Pl anet # 1 M3 M1 ..... .... Planet # 2 Planet # 3 Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 of mass M, is directly between these two planets. What is the force F12 on planet #1 due to the gravitational force of planet #2 at the position r in the above figure? O F12 = GM,M2 / 3 O F12 = GM1 / r? O F12 = GM1M2/r O F12 = GM1M2 /? O F12 = GM,M2r? %3D %3D !3! %3D %3D Submit Answer Tries 0/2 What is the direction of the force F12? toward planet 1 perpendicular to the line joining planet 1 and planet 2 toward planet 3 toward planet 2 Submit Answer Tries 0/2 What is the force F13 on planet #1 due to the gravitational force of planet #3 at the position r in the above figure? F13 = GM1M3 / R? %3D F13 = GM1M3(R-r)² F13 = GM1M3/ (R-r) %3D %3D F13 = GM1M3/ r2 F13 = GM1M3 / (R-r)2 Submit Answer Tries 0/2 What is the direction of the force F13? toward planet 2 toward planet 1 perpendicular to the line joining planet 1 and planet 3 O toward planet 3

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### Explanation of Gravitational Forces Between Planets

The scenario depicts three planets interacting through gravitational forces:

- **Planet #1** with mass \( M_1 \)
- **Planet #2** with mass \( M_2 \)
- **Planet #3** with mass \( M_3 \)

Planet #2 and Planet #3 are separated by a distance \( R \). Planet #1 is at position \( r \) between them.

#### Diagram Overview
- Planet #3 is on the left, shown in red, followed by planet #1 in green, and planet #2 in blue on the right.
- The arrow indicates the direction from planet #3 through planet #1 to planet #2.

### Questions and Explanations

1. **What is the force \( F_{12} \) on planet #1 due to the gravitational force of planet #2 at the position \( r \)?**

   Multiple choice options:
   - \( F_{12} = \frac{GM_1M_2}{r^3} \)
   - \( F_{12} = \frac{GM_1}{r^2} \)
   - \( F_{12} = \frac{GM_1M_2}{r} \)
   - \( F_{12} = \frac{GM_1M_2}{r^2} \) [Correct choice]
   - \( F_{12} = GM_1M_2r^2 \)

2. **What is the direction of the force \( F_{12} \)?**
   
   Choices:
   - Toward planet 1
   - Perpendicular to the line joining planet 1 and planet 2
   - Toward planet 3
   - Toward planet 2 [Correct choice]

3. **What is the force \( F_{13} \) on planet #1 due to the gravitational force of planet #3 at the position \( r \)?**

   Multiple choice options:
   - \( F_{13} = \frac{GM_1M_3}{R^2} \)
   - \( F_{13} = \frac{GM_1M_3(R-r)^2}{R} \)
   - \( F_{13} = \frac{GM_1M_3}{(R-r)} \)
   - \( F_{13} = \frac{GM_1
Transcribed Image Text:### Explanation of Gravitational Forces Between Planets The scenario depicts three planets interacting through gravitational forces: - **Planet #1** with mass \( M_1 \) - **Planet #2** with mass \( M_2 \) - **Planet #3** with mass \( M_3 \) Planet #2 and Planet #3 are separated by a distance \( R \). Planet #1 is at position \( r \) between them. #### Diagram Overview - Planet #3 is on the left, shown in red, followed by planet #1 in green, and planet #2 in blue on the right. - The arrow indicates the direction from planet #3 through planet #1 to planet #2. ### Questions and Explanations 1. **What is the force \( F_{12} \) on planet #1 due to the gravitational force of planet #2 at the position \( r \)?** Multiple choice options: - \( F_{12} = \frac{GM_1M_2}{r^3} \) - \( F_{12} = \frac{GM_1}{r^2} \) - \( F_{12} = \frac{GM_1M_2}{r} \) - \( F_{12} = \frac{GM_1M_2}{r^2} \) [Correct choice] - \( F_{12} = GM_1M_2r^2 \) 2. **What is the direction of the force \( F_{12} \)?** Choices: - Toward planet 1 - Perpendicular to the line joining planet 1 and planet 2 - Toward planet 3 - Toward planet 2 [Correct choice] 3. **What is the force \( F_{13} \) on planet #1 due to the gravitational force of planet #3 at the position \( r \)?** Multiple choice options: - \( F_{13} = \frac{GM_1M_3}{R^2} \) - \( F_{13} = \frac{GM_1M_3(R-r)^2}{R} \) - \( F_{13} = \frac{GM_1M_3}{(R-r)} \) - \( F_{13} = \frac{GM_1
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