What is the work done by the force of gravity on a satellite moving round the Earth ? Justify your answer.

Explanation

To determine the work done by the force of gravity on a satellite moving around the Earth, we can follow these steps:

### Step 1: Understand the motion of the satellite
The satellite is in circular motion around the Earth. The gravitational force acts towards the center of the Earth, while the satellite moves along its circular path.

**Hint:** Consider the direction of the satellite's velocity and the gravitational force.

### Step 2: Define the vectors involved
- **Displacement vector (ds)**: This vector is tangent to the circular path of the satellite and points in the direction of its velocity.
- **Gravitational force vector (F)**: This vector points towards the center of the Earth.

**Hint:** Remember that the displacement vector is always tangent to the path of motion.

### Step 3: Determine the angle between the force and displacement
The angle (θ) between the gravitational force vector and the displacement vector is 90 degrees (90°) because the gravitational force acts radially inward while the displacement is tangential to the circular path.

**Hint:** Recall that the angle between perpendicular vectors is 90 degrees.

### Step 4: Use the work done formula
The work done (W) by a force is given by the formula:
\[ W = F \cdot ds = F \cdot ds \cdot \cos(\theta) \]

Since θ = 90°, we have:
\[ \cos(90°) = 0 \]

Thus, the work done by the gravitational force is:
\[ W = F \cdot ds \cdot 0 = 0 \]

**Hint:** Remember that the cosine of 90 degrees is zero, which leads to zero work done.

### Step 5: Consider the total displacement of the satellite
After completing one full orbit, the satellite returns to its starting point. Therefore, the total displacement of the satellite is zero.

**Hint:** Think about what happens to the position of the satellite after one complete revolution.

### Step 6: Conclude the work done
Since the total displacement is zero, we can also conclude that the work done by the gravitational force on the satellite is zero.

**Final Answer:** The work done by the force of gravity on a satellite moving around the Earth is zero because the gravitational force is perpendicular to the displacement of the satellite, and the total displacement after one complete orbit is also zero.