Statement I: Two satellites are following one another in the same circular orbit. If one satellite tries to catch another (leading one) satellite, then it can be done by increasing its speed without changing the orbit.
Statement II: The energy of earth-satellite system in circular orbit is given by `E = (-Gms)//(2a)`, where `r` is the radius of the circular orbit.

Options

A. Statement I is True, Statement II is True: Statement II is a correct explanation for Statement I.
B. Statement I is True, Statement II is True: Statement II is Not a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To analyze the given statements, we will evaluate each statement step by step.

### Step 1: Understanding Statement I
Statement I claims that if one satellite tries to catch another satellite in the same circular orbit, it can do so by increasing its speed without changing the orbit.

- **Analysis**: In a circular orbit, the gravitational force provides the necessary centripetal force to keep the satellite in orbit. If one satellite increases its speed, it will gain kinetic energy. However, this increase in speed will cause the satellite to move to a higher orbit because the gravitational force will no longer be sufficient to maintain the original circular orbit. Thus, the orbit will change.

### Conclusion for Statement I
- **Result**: Statement I is **false**. Increasing speed will change the orbit.

### Step 2: Understanding Statement II
Statement II states that the energy of the Earth-satellite system in a circular orbit is given by the formula \( E = -\frac{G m_s m_e}{2r} \), where \( r \) is the radius of the circular orbit.

- **Analysis**: This formula is indeed correct. The total mechanical energy of a satellite in a circular orbit is negative, indicating that the satellite is in a bound system. The energy depends on the gravitational constant \( G \), the mass of the satellite \( m_s \), the mass of the Earth \( m_e \), and the radius \( r \) of the orbit.

### Conclusion for Statement II
- **Result**: Statement II is **true**. The formula accurately describes the energy of the Earth-satellite system in a circular orbit.

### Final Evaluation
- Since Statement I is false and Statement II is true, we can conclude:
- The correct option is **Option 4**: Statement I is false, Statement II is true.