# Verify solar radiation torques on a satellite

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?

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:

$$F_\mathrm{s}=\frac{\phi }{c}$$

Where:
$$c$$ = speed of light
$$\phi$$ = Solar constant at your distance from the sun

My Recommendation

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

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

Where:
$$c$$ = Speed of light
$$\phi$$ = Solar constant at your distance from the sun
$$A_\mathrm{s}$$ = Surface area exposed to the sun
$$q$$ = Reflectance factor (A value between 0-1)
$$\mathrm{cp_{s}}$$ = Spacecraft center of pressure
$$\mathrm{cm}$$ = Spacecraft center of mass
$$\varphi$$ = Angle of incidence
$$\mathrm{SRP}$$ = Solar Radiation Pressure Torque

Example: For the FireSat II from SMAD, at distance of $$1\,\mathrm{AU}$$ from the sun, with an area of $$1.3\,\mathrm{m^2}$$ facing the sun at an incidence angle of $$0\,^\circ$$ with a center of pressure - center of mass offset of $$0.1\,\mathrm{m}$$.

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

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

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

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

Anyways, I hope this helps with your attitude simulator and make sure to use units; without units 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! Commented Aug 6, 2018 at 17:43
• 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
Commented Aug 10, 2018 at 12:34
• @uhoh yep I posted onto meta here- looks like it’s just due to typefaces
– Jack
Commented Aug 11, 2018 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
Commented Aug 11, 2018 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. Commented Aug 12, 2018 at 19:11