Mission Design for the CubeSat OUFTI-1

CHAPTER 5.MISSION ANALYSIS5.3.3 The solar radiation pressureSolar radiation pressure generates a force in all the direction and varies as afunction of sun, earth and satellite position. It makes vary periodically all theorbital elements and it’s especially intense for small satellites at high altitude:it needs to be considered for the OUFTI-1 orbit.The following formulas are an approximation of the solar pressure accelerationeffect averaging the eclipses and the sunlight.The perturbing acceleration of an earth satellite can be computed by means ofthe following equation:a sum = 0.97 · 10 −7 g (1 + R) S W(5.18)where R ∈ [−1, 1] is the optical reflection constant (-1 if transparent body, 0 ifblackbody, 1 if mirror), g the gravitation acceleration at sea level, S the effectivesatellite projected area and W the total weight.We used R=0.6 to take into account the solar cells and the thermal coating:this value is probably elevated but, not having precise details on the surfaces,we preferred to overestimate the perturbing force.Anyway, the solar perturbing force is much smaller than the atmospheric drag.The direction of a sun is perpendicular to the effective area and its normalizedcomponents along the satellite orbit radius vector, perpendicular to it in theorbit plane and along the orbit normal are:( ) i ( F r,sun = cos 2 cos 2 ɛ2 2( ) i ( − sin 2 sin 2 ɛ2 2)cos (λ ⊙ − ϑ − Ω))cos (λ ⊙ − ϑ + Ω)− 1 2 sin (i) sin (ɛ) [cos (λ ⊙ − ϑ) − cos (−λ ⊙ − ϑ)]( ) i ( − sin 2 cos 2 ɛ)cos (−λ ⊙ − ϑ + Ω)2 2( ) i ( − cos 2 sin 2 ɛ)mcos (−λ ⊙ − ϑ − Ω)2 2s( )2i ( F ϑ,sun = cos 2 cos 2 ɛ)sin (λ ⊙ − ϑ − Ω)2 2( ) i ( − sin 2 sin 2 ɛ)sin (λ ⊙ − ϑ + Ω)2 2− 1 2 sin (i) sin (ɛ) [sin (λ ⊙ − ϑ) − sin (−λ ⊙ − ϑ)]( ) i ( − sin 2 cos 2 ɛ)sin (−λ ⊙ − ϑ + Ω)2 2( ) i ( − cos 2 sin 2 ɛ)sin (−λ ⊙ − ϑ − Ω)2 2(5.19)ms 2Galli Stefania 43 University of Liège