A satellite is orbiting the earth, if its distance from the earth is increased, its

Options

A. angular velocity would increase
B. linear velocity would increase
C. angular velocity would decrease
D. time period would increase

Explanation

To solve the problem, we need to analyze how the various properties of a satellite in orbit change when its distance from the Earth is increased. We will look at angular velocity, linear velocity, and time period.

### Step-by-Step Solution:

1. **Understanding Linear Velocity**:
The linear velocity \( v \) of a satellite in orbit is given by the formula:
\[ v = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the center of the Earth to the satellite.

2. **Effect of Increasing Distance on Linear Velocity**:
If the distance \( r \) is increased, the linear velocity \( v \) will change as follows:
- Since \( r \) is in the denominator under the square root, increasing \( r \) will result in a decrease in \( v \).
- Therefore, the linear velocity **decreases** when the distance from the Earth increases.

3. **Understanding Angular Velocity**:
The angular velocity \( \omega \) of the satellite can be expressed in terms of linear velocity:
\[ \omega = \frac{v}{r} \]
Substituting the expression for \( v \):
\[ \omega = \frac{\sqrt{\frac{GM}{r}}}{r} = \sqrt{\frac{GM}{r^3}} \]

4. **Effect of Increasing Distance on Angular Velocity**:
- As \( r \) increases, the term \( r^3 \) in the denominator increases faster than the numerator remains constant.
- Thus, \( \omega \) will **decrease** as \( r \) increases.

5. **Understanding Time Period**:
The time period \( T \) of the satellite's orbit is given by:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]

6. **Effect of Increasing Distance on Time Period**:
- As \( r \) increases, \( r^3 \) increases, resulting in an increase in \( T \).
- Therefore, the time period **increases** when the distance from the Earth increases.

### Summary of Results:
- **Linear Velocity**: Decreases (Option 2 is false)
- **Angular Velocity**: Decreases (Option 3 is correct)
- **Time Period**: Increases (Option 4 is correct)

### Final Answer:
- The correct options are: Angular velocity decreases (Option 3) and Time period increases (Option 4).