{\bigoplus\bigodot}}{\left|\overset{\rightharpoonup}{r}_{\bigoplus\bigodot}\right|} $$

The code to calculate the acceleration (Julia language):

function solar_pressure(y,date)
  st_bar_sun = state(spk, 0, 10, date) 
  st_bar_moon_earth = state(spk, 0, 3, date) 
  st_bar_me_earth = state(spk, 3, 399, date)
  sun_cord  = (st_bar_sun - (st_bar_moon_earth + st_bar_me_earth))*1000
  r_sat_sun = [sun_cord[1] - y[1], sun_cord[2] - y[2], sun_cord[3] - y[3]]
  r_sat_sun_scalar = sqrt(r_sat_sun[1]^2 + r_sat_sun[2]^2 + r_sat_sun[3]^2)

  return -(r_sat_sun/r_sat_sun_scalar)*p_srp*C_r*A_sr/sat_mass
end

Answer 1

You can find a ton of information by looking in the "General Mission Analysis Tool (GMAT) Mathematical Specifications" (located at <GMAT installation directory>\<version>\docs\GMATMathSpec.pdf, or find the latest version here)

You can look at section "4.2.4 Solar Radiation Pressure", here is the R2018a version:

4.2.4 Solar Radiation Pressure

$$\mathbf{a}_s = -P_{SR}\displaystyle\frac{C_R > A}{m_s}\hat{\mathbf{s}}$$

where $\hat{\mathbf{s}}$ is a unitized vector pointing from the spacecraft to the sun

$$\mathbf{s} = \mathbf{r}_s - \mathbf{r}$$

where $\mathbf{r}_s$ is the Sun's position vector and $\mathbf{r}$ is the spacecrafts position vector.

$$\mathbf{A}_{s} = \mathbf{D}_{s} = \mathbf{0}_{3\times3}$$

$$\mathbf{B}_{s} = \mathbf{I}_{3\times3}$$

$$\mathbf{C}_{s} = P_{SR}\displaystyle\frac{ C_R A > }{m_s}\left( \frac{1}{s^3}\mathbf{I}_3 - 3 \frac{ \mathbf{s}\mathbf{s}^T}{s^5}\right)$$

where

$$s = \| \mathbf{s} \|$$

Additionally in "Table 4.1: Force Models Available in GMAT" they note the following equation for Solar Radiation Pressure:

$$ \frac{ P_{SR}C_R A_{\odot} }{m_s}\hat{\mathbf{r}}_{s\odot} $$

In order to find $P_{SR}$ we need to look at src/base/forcemodel/SolarRadiationPressure.cpp

157:   flux                (1367.0),                  // W/m^2, IERS 1996
158:   fluxPressure        (flux / GmatPhysicalConstants::c),   // converted to N/m^2

and TAT-C/cpp/GMATsrc/util/GmatConstants.hpp

114:   const Real c                                = 299792458.0;  // m/s

We can then calculate $P_{SR}$ as:

$$ \frac{1367.0 \frac{W}{m^2}}{299792458.0 \frac{m}{s}} = 4.5598 \cdot 10^{-6} \frac{N}{m^2}$$