8) 22. I,b) -36.8, 15.8, d) -27.9 2. A satellite of mass m orbits the planet Jup

Question

8) 22. I,b) -36.8, 15.8, d) -27.9 2. A satellite of mass m orbits the planet Jupiter. Jupiter has a mass of M- 1.898x102 kg and a radius of R - 7.149x10'm. The distance from the center of Jupiter to the satellite is r and the satellite's mass is m Let r-6x106 m and m = 20.0 kg. A) Find the force F exerted on the planet by the satellite. a) 70,330N, b) 181 N,c) 23.8 N, B) Find the speed v (in m/s) of the satellite. d) 12.2N a) 1.45x 10, b) 2.67x10, c) 7.36x10, d) 1.92x103 C) Find the total mechanical energy E (in J) of the satellite. a) -3.67x107, b) -2.11x10",c) -5.41x10*, d) -7.14x10' D) Find the value of the acceleration of gravity g (in m/s) on the surface of the planet. a) 24.8, Find the time T for the satellite to make one complete revolution around the planet. a) 1.97x104s, b) 2.60x102 s, c) 1.41x10's, d) 5.12x10s b) 3.70, c) 3.73, d) 8.87 E)

Explanation / Answer

(A) F = G M m / r^2

= (6.67 x 10^-11) (1.898 x 10^27) (20) / (7.149 x 10^7 + 6 x 10^6)^2

= 70331 N

Ans(a)

(B) F = m v^2 / r

70331 = 20 v^2 / (6 x 10^6)

v = 1.45 x 10^5 m/s

Ans(a)

(C) E = PE + KE = - G M m / r + m v^2 /2

= - m v^2 + m v^2 /2

= - m v^2 / 2

= - 20 x (1.45 x 10^5)^2 /2

= -2.11 x 10^11 Ans(b)

(D) a = G M / R^2 = 24.8 m/s^2

Ans (a)

E) T = 2 pi r /v = 260 s

Ans(b)

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