An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. The following quantities increases for the satellite as a result of this change

Options

A. gravitational potential energy
B. angular velocity
C. linear orbital velocity
D. centripetal acceleration

Explanation

To solve the question regarding the changes in quantities for a satellite moved from one stable circular orbit to another larger stable circular orbit, we will analyze each quantity step by step.

### Step 1: Understanding Gravitational Potential Energy
The gravitational potential energy (U) of a satellite in orbit can be expressed as:
\[ U = -\frac{G M m}{r} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the satellite,
- \( r \) is the distance from the center of the Earth to the satellite.

**Hint:** Remember that gravitational potential energy is negative and inversely proportional to the distance \( r \).

### Step 2: Analyzing the Change in Gravitational Potential Energy
When the satellite moves to a larger orbit, the value of \( r \) increases. Since gravitational potential energy is inversely proportional to \( r \), as \( r \) increases, the absolute value of \( U \) decreases, but since it is negative, this means that \( U \) becomes less negative (i.e., increases).

**Conclusion for Step 2:** Gravitational potential energy increases.

### Step 3: Understanding Angular Velocity
The angular velocity (\( \omega \)) of a satellite in a circular orbit can be given by:
\[ \omega = \sqrt{\frac{G M}{r^3}} \]

**Hint:** Angular velocity is related to the radius of the orbit.

### Step 4: Analyzing the Change in Angular Velocity
From the formula, we can see that angular velocity is inversely proportional to the square root of \( r^3 \). As \( r \) increases, \( \omega \) will decrease.

**Conclusion for Step 4:** Angular velocity decreases.

### Step 5: Understanding Linear Orbital Velocity
The linear orbital velocity (\( V \)) can be expressed as:
\[ V = \sqrt{\frac{G M}{r}} \]

**Hint:** Linear velocity is also dependent on the radius of the orbit.

### Step 6: Analyzing the Change in Linear Orbital Velocity
Similar to angular velocity, linear orbital velocity is inversely proportional to the square root of \( r \). Therefore, as \( r \) increases, \( V \) will also decrease.

**Conclusion for Step 6:** Linear orbital velocity decreases.

### Step 7: Understanding Centripetal Acceleration
Centripetal acceleration (\( a_c \)) can be expressed as:
\[ a_c = \frac{V^2}{r} = \frac{G M}{r^2} \]

**Hint:** Centripetal acceleration is related to the radius squared.

### Step 8: Analyzing the Change in Centripetal Acceleration
From the formula, centripetal acceleration is inversely proportional to \( r^2 \). As \( r \) increases, \( a_c \) will decrease.

**Conclusion for Step 8:** Centripetal acceleration decreases.

### Final Conclusion
After analyzing all the quantities:
- Gravitational potential energy increases.
- Angular velocity decreases.
- Linear orbital velocity decreases.
- Centripetal acceleration decreases.

Thus, the only quantity that increases when the satellite is moved to a larger stable circular orbit is **gravitational potential energy**.

### Answer
The correct answer is: **Gravitational potential energy increases.**