By Giulio Avanzini
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A second tangential burn ∆v = v2 − v1 in 1 parallel to the velocity vector (thus avoiding misalignment losses) will raise the perigee of the orbit up to r2 . The total energy increase is obtained by means of two increments of kinetic energy: ∆E = v02 v22 v12 v 2 ∆v 2 + − = 0 + + v1 ∆v 2 2 2 2 2 The comparison between the square of the total velocity increment (∆vtot = v0 + ∆v) and the equivalent velocity increment on the ground (v0eq ) provides 2 v02 ∆vtot (v0 + ∆v)2 − eq = − ∆E = (v0 − v1 )∆v 2 2 2 40 G.
At an altitude of 42,200 km this geostationary (GEO) satellite sees almost a half of the Earth’s surface. Three satellites, 120 deg apart, cover the whole Earth, except for small regions around the poles, while being able to communicate between 48 G. Colasurdo, G. Avanzini - Astrodynamics – 4. 4: Stable and unstable longitudes for GEO satellites. them. Such a satellite is extremely useful for communications, altough high power antennas are necessary. The reconnaissance role is difficult, if not impossible, as photographic resolution is poor from an altitude of 35800 km.
The integration step can be chosen larger than in Cowell’s method, at least until perturbations accumulate and ∆r becomes large. 3, p. 3, p. 390-96). The method of variation of orbital parameters rewrites the vector equation of perturbed motion as a system of differential equation for the orbital parameters of the osculating orbit. Only the rate of change of the osculating parameters, which derives from the perturbing forces, is integrated. 4, p. 4, p. 396-410). 2 General perturbations General perturbations cover the analytical methods in which a perturbing acceleration is selected, expanded into series, which are opportunely truncated and integrated termwise.