Question

select the word or phrase to complete the sentence.
use the formula ( f = g \frac { m _ { 1 } m _ { 2 } } { d ^ { 2 } } ), where

• ( f ) = force of gravity
• ( g ) = universal gravitational constant
• ( m _ { 1 } ) and ( m _ { 2 } ) = masses of the two objects
• ( d ) = distance between the center of two objects

scientists estimate that the moon gets farther away from earth by 3.8 centimeters each year. as the distance increases over time, the gravitational force between the two objects

Explanation:

Step1: Analyze the formula \(F = G\frac{m_1m_2}{d^2}\)

In the formula \(F = G\frac{m_1m_2}{d^2}\), \(G\) (universal gravitational constant) is a constant, and assume \(m_1\) (mass of Earth) and \(m_2\) (mass of the Moon) are approximately constant in the context of the problem.

Step2: Consider the relationship between \(F\) and \(d\)

We can rewrite the formula as \(F=\frac{Gm_1m_2}{d^2}\). Let \(k = Gm_1m_2\) (a constant). Then \(F=\frac{k}{d^2}\). As \(d\) (distance) increases, since \(k>0\), when \(d_1\frac{k}{d_2^2}\).

Answer:

decreases