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/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