Question

Use the universal law of gravitation to solve the following problems. b. The force of gravity between a planet and its moon is 371 N. If the planet has a mass of 4 × 1022 kg and the moon has a mass of 5 × 105 kg, what is the distance between their centers? (1 point)

Answer 1

Approximately
`6.00 * 10^(7)\; {\rm m}`.

Step-by-step explanation:

The magnitude
`F` of the gravitational attraction between two objects in space is:

`\displaystyle F = (G\, M\, m)/(r^(2))`,

Where:

• 
  `G \approx 6.67 * 10^(-11)\; {\rm N\cdot m^(2)\cdot kg^(-2)` is the gravitational constant,
• 
  `M` and
  `m` are the mass of the two objects, and
• 
  `r` is the distance between the center of mass of the two objects.

In this question,
`M`,
`m`, and the magnitude of the gravitational attraction are given. Rearrange the equation above to find an expression for distance
`r`:

`\begin{aligned}r^(2) = (G\, M\, m)/(F)\end{aligned}`.

`\begin{aligned}r = \sqrt{(G\, M\, m)/(F)}\end{aligned}`.

Substitute
`M = 4 * 10^(22)\; {\rm kg}` and
`m = 5* 10^(5)\; {\rm kg}` into the expression:

`\begin{aligned}r &= \sqrt{(G\, M\, m)/(F)} \\ &= \sqrt{((6.67 * 10^(-11))\, (4 * 10^(22))* (5 * 10^(5)))/((371))}\; {\rm m} \\ &\approx 6.00 * 10^(7)\; {\rm m}\end{aligned}`.

In other words, the distance between the center of mass of this planet and its moon would be approximately
`6.00 * 10^(7)\; {\rm m}`.