For a satellite to apper satationery to an observer on earth.

Options

A. It must be rotating about the earth's axis
B. it must be rotating in the equatorial plane
C. Its angular velocity must be from west to east .
D. its time period must be 24 hours .

Answer

To determine the conditions for a satellite to appear stationary to an observer on Earth, we need to analyze the requirements for a geostationary satellite. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Geostationary Satellites
A geostationary satellite is one that orbits the Earth at the same rotational speed as the Earth itself. This means that as the Earth rotates on its axis, the satellite remains in the same position relative to the surface of the Earth.

**Hint:** Think about how the satellite's orbit relates to the Earth's rotation.

### Step 2: Determine the Required Orbital Plane
For a satellite to appear stationary, it must orbit in the equatorial plane of the Earth. This is because the Earth rotates around its axis, and the satellite must be in sync with this rotation.

**Hint:** Visualize the Earth and the satellite's orbit to see how they must align.

### Step 3: Analyze the Direction of Rotation
The satellite must rotate in the same direction as the Earth's rotation, which is from west to east. This ensures that as the Earth spins, the satellite moves in a way that keeps it directly above the same point on the equator.

**Hint:** Consider the direction of the Earth's rotation and how the satellite must match it.

### Step 4: Match Angular Velocities
The angular velocity of the satellite must be equal to the angular velocity of the Earth. This means that both the satellite and the Earth complete one full rotation in the same amount of time.

**Hint:** Recall the relationship between angular velocity and the time taken for one complete rotation.

### Step 5: Set the Time Period
The time period of the satellite's orbit must be 24 hours. This is the same time it takes for the Earth to complete one full rotation. If the satellite's orbital period is different, it will not appear stationary to an observer on Earth.

**Hint:** Think about how the time period affects the position of the satellite relative to the observer.

### Conclusion
For a satellite to appear stationary to an observer on Earth, it must:
1. Orbit in the equatorial plane.
2. Rotate in the same direction as the Earth (west to east).
3. Have an angular velocity equal to that of the Earth.
4. Have a time period of 24 hours.

Thus, all the conditions mentioned in the question (options A, B, C, and D) are correct.