Chapter 8, Problem 8.23P

If a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.

What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?

Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?

Show that for eccentricity equal to one in Equation 13.10 for conic sections, the path is a parabola. Do this by substituting Cartersian coordinates, x and y, for the polar coordinates, r and , and showing that it has the general form for a parabola, x=ay2+by+c .

If you wanted to place a satellite in a geosynchronous orbit, at what height above the Earth's surface should you place it? (Earth's mass = 5.98x10^24, Earth's radius = 6x10^6, G = 6.67x10^-11) For the previous situation using the given answer, what is the difference in potential energy between the Earth's surface and the satellite height for a satellite with 1 kg mass?

A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is ℎp=223.0 km,hp=223.0 km, and it is moving with a speed of ?p=8.150 km/s.vp=8.150 km/s. The gravitational constant ?G equals 6.67×10−11 m3·kg−1·s−26.67×10−11 m3·kg−1·s−2 and the mass of Earth equals 5.972×1024 kg.5.972×1024 kg. When the satellite reaches its apogee, at its farthest point from the Earth, what is its height ℎaha above the ground? For this problem, choose gravitational potential energy of the satellite to be 00 at an infinite distance from Earth.

What minimum energy is required to take a stationary 3.5 ×103 kg satellite from the surface of the Earth and put it into a circular orbit with a radius of 6.88 ×106 m and an orbital speed of 7.61×103 m s? (Ignore Earth’s rotation.)

A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.4 × 107 m. The mass of the planet is M = 4.4 × 1024 kg. Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite.  F =    Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R.  ac =    Express the speed v in terms of G, M and R.  v = Calculate the numerical value of v, in m/s.  v =

A satellite m = 500 kg orbits the earth at a distance d = 225km , above the surface of the planet. The radius of the earth is r_{i} = 6.38 * 10 ^ 6 * m and the gravitational constant G = 6.67 * 10 ^ - 11 * N * m ^ 2 / k * g ^ 2 and the Earth's mass is m_{e} = 5.98 * 10 ^ 24 * kg What is the speed of the satellite in m/s?