Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Orbit ComputationInter Satellite Linkst= t −Time from ephemeris reference epoch Eq. 4.4-9kt oen = n0+ ∆nCorrected mean motion Eq. 4.4-10Mk= M + n ⋅ tMean anomaly Eq. 4.4-110kMk= Ek− e ⋅sinEKepler's equation for eccentrickanomaly, solved by iterationEq. 4.4-12νk⎛= arctan⎜⎜⎝21−e sin Ecos E − ekk⎞⎟⎟⎠True anomaly Eq. 4.4-13Ek⎛ e + cosνk= arccos⎜⎝1+e ⋅ cosνk⎞⎟⎠Eccentric anomaly Eq. 4.4-14Φk= νk+ ωArgument of latitude Eq. 4.4-15δ uΦ Argument of latitude correction Eq. 4.4-16k= Cus⋅ sin 2Φk+ Cuc⋅ cos 2k= Crs⋅ sin 2Φk+ Crc⋅ cos 2kkδ rΦ Radius correction Eq. 4.4-17δ iΦ Correction to inclination Eq. 4.4-18k= Cis⋅sin 2Φk+ Cic⋅ cos 2kurikkk= Φ + δuCorrected argument of latitude Eq. 4.4-19kk( 1−e ⋅ cos Ek) + δrk= A ⋅Corrected radius Eq. 4.4-20= i + δi+ IDOT ⋅ tCorrected inclination Eq. 4.4-210kkΩk= Ω0+( Ω − ΩDE) ⋅ tk− ΩDE⋅ toeD Corrected longitude of ascendingnodeEq. 4.4-22x′ky′k= rk= rk⋅ cos u⋅sin ukkPosition in orbital planeEq. 4.4-23xyzkkk= x′k= x′sin Ωk= sin icosΩkkk− y′k+ y′kcosicosikksin ΩcosΩkkPosition in Earth-Centered-Earth-Fixed coordinatesEq. 4.4-24This propagator accounts for secular as well periodic perturbations, as can be seen from theequation. Period of validity is 4 hours.Page 66R. Wolf