Two satellites of different masses are in the same circular orbit about the Earth. Which one of the following statements is true concerning the magnitude of the gravitational force that acts on each of them ?

Options

A. The magnitude of the gravitational force is zero new-tons for both satellites.
B. The magnitude of the gravitational force is the same for both satellites, but not zero newtons.
C. The magnitude of the gravitational force is zero new-tons for one, but not for the other.
D. The magnitude of the gravitational force depends on their masses.

Answer

To solve the problem, we need to analyze the gravitational force acting on two satellites of different masses that are in the same circular orbit around the Earth.

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force \( F \) acting on an object due to another object (in this case, the Earth) can be calculated using Newton's law of universal gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( G \) is the gravitational constant,
- \( m_1 \) is the mass of the first object (satellite),
- \( m_2 \) is the mass of the second object (Earth),
- \( r \) is the distance between the centers of the two masses.

2. **Identifying the Masses**:
Let’s denote the mass of the first satellite as \( M_1 \) and the mass of the second satellite as \( M_2 \). Both satellites are in the same circular orbit, meaning they are at the same distance \( r \) from the center of the Earth.

3. **Calculating the Gravitational Force on Each Satellite**:
- For the first satellite:
\[ F_1 = \frac{G \cdot M_1 \cdot M_E}{r^2} \]
- For the second satellite:
\[ F_2 = \frac{G \cdot M_2 \cdot M_E}{r^2} \]
where \( M_E \) is the mass of the Earth.

4. **Comparing the Forces**:
Since both satellites are in the same orbit, they experience gravitational forces that depend on their respective masses:
- \( F_1 \) and \( F_2 \) will be different unless \( M_1 = M_2 \). Therefore, the gravitational force acting on each satellite is not the same due to their different masses.

5. **Conclusion**:
The correct statement concerning the magnitude of the gravitational force that acts on each of the satellites is that the gravitational force depends on their masses. The forces are different for each satellite because they have different masses, even though they are in the same orbit.

### Final Answer:
The magnitude of gravitational force depends on their masses.