A planet is revolving round the sun is elliptical orbit. Velocity at perigee position ( nearest) is `v_(1)` and at apogee position ( farthest) is `v_(2)`. Both these velocities are perpendicular to the line joining centre of sun and planet. `r_(1)` is the minimum distance and `r_(2)` the maximum distance.
When the planet is at perigee position, it wants to revolve in a circular orbit by itselff. For this, value of G

Options

A. a.should increase
B. b.should decrease
C. c. will not depends on the value of G
D. d. data is insufficient

Answer

To solve the problem, we need to analyze the conditions under which a planet, at its perigee position, can maintain a circular orbit around the Sun.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- The planet is in an elliptical orbit around the Sun.
- At perigee (the closest point), the velocity is \( v_1 \).
- At apogee (the farthest point), the velocity is \( v_2 \).
- We need to determine the value of gravitational constant \( G \) when the planet at perigee wants to revolve in a circular orbit.

2. **Orbital Velocity Formula**:
- The orbital velocity \( v_0 \) for a circular orbit is given by:
\[ v_0 = \sqrt{\frac{GM}{R}} \]
- Here, \( G \) is the gravitational constant, \( M \) is the mass of the Sun, and \( R \) is the radius of the orbit.

3. **Condition for Circular Orbit**:
- For the planet to maintain a circular orbit at perigee, its velocity \( v_1 \) must equal the circular orbital velocity \( v_0 \):
\[ v_1 = v_0 \]

4. **Substituting the Orbital Velocity**:
- From the above condition, we can write:
\[ v_1 = \sqrt{\frac{GM}{r_1}} \]
- Where \( r_1 \) is the distance from the Sun to the planet at perigee.

5. **Setting Up the Equation**:
- To maintain a circular orbit, we need:
\[ v_1 = \sqrt{\frac{GM}{r_1}} \implies v_1^2 = \frac{GM}{r_1} \]

6. **Finding the Expression for \( G \)**:
- Rearranging the equation gives us:
\[ G = \frac{v_1^2 r_1}{M} \]

7. **Conclusion**:
- Since \( v_1 \) is greater than \( v_2 \) (the velocity at apogee), and for the planet to revolve in a circular orbit at perigee, \( G \) must be sufficient to ensure that the velocity \( v_1 \) can be achieved. Therefore, if \( v_1 \) is greater than the required orbital velocity, \( G \) must increase to maintain this condition.

### Final Answer:
- The value of \( G \) must **increase** for the planet at perigee to revolve in a circular orbit.