Astrodynamics by Giulio Avanzini

By Giulio Avanzini

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The latter parameter is related to the power required for data transmission. , the time to cover a unit arc of the ground track). Note that the visibility zone is a circle on the sphere. On a cartographic representation of the Earth surface, the same zone is again a circle for an equatorial base, but is increasingly deformed for bases located at increasing latitudes. Appendix A - Spherical Trigonometry Consider a sphere of unit radius. The curve of intersection of the sphere and a plane passing through the center is a great circle.

An error in any direction on the flight path angle lowers the perigee. From the equation for the orbit parameter it is possible to express the eccentricity, h2 = p = a(1 − e2 ) ⇒ e = µ 1− h2 µa where the angular momentum vector in 1, after application of the ∆v, is given by h = r1 v2 cos ϕ. 6 km. 5 Perturbations Keplerian trajectories are conic sections that describe the relative motion of two spherically symmetric bodies under the action of their mutual gravitational attraction only. A real spacecraft is acted upon by several forces, together with the gravitational pull from the closest planet which, by the way, is never perfectly spherical.

Avanzini - Astrodynamics – 3. Three-Dimensional Analysis of Motion 35 The eigenvector relative to the first eigenvalue satisfies the relation Ta = 1 · a This means that there is a direction a which is not changed under the action of transformation matrix T . If T represents a coordinate change, the vector a will be represented by the same components in both the considered reference frames. For this reason, the transformation that takes the initial frame onto the final one can be considered as a single rotation α about the Euler ˆ.

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