College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Question:**
What would happen to the gravitational force felt between two planets if the mass of one planet were doubled?
**Explanation:**
This question pertains to Newton's Universal Law of Gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by distance \( r \) is given by the formula:
\[
F = G \frac{m_1 \cdot m_2}{r^2}
\]
where \( G \) is the gravitational constant.
**Analysis:**
If the mass of one planet, say \( m_1 \), is doubled, the new force \( F' \) can be calculated as:
\[
F' = G \frac{(2 \cdot m_1) \cdot m_2}{r^2}
\]
This simplifies to:
\[
F' = 2 \cdot G \frac{m_1 \cdot m_2}{r^2} = 2 \cdot F
\]
Therefore, the gravitational force would double if the mass of one planet were doubled, assuming the distance between the two planets remains constant.](https://content.bartleby.com/qna-images/question/c1357887-becf-4289-b67d-2b8f988a0b81/320425d9-761c-409d-b898-9ae319a3e150/m74hb9_processed.png)
Transcribed Image Text:**Question:**
What would happen to the gravitational force felt between two planets if the mass of one planet were doubled?
**Explanation:**
This question pertains to Newton's Universal Law of Gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by distance \( r \) is given by the formula:
\[
F = G \frac{m_1 \cdot m_2}{r^2}
\]
where \( G \) is the gravitational constant.
**Analysis:**
If the mass of one planet, say \( m_1 \), is doubled, the new force \( F' \) can be calculated as:
\[
F' = G \frac{(2 \cdot m_1) \cdot m_2}{r^2}
\]
This simplifies to:
\[
F' = 2 \cdot G \frac{m_1 \cdot m_2}{r^2} = 2 \cdot F
\]
Therefore, the gravitational force would double if the mass of one planet were doubled, assuming the distance between the two planets remains constant.
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