Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Orbit ComputationInter Satellite Linksarrnen+m+1anen+m+31⋅mr1⋅mrn⎛ ae ⎞⎜ ⎟r=⎝ ⎠r⎛ ae ⎞⎜ ⎟⎝ r=⎠3rnEq. 4.2-45which is desirable even for lower degrees of spherical harmonics. The ratio of earth'sequatorial radius and satellite orbit radius is always between 0 and 1, enhancing numericalstability. However, using the dimensionless values η and ξ doesn't increase computationalload.4.2.2 Third Body AttractionThe attraction acting on an orbiting satellite due to the other celestial bodies in the solarsystem, mainly Sun and Moon, could basically be computed like the acceleration from theearth's gravity field. However, due to the usually large distances it is sufficient to neglect allhigher order terms, and regard the gravity field of celestial bodies as perfect spheres. Theresulting acceleration, with respect to an earth centred inertial fixed reference frame, can beobtained from the following equation.d r2dtr[ | r− r− r |2S,MrS,M= GMS,M−3 3S,MrSun,MoonS,M]Eq. 4.2-46withr Radius vector, S,M being indices for Sun and Moon. Without index meanssatellites radius vector.GM Gravity constant of perturbing body (Sun, Moon)This equation holds also for the major planets, although the influence even from Jupiter isseveral orders of magnitude lower than lunisolar perturbations. It is also referred to as thedirect tidal effect.4.2.3 Solar PressureThe acceleration acting on an orbiting body due Solar radiation pressure can be obtained fromthe following expression, which simply characterises the satellite by it's cross section andmass.adcR⋅ A= µ ⋅ Ps⋅ ⋅ am2s r − r⋅ | r − rs3s|Eq. 4.2-47Page 32R. Wolf