Chapter 13, Problem 120P

2B Show that in a field of attractive forces F(r) a body of mass m can always perform circular motion of radius r0 with constant angular velocity w. Also show that the velocity u of the circular orbit is given by the relation u² == ToF (1) m

determine (a) the speed of the vehich as it approaches B on the elliptic path, (b) the amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.

A rocket injects a satellite with a certain horizontal velocity from height of 880 km from the surface of the earth. The velocity of the satellite at appoint distance 10 000 km from the center of the earth is observed to be 10 km/s. if the apogee distance of the satellite orbit is 18000 km. Determine the direction of the satellite make with the horizontal. (assume that the radius of the earth is 6380 km and u = 39.8 x 10 m /s)

A spacecraft approaching the planet Saturn reaches point A with a velocity vA of magnitude 68.8 × 103 ft/s. It is to be placed in an elliptic orbit about Saturn so that it will be able to periodically examine Tethys, one of Saturn’s moons. Tethys is in a circular orbit of radius 183 × 103 mi about the center of Saturn, traveling at a speed of 37.2 × 103 ft/s. Determine (a) the decrease in speed required by the spacecraft at A to achieve the desired orbit, (b) the speed of the spacecraft when it reaches the orbit of Tethys at B.

A spacecraft traveling along a parabolic path toward the planet Jupiter is expected to reach point vA of magnitude 26.9 km/s. Its engines will then be fired to slow it down, placing it into an elliptic orbit which will bring it to within 100 × 103 km of Jupiter. Determine the decrease in speed ? v at point A which will place the spacecraft into the required orbit. The mass of Jupiter is 319 times the mass of the earth.

The Clementine spacecraft described an elliptic orbit of minimum altitude hA = 400 km and maximum altitude hB = 2940 km above the surface of the moon. Knowing that the radius of the moon is 1737 km and that the mass of the moon is 0.01230 times the mass of the earth, determine the periodic time of the spacecraft.

Just after launch from the earth, the space-shuttle orbiter is in the 36 x 162-mi orbit shown. At the apogee point A, its speed is 17211 mi/hr. If nothing were done to modify the orbit, what would its speed be at the perigee P? Neglect aerodynamic drag. (Note that the normal practice is to add speed at A, which raises the perigee altitude to a value that is well above the bulk of the atmosphere.) The radius of the earth is 3959 mi. 17211 mi/hr 36 mi 162 mi-

During lecture we discussed that an elliptical orbit is not necessarily helpful to escapeEarth, and we said we would not investigate that further (but you are welcome on yourown).However, it is useful to investigate the radius of the “best” (ie, lowest Δv) circular parkingorbit. For this problem consider the following “steps” to Escape Earth:1. A Hohmann transfer from the surface to the parking orbit (i.e., 2 Δv’s).Assumptions:a. launch exactly from the equator with zero velocity relative to thegroundb. there is no atmosphere, mountains, obstacles, etc - the Δv canhappen in the tangential direction from the groundc. Simplify for now and use the Earth rotation = 1 revolution in 24hours2. A Δv from the parking orbit to escape Earth3. The target velocity is exactly vesc (i.e., there is no v∞ for a specificdestination, we just want to escape Earth)For all Δv’s you can ignore the direction, only consider magnitude.a. Develop an equation (or function in Matlab or a spreadsheet) which takes…

A space probe is to be placed in a circular orbit of 5600-mi radius about the planet Venus in a specified plane. As the probe reaches A, the point of its original trajectory closest to Venus, it is inserted in a first elliptic transfer orbit by reducing its speed by ΔvA. This orbit brings it to point B with a much reduced velocity. There the probe is inserted in a second transfer orbit located in the specified plane by changing the direction of its velocity and further reducing its speed by ΔvB. Finally, as the probe reaches point C, it is inserted in the desired circular orbit by reducing its speed by ΔvC. Knowing that the mass of Venus is 0.82 times the mass of the earth, that rA = 9.3 × 103 mi and rB = 190 × 103 mi, and that the probe approaches A on a parabolic trajectory, determine by how much the velocity of the probe should be reduced (a) at A, (b) at B, (c) at C.