Question

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?

Answer #1

Gravitational force is proportional to (1/d^{2}).

K = Proportionality constant

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

Distance from Earth's center = d_{1} = 10000 miles

Gravitational force at 'd_{1}' distance = F_{1}
= 520 pounds

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

Distance from the Earth's center = d_{2} =
4d_{1}

Gravitational force at 'd_{2}' distance =
F_{2}

F_{1} = K/d_{1}^{2}

F_{2} = K/d_{2}^{2}

K = F_{1}d_{1}^{2} =
F_{2}d_{2}^{2}

F_{1}d_{1}^{2} =
F_{2}(4d_{1})^{2}

F_{1} = 16F_{2}

F_{2} = 520/16

F_{2} = 32.5 pounds

F_{2} = 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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