Giulio Avanzini's Astrodynamics PDF

By Giulio Avanzini

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Suppose that the satellite overflies point S of declination δ at time t. Consider the meridians passing through S and the ascending node N. Complete a spherical triangle NMP with an equatorial arc of angular length ∆α between the meridians, the third vertex being the pole P. The ground track will split this triangle into two smaller ones (NMS and NSP). By applying the law of sines to both triangles, one obtains sin i sin δ sin θ sin ∆α = = sin(π/2) sin θ sin(π/2) sin(π/2 − δ) = sin(π/2 − i) sin(π − ψ) ⇒ ⇒ sin δ = sin i sin θ sin ∆α = cos i sin θ cos δ The equations on the right side provide the satellite track in a non–rotating frame.

Satellite reconfiguration and orbital maneuvers usually occur in sight of a command station. The analysis of the ground track is therefore essential. According to the equation cos i = cos δ sin ψ G. Colasurdo, G. Avanzini - Astrodynamics – 4. Earth Satellites 47 the ground track crosses the equator at an angle equal to the orbital inclination. The maximum latitude North or South of the equator that a satellite pass over just equals the orbit plane inclination i (π − i, for retrograde orbits). A global surveillance satellite should be in polar orbit to overfly the Earth’s entire surface.

In fact, all Russian manned missions are launched from Baikonur, as well as all geostationary, lunar, planetary, and ocean surveillance missions. All Space Station flights using Russian launch vehicles are launched from Baikonur, since all nonmilitary launches take place there. Baikonur is also the only Russian site that has been used to inject satellites into retrograde orbits. 4◦ E, has launched the most satellites since the beginning of the Space Age. Plesetsk’s location makes it ideal for launching into polar or high-inclination orbits (63 to 83◦ inclination), typical for military reconnaissance and weather satellites.

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Astrodynamics by Giulio Avanzini

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