The following figure shows two satellites in Earth orbits: Satellite A is in a circular orbit with an altitude of 9,622 km, while Satellite B is in an elliptical orbit with an apogee altitude of 9,622 km. At the instant shown in Figure P2, Satellite B is passing through the apogee while Satellite A is ahead of Satellite B with an angular separation of 120 deg. Determine the perigee altitude of the elliptical orbit so that Satellites A and B occupy the same radial position when Satellite A firstly arrives the apogee point (in other words, Satellites A and B perform a rendezvous maneuver at apogee of satellite B).
The following figure shows two satellites in Earth orbits: Satellite A is in a circular orbit with an altitude of 9,622 km, while Satellite B is in an elliptical orbit with an apogee altitude of 9,622 km. At the instant shown in Figure P2, Satellite B is passing through the apogee while Satellite A is ahead of Satellite B with an angular separation of 120 deg. Determine the perigee altitude of the elliptical orbit so that Satellites A and B occupy the same radial position when Satellite A firstly arrives the apogee point (in other words, Satellites A and B perform a rendezvous maneuver at apogee of satellite B).
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Question
The following figure shows two satellites in Earth orbits: Satellite A is in a circular orbit with an altitude of 9,622 km, while Satellite B is in an elliptical orbit with an apogee altitude of 9,622 km. At the instant shown in Figure P2, Satellite B is passing through the apogee while Satellite A is ahead of Satellite B with an angular separation of 120 deg. Determine the perigee altitude of the elliptical orbit so that Satellites A and B occupy the same radial position when Satellite A firstly arrives the apogee point (in other words, Satellites A and B perform a rendezvous maneuver at apogee of satellite B).
Transcribed Image Text:Satellite A
120°
Satellite B
Expert Solution
Hint :
- The Perigee Heights formula is defined as the point in the orbit of an object (such as a satellite) orbiting the earth that is nearest to the center of the earth and is represented as hp = RP-Re or Perigee height = Radius of perigee-Radius of Earth.
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Perigee is the point in an orbit at which the orbiting body is closest to the object it orbits. Thus, the Radius of Perigee represents the minimum distance between an orbiting body and the object it orbits. The radius of Perigee may be contrasted to which is the maximum distance between orbiting and orbiting bodies.
This equation produces the Radius of Perigee rp, based on the length of the semi-major axis (a) and eccentricity (e) of orbit. Distances are measured from the centers of bodies.
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