An astronaut is heading east in a circular equatorial orbit about the Earth at an altitude h=3r0. At 0˚ longitude, he applies a velocity increment which ΔV1, places him in a polar orbit whose perigee grazes the Earth’s surface 180 deg away in central angle on the equator. What is the magnitude of ΔV1? What is the angle between and the original circular orbit velocity? ΔV1 What is the retro velocity increment at perigee that will reduce his ΔV2 total velocity to zero (soft-land)? A satellite is in a polar orbit (orbit 1 on the sketch) about a spherical Earth with no atmosphere. Its perigee and apogee are in the equatorial plane. The perigee altitude is 400 n.mi.; the apogee altitude is 2000 n.mi. Transfer from orbit 2 to orbit 1 can occur in several ways. Determine the total for transfer via ΔV circular orbit 3 from apogee to apogee. Determine the total for transfer via ΔV circular orbit 4 from perigee to perigee. Determine the single at point X to ΔV accomplish the transfer. Would the at point Y be identical in magnitude? In ΔV direction? At an arbitrary point, 1, in an initial orbit i, a velocity increment is added ΔV in the radial direction. A final orbit f is thus achieved. Compare the angular moment h and the semilatus recta p in the two orbits. Determine the radius in the final orbit at the point that is 180 deg in central angle away from point 1. Boris, a Russian cosmonaut, is in a circular equatorial orbit of radius r=1.44r0 about the moon (see sketch). He decides to pay a surprise visit to his American friends camped at the North Pole by transferring with into ΔV1 a polar elliptical orbit whose pericenter is at the camp. When Bpris reaches the camp, he retrofires with to reduce his total velocity to 0. Determine ΔV2 and in meters per second. For the moon, Vc0 ==1679 m/s. ΔV1 ΔV2
An astronaut is heading east in a circular equatorial orbit about the Earth at an altitude h=3r0. At 0˚ longitude, he applies a velocity increment ΔV1, which places him in a polar orbit whose perigee grazes the Earth’s surface 180 deg away in central angle on the equator. What is the magnitude of ΔV1? What is the angle between ΔV1 and the original circular orbit velocity? What is the retro velocity increment ΔV2 at perigee that will reduce his total velocity to zero (soft-land)? A satellite is in a polar orbit (orbit 1 on the sketch) about a spherical Earth with no atmosphere. Its perigee and apogee are in the equatorial plane. The perigee altitude is 400 n.mi.; the apogee altitude is 2000 n.mi. Transfer from orbit 2 to orbit 1 can occur in several ways. Determine the total ΔV for transfer via circular orbit 3 from apogee to apogee. Determine the total ΔV for transfer via circular orbit 4 from perigee to perigee. Determine the single ΔV at point X to accomplish the transfer. Would the ΔV at point Y be identical in magnitude? In direction? At an arbitrary point, 1, in an initial orbit i, a velocity increment ΔV is added in the radial direction. A final orbit f is thus achieved. Compare the angular moment h and the semilatus recta p in the two orbits. Determine the radius in the final orbit at the point that is 180 deg in central angle away from point 1. Boris, a Russian cosmonaut, is in a circular equatorial orbit of radius r=1.44r0 about the moon (see sketch). He decides to pay a surprise visit to his American friends camped at the North Pole by transferring with ΔV1 into a polar elliptical orbit whose pericenter is at the camp. When Bpris reaches the camp, he retrofires with ΔV2 to reduce his total velocity to 0. Determine ΔV1 and ΔV2 in meters per second. For the moon, Vc0 ==1679 m/s.
Space_Mechanics_Chapter_10_OrbitalManeuvers.docx