Question

The diagram below shows two celestial bodies with the same mass, M, placed a distance, D, apart.






What would increase the gravitational force between the two bodies?
Responses
A Maintaining M and increasing DMaintaining M and increasing D
B Decreasing M and maintaining DDecreasing M and maintaining D
C Decreasing M and increasing DDecreasing M and increasing D
D Increasing M and decreasing DIncreasing M and decreasing D
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Answers

GPT-4o mini
To increase the gravitational force between two celestial bodies, we can refer to Newton's Law of Universal Gravitation, which states:

\[ F = G \frac{M_1 M_2}{D^2} \]

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( M_1 \) and \( M_2 \) are the masses of the two bodies, and
- \( D \) is the distance between the centers of the two bodies.

Based on this formula, the gravitational force can be increased by either increasing the masses (M) of the bodies or decreasing the distance (D) between them.

Now, evaluating the response options:

A. **Maintaining M and increasing D** - This would decrease the gravitational force, since increasing D increases the denominator in the equation.

B. **Decreasing M and maintaining D** - This would decrease the gravitational force, since decreasing M decreases the numerator in the equation.

C. **Decreasing M and increasing D** - This would decrease the gravitational force for both reasons mentioned above.

D. **Increasing M and decreasing D** - This would increase the gravitational force, since increasing M increases the numerator, and decreasing D decreases the denominator.

Thus, the correct answer that would increase the gravitational force between the two bodies is:

**D. Increasing M and decreasing D**.

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