Let `F_1` be the magnitude of the gravitational force exerted on the Sun by Earth and `F_2` be the magnitude of the force exerted on Earth by the Sun. Then:

Options

A. `F_1` is much greater than `F_2`
B. `F_1` is slightly greater than `F_2`
C. `F_1` is equal to `F_2`
D. `F_1` is slightly less than `F_2`

Explanation

To solve the problem, we need to analyze the gravitational forces exerted between the Earth and the Sun using Newton's Law of Gravitation.

### Step-by-Step Solution:

1. **Understanding the Gravitational Force**: According to Newton's Law of Gravitation, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant.

2. **Identifying the Forces**: In our case:
- Let \( m_s \) be the mass of the Sun.
- Let \( m_e \) be the mass of the Earth.
- The distance between the Earth and the Sun is \( r \).

The gravitational force exerted on the Sun by the Earth is denoted as \( F_1 \), and the gravitational force exerted on the Earth by the Sun is denoted as \( F_2 \).

3. **Applying the Formula**:
- The gravitational force \( F_1 \) (force on the Sun due to Earth) can be expressed as:
\[ F_1 = G \frac{m_e m_s}{r^2} \]
- The gravitational force \( F_2 \) (force on the Earth due to Sun) can be expressed as:
\[ F_2 = G \frac{m_s m_e}{r^2} \]

4. **Comparing the Forces**: From the equations for \( F_1 \) and \( F_2 \), we can see that:
\[ F_1 = F_2 \]
This shows that the magnitudes of the gravitational forces are equal.

5. **Conclusion**: According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. Thus, the gravitational force exerted by the Earth on the Sun is equal in magnitude and opposite in direction to the gravitational force exerted by the Sun on the Earth.

### Final Answer:
\[ F_1 = F_2 \]