Chapter 13, Problem 21A

The planet and its moon gravitationally attract each other. Rank gravitational attractions between them from greatest to least.

To determine

To rank: The gravitational attraction between the planet and its moon from greatest to least.

Answer to Problem 21A

  $B= C>A>D$ .

Explanation of Solution

Given:

The masses along with the separation between the planets and their moon is shown in figure 1.

  

Figure 1

Formula used:

If $A$ and $B$ are the two objects having masses $m_A$ and $m_B$ respectively which are separated by a distance $d$ , then the expression for gravitational force is given by,

  $F\text{ = G}\frac{m_A{m}_B}{d^2}$$\left(1\right)$

Where $\text{ G}$ is gravitational constant, $\text{ G}=6.674\times {10}^{-11}\text{ N}\cdot {\text{m}}^2/{\text{kg}}^2$

Calculation:

The gravitational attraction between the planet A and its moon is,

  $F\text{ = G}\frac{Mm}{d^2}$

The gravitational attraction between the planet B and its moon is,

  $\begin{array}{c}F\text{ = G}\frac{\left(2M\right)m}{d^2}\\ =\text{G}\frac{2Mm}{d^2}\end{array}$

The gravitational attraction between the planet C and its moon is,

  $\begin{array}{c}F\text{ = G}\frac{M\left(2m\right)}{d^2}\\ =\text{G}\frac{2Mm}{d^2}\end{array}$

The gravitational attraction between the planet D and its moon is,

  $\begin{array}{c}F\text{ = G}\frac{M\left(2m\right)}{{\left(2d\right)}^2}\\ =\text{G}\frac{2Mm}{4d^2}\end{array}$

Conclusion:

The rank of gravitational attraction between the planet and its moon from greatest to least is m

  $B= C>A>D$ .