Rock

Classical Mechanics Level 2

A rock is orbiting the sun at a distance of 6.0 AU 6.0\text{ AU} (astronomical units). The rock experiences 5400 N 5400\text{ N} of gravitational force from the sun.

How much gravitational force would the same rock experience at a distance of 9.0 AU 9.0\text{ AU} from the sun?

3600 N 3600 \text{ N} 5400 N 5400 \text{ N} 12150 N 12150 \text{ N} 8100 N 8100 \text{ N} 600 N 600 \text{ N} 2939 N 2939 \text{ N} 2400 N 2400\text{ N}

Arjen Vreugdenhil by Arjen Vreugdenhil , 44, USA

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1 solution

Since the force is proportional to the inverse square of the distance ( F ∝ 1 / r 2 F \propto 1/r^2 ), multiplying the distance by 1.5 results in a force of F ′ = F ⋅ 1 ( 1.5 ) 2 = 5400 2.25 = 2400 N . F' = F\cdot \frac 1{(1.5)^2} = \frac{5400}{2.25} = \boxed{2400\ \text{N}}.

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