Mission Design for the CubeSat OUFTI-1

CHAPTER 5.MISSION ANALYSIS• if m = n the potential depends only on longitude. This effect, calledsectorial harmonics, is used to consider the difference in density betweenthe oceans and the continents. They are also called C mm = J mm• if m ≠ n and m ≠ 0 the potential depends both on latitude and longitude.This effect, called tesseral harmonics, is used to take into account greatmass concentration (Ex. the Himalaya).Figure 5.13: Earth oblateness and not uniform mass effect: zonal harmonics(left), sectorial harmonics (middle) and tesseral harmonics (right)The most important effect is the J 2 : all the others are usually neglected withthe exception of the J 22 effect that needs to be considered for geostationary orbit.In OUFTI-1 case, the only harmonic considered is J 2 : its principal effectsare the secular motions of the ascending node and of the perigee.The motion of the ascending node and therefore the variation of its right ascensionΩ occurs because of the added attraction of earth’s equatorial bulge, whichintroduces a force components toward the equator. The resultant accelerationcauses the satellite to reach the equator before the crossing point for a sphericalearth. The secular nodal variation of Ω can be numerically evaluated with theformula:˙Ω = −9.9639 ( ) 3Re 5degcos(i)(1 − e 2 ) 2 aday(5.15)The secular motion of perigee occurs because the force is no longer proportionalto the inverse square radius and the orbit is consequently no longer aclosed ellipse. It can be expressed as:˙ω = −9.9639 ( ) 3 (Re 5(1 − e 2 ) 2 2 − 5 )a 2 sin2 (i)5.3.2 The atmospheric dragdegday(5.16)For low earth orbit, the effect of the residual atmosphere is often the mainperturbation. Drag acts in the opposite direction of the velocity vector andGalli Stefania 41 University of Liège