The average distance separating Earth and the Moon (center to center) is 384, 00

Question

The average distance separating Earth and the Moon (center to center) is 384, 000 km. Use the data in the table to find the net gravitational force exerted by Earth and the Moon on a 3.00 times 10^4 -kg spaceship located halfway between them. N A satellite has a mass of 213 kg and is located at 1.95 times 10^6 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location? J (b) What Is the magnitude of the gravitational force on the satellite? N A satellite is in a circular orbit around the Earth at an altitude of 2.38 times 10^6 m. (a) Find the period of the orbit. h (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s^2 toward the center of the earth

Explanation / Answer

1)

Me = 5.98 x 10^24 kg

Mm = 7.36 x 10^22 kg

m = 3 x 10^4 kg

G = 6.67259 x 10^-11 Nm^2/kg^2

Distance from ship to either body D = (384 x 6)/2 = 192 x 10^6 m

Fnet = GMe*m/D^2 - GMm*m/D^2

Fnet = [G*m/D^2]*(Me - Mm)

Fnet = 320.73 N

2)

a.

PE = -G Mm/r = - (6.67259 x 10^-11 x 5.98 x 10^24 x 213) / (6.38 x 10^6 + 1.95 x 10^6)

PE = -1.020 x 10^10 J

b.

F = G Mm/r^2

F = (6.67259 x 10^-11 x 5.98 x 10^24 x 213) / (6.38 x 10^6 + 1.95 x 10^6)^2

F = 1224.87 N

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