By Giulio Avanzini
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Orbit circularity is an appreciate characteristic, but is rarely mandatory, as it implies the costs of a precise injection or the need of corrective maneuvers. High-ellipticity orbits are often used for space probes, as the spacecraft operates at high altitudes for a large part of its lifetime and the launch energy is lower in respect to a circular orbit with the same apogee. A satellite on a circular direct equatorial orbit with a period equal to a sidereal day is motionless with respect to the ground.
A constellation of three satellites with displaced ascending nodes (∆Ω = 120 deg) allows for the continuous coverage of the target region. 4 deg is mandatory in order to avoid the rotation of the line–of–apsides induced by the J2 effect. 986 deg per day) that equals the mean angular motion of the Earth about the Sun. 76 deg. Sun-synchronous satellites are very attractive for Earth observation because of constant ground lighting conditions; a suitable orbital period would add a synchronism with the ground.
One preliminarily computes the components of the constant vectors h = r × v and e = v×h r − µ r and therefore the unit vectors e g3 × k ˆ = h ; ˆi = r ; n ˆ1 = ˆ= k ; p h r e ||g 3 × k|| These vectors, centered in the center of mass of the primary body, define respectively the directions normal to the orbit plane, and towards the spacecraft, the ascending node, and the pericenter, respectively. The orbital elements are thus given by 1. p = h2 /µ 2. e = ||ˆ e|| 3. ˆ·g ˆ 3 = k3 cos i = k 4. ˆ ·g ˆ 1 = n3 cos Ω = n (Ω > π, if n2 < 0) 5.
Astrodynamics by Giulio Avanzini