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Let's analyze the problem in the image.

We are given a scenario where the gravitational force \( F \) between the Sun and the planet Mercury is provided as \( 1.31 \times 10^{22} \, N \). The question is about how the gravitational force changes when:

1. **The mass of Mercury is doubled**.
2. **The distance between the Sun and Mercury is doubled**.

### Key Concept: Newton's Law of Universal Gravitation
The gravitational force between two masses is given by the equation:

\[
F = G \frac{m_1 m_2}{r^2}
\]

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.

#### First scenario: The mass of Mercury doubles.
If the mass of Mercury (let's say \( m_2 \)) doubles, then the gravitational force \( F \) is directly proportional to \( m_2 \). Therefore, if \( m_2 \) doubles, the force will also double, or increase by a factor of **2**.

#### Second scenario: The distance doubles.
The force of gravity is inversely proportional to the square of the distance (\( r^2 \)). So, if the distance between the Sun and Mercury is doubled, the force will decrease by a factor of:

\[
\left( \frac{1}{2^2} \right) = \frac{1}{4}
\]

Thus, the force will decrease by a factor of **4**.

### Correct Answer:
From this analysis, the gravitational force:
1. **Increases by a factor of 2** when the mass of Mercury doubles.
2. **Decreases by a factor of 4** when the distance between the Sun and Mercury doubles.

So the correct answer is **Option B**: "increase; 2; decrease; 4."

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Would you like more details on any part of the explanation?

Here are five related questions for practice:
1. How does the gravitational force change if both masses are doubled?
2. If the distance between two objects triples, by what factor does the gravitational force change?
3. What happens to the gravitational force if the distance is halved?
4. How does the gravitational constant \( G \) affect the force of gravity between two objects?
5. What is the physical significance of the inverse-square law in gravity?

**Tip:** The gravitational force is highly sensitive to changes in distance due to the inverse-square law. Even small changes in distance can greatly affect the force.

The force of gravity, F, between the Sun and the planet Mercury is 1.31 x 10^22 N. If the mass of Mercury doubled, the force of gravity between the Sun and Mercury will ______ by a factor of ______. If the distance between the two objects doubled, the force of gravity will ______ by a factor of ______.

Analyze how the gravitational force changes when the mass of Mercury doubles and the distance between the Sun and Mercury doubles. Understand key concepts like Newton's Law of Universal Gravitation and the inverse-square law. Ideal for students in Grades 9-12.

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