10 Orbital Maneuvers Sir Isaac Newton (1643-1727). English Physicist, Astronomer and Mathematician who described and the three , laying the groundwork for , which dominated the scientific view of the physical for the next three centuries and is the basis for modern engineering. Philosophy is such an impertinently litigious lady that a man had as good be engaged in lawsuits as to have to do with her. Isaac Newton in a letter to his friend Edmund Halley, June 20, 1687 Introduction Orbital Energy Spacecraft is not inserted in an orbit to stay forever! A spacecraft may need to change its orbit once or more during its life time due to many reasons. A launch vehicle may insert a geostationary (GEO) satellite into an initial low Earth orbit (LEO) which is much lower than the final operational orbit. Then, the satellite should transfer from the initial orbit to its final orbit. Another need may arise if a surveillance satellite has to change its orbit in order to track a new target. Interplanetary missions usually require many orbit transfers until the spacecraft is inserted into the operational orbit or to use the same spacecraft to accomplish more than one mission. At the satellite end of life (EOF), the satellite may be kicked out of its orbit whether to reenter the Earth’s atmosphere or to rest in a graveyard orbit.
Figure 109.General coplanar transfer between circular orbits. Orbit Change A velocity change which lies in the plane of the orbit can change its size or shape, or rotate the line of apsides. To change the orientation of the orbit plane in space, DV should have a component which is perpendicular to the orbital plane. Figure 1010.Out-of-plane orbit change. Simple Plane Change Orbital maneuvers are characterized by a change in orbital velocity. If a velocity increment ΔV, which is a vector, is added to a satellite velocity, V1, also a vector, then a new satellite velocity V2, results. A finite ΔV which does not change the speed and flight-path angle of the satellite, will only change the plane of the orbit. Thus, the maneuver is called simple plane change. A plane change maneuver rotates the orbit plane in inertial space while holding the size and shape, a and e fixed. During a circular orbit plane change, through an angle θ, the ΔV is applied so as to rotate the velocity, V through the angle θ. The resulting velocity triangle is isosceles, as observed in Fig. from the right triangle,
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.