Model and calculation of orbital satellite apparent magnitude

Apparent magnitude represents the observed level of aster to human eyes. The calculation of the satellite apparent magnitude is useful for the design of the optical system to observe and track the satellite.Based on the principle of astronomy,dynamics of orbits, radiometry,photometry and computational mathematics, a physical mathematical model for computing satellite magnitude was built. Firstly, the amount of visible light energy reflected by orbit satellite was calculated. Secondly, the calculation method was given after deducing the association character of human eyes. Then a kind of brevity method to calculate the apparent magnitude for grey-reflection satellite was given. Finally, the calculated curve for apparent magnitude observed from subastral point was obtained. The result shows that the apparent magnitude observed from subastral point varies obviously with the change of the satellite position in orbit.The magnitude difference for one satellite under different subastral points is up to 5 magnitudes only within sunshine region.