Chapter 11.5, Problem 11.160P

Satellites A and B are traveling in the same plane in circular orbits around the earth at altitudes of 120 and 200 mi, respectively. If at t = 0 the satellites are aligned as shown and knowing that the radius of the earth is R = 3960 mi, determine when the satellites will next be radially aligned. (See the information given in Probs. 11.153 and 11.154.)

Fig. P11.160

11.153 and 11.154 A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)², where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 m/s², determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.

11.153 Earth: (v_mean)_orbit = 107 Mm/h.

11.154 Saturn: (v_mean)_orbit = 34.7 Mm/h.