Question

date in the year 2013 | distance between moon and earth (km)
january 10 | 360,048
april 15 | 404,863
september 15 | 367,389
december 19 | 406,276
the table shows the distance between the moon and earth on different dates. on which date is the gravitational force between earth and the moon the greatest?
january 10
april 15
september 15
december 19

Explanation:

Step1: Recall gravitational force law

Newton's law of universal gravitation states $F = G\frac{m_1m_2}{r^2}$, where $F$ is gravitational force, $G$ is the gravitational constant, $m_1,m_2$ are the masses of Earth and Moon, and $r$ is the distance between them.

Step2: Relate force to distance

Since $G$, $m_1$, and $m_2$ are constant, $F$ is inversely proportional to $r^2$. A smaller $r$ gives a larger $F$.

Step3: Identify smallest distance

Compare the distances:

• January 10: $360,048$ km
• April 15: $404,863$ km
• September 15: $367,389$ km
• December 19: $406,276$ km

The smallest distance is $360,048$ km (January 10).

Answer:

January 10