Astrodynamics by Giulio Avanzini

By Giulio Avanzini

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The first stage booster falls to the Earth several hundreds kilometers downrange and the launch azimuth is constrained to assure the passage over uninhabited and traffic–free regions. 9, the same rocket has a greater payload for launches from a base close to the equator (δ → 0), and for an easterly launch (ψ = π/2). The orbital inclination will be the minimum achievable and equal to the latitude of the launch site. Greater inclinations, up to the limit value π − δ, are achievable from the same site with payload reduction; retrograde orbits require a westerly launch.

Colasurdo, G. Avanzini - Astrodynamics – 3. Three-Dimensional Analysis of Motion The second equation of dynamics ma|I = f , when written in a rotating frame becomes m d2 r dt2 R = f + m2ω × v|R + mω × (ω × r) where, together with the resultant of the applied forces f , two apparent forces f co = −2mω × v|R and f cf = −mω × (ω × r) (named Coriolis and centrifugal force, respectively) must be added. 9 Topocentric Reference Frame The launch of a satellite or a radar observation is made from a point on the Earth surface.

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.

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