Question

# 1. A space probe is launched from Earth, headed for deep space. At a distance of...

1. A space probe is launched from Earth, headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on the space probe is 520 pounds. If the gravitational force acting on the probe is proportional to 1/d2, what is the force in Newtons when the probe is four times as far from Earth's center?

Gravitational force is proportional to (1/d2).

K = Proportionality constant

The space probe is at a distance of 10000 miles from the Earth's center.

Distance from Earth's center = d1 = 10000 miles

Gravitational force at 'd1' distance = F1 = 520 pounds

Now the space probe is four times as far from the Earth's center.

Distance from the Earth's center = d2 = 4d1

Gravitational force at 'd2' distance = F2

F1 = K/d12

F2 = K/d22

K = F1d12 = F2d22

F1d12 = F2(4d1)2

F1 = 16F2

F2 = 520/16

F2 = 32.5 pounds

F2 = 144.56 N

The force when the probe is four times as far from the Earth's center = 144.56 N

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