I'm creating a design support system for Attitude control design of a spacecraft. For the attitude simulator, I have made a function to compute the solar radiation torque acting on the satellite which is defined as: $M_{sp} = F_s(C_{ps} - C_g)$ Where, $M_{sp}$ the solar radiation torque acting on the satellite, $F_s$ is the solar radiation pressure, $C_{ps}$ centre of pressure of the surface facing the Sun and $C_g$ centre of mass of the satellite.

What I would like to do is verify this function, with some numerical results. I have tried looking for it, books such as Spacecraft attitude dynamics and Control (Bong Wie), Spacecraft Attitude dynamics: A practical approach (Marc J Sidl), Analytics of Space Mechanics (Hanspeter Schaub) and a few papers discussing about the solar radiation disturbances, unfortunately, haven't found any numerical values for verification.

Does somebody know any resources/references to find numerical values?

Thanks in advance!

up vote 4 down vote accepted
+100

The equation you listed above is greatly simplified and fails to account for additional elements such as the spacecraft surface area exposed to the sun. Assuming you calculate solar radiation pressure as the following:

$$ F_{s}=\frac{\phi }{c}$$ Where:

c = speed of light

ϕ = Solar constant at your distance from the sun

My Recommendation

I would recommend changing your equation to account for spacecraft surface area, add a rectangle factor, and possible add an angle of incidence parameter (sun vector relative to the spacecraft)

New Solar Radiation Pressure Equation: $$ SRP = \frac{\phi}{c}A_{s}(1+q)(cp_{s}-cm)cos(\varphi ) $$

Where

c = Speed of light

ϕ = Solar constant at your distance from the sun

As = Surface area exposed to the sun

q = Reflectance factor (A value between 0-1)

cps = Spacecraft center of pressure

cm = Spacecraft center of mass

φ = Angle of incidence

SRP = Solar Radiation Pressure Torque

Example: For the FireSat II from SMAD, at distance of 1 AU from the sun and has an area of 1.3 m^2 facing the sun at an incidence angle of 0 degrees with a center of pressure - center of mass offset of 0.1 meters.

$$ SRP = =\frac{1367 W/m^2}{299792458 m/s}(1.3 m^2)(1+0.6)(0.1 m)cos(0) $$

$$ SRP = 9.6\times 10^{-7} Nm $$


Other factors to consider: Depending on the spacecraft and its configuration make sure to considered the following:

  • Solar Radiation Pressure
  • Atmospheric drag (depends on spacecraft location)
  • Magnetic Field (if around a planet that contains a magnetic field)
  • Gravity gradient
  • Primary Thruster/ACS Thruster miss-alignment

Anyways, I hope this helps with your attitude simulator and make sure to use units, without unit's these values are meaningless.

  • Thanks for the answer, greatly appreciated! I indeed use the same equation, as you mentioned above to calculate the solar radiation pressure $F_s$ to take it into account the spacecraft surface area, the unit vector facing the sun and reluctance factor. I have a separate model for calculation of $F_s$ hence, did not mention it here! – srikarad Aug 6 at 17:43
  • 1
    It's great when someone takes the time to write a clear, well sourced (and in this case well-formatted as well) answer to a question! – uhoh Aug 10 at 12:34
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    @uhoh yep I posted onto meta here- looks like it’s just due to typefaces – Jack Aug 11 at 9:31
  • @Jack I think it's really great that you took the time to sort this complex thing out and then write a clear, documenting post about it. I had a run-in with an apostrophe myself once. – uhoh Aug 11 at 16:36
  • I will also recommend you to read "Analytical technique for satellite projected cross-sectional area calculation". This paper can help you find the sun vector projected cross-sectional area in any satellite orientation. – Eviatar.E Aug 12 at 19:11

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