A satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing about a point on the equator is:

Options

A. 48 hrs
B. 24 hrs
C. 12 hrs
D. never

Explanation

To solve the problem of finding the time interval between successive passes of a geostationary satellite moving in the opposite direction (east to west) over a point on the equator, we can follow these steps:

### Step 1: Understand the concept of geostationary orbit
A geostationary satellite orbits the Earth at a height where its orbital period matches the Earth's rotation period. This means that for an observer on the surface of the Earth, the satellite appears to be stationary above a fixed point on the equator.

### Step 2: Determine the Earth's rotation period
The Earth rotates once every 24 hours (or 86400 seconds). This is the time it takes for a point on the equator to complete one full rotation relative to the stars.

### Step 3: Analyze the satellite's motion
In this case, the satellite is in a geostationary orbit but is moving in the opposite direction (east to west). While the Earth rotates in one direction, the satellite moves in the opposite direction.

### Step 4: Calculate the relative angular velocity
Let the angular velocity of the Earth be denoted as \( \omega \). Since the satellite is moving in the opposite direction, its effective angular velocity relative to a point on the Earth's surface is:
\[ \text{Effective angular velocity} = \omega + \omega = 2\omega \]
This means the satellite appears to move twice as fast as the Earth's rotation from the perspective of an observer on the ground.

### Step 5: Determine the time interval for the satellite's passes
Since the effective angular velocity of the satellite is \( 2\omega \), the time it takes for the satellite to pass over the same point on the equator can be calculated as follows:
- The Earth takes 24 hours to complete one rotation at angular velocity \( \omega \).
- Therefore, at an angular velocity of \( 2\omega \), the time taken for the satellite to complete one full pass over the same point is:
\[ \text{Time interval} = \frac{24 \text{ hours}}{2} = 12 \text{ hours} \]

### Conclusion
The time interval between successive passes of the satellite over a point on the equator is **12 hours**.

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