When energy of a satellite - planet system is positive then satellite will

Options

A. Move around planet in circular orbit
B. Move around planet inelliptical orbit
C. Escape out with minimum speed
D. Escape out with speed greater than escape velocity

Answer

To solve the problem, we need to understand the relationship between the energy of a satellite-planet system and the motion of the satellite.

### Step-by-Step Solution:

1. **Understanding Total Energy of the Satellite-Planet System**:
The total mechanical energy (E) of a satellite in orbit around a planet is given by the sum of its kinetic energy (K.E.) and potential energy (P.E.). The formula for total energy is:
\[ E = K.E. + P.E. \]
where \( K.E. = \frac{1}{2}mv^2 \) and \( P.E. = -\frac{GMm}{r} \).

2. **Condition for Escape**:
For a satellite to escape the gravitational pull of a planet, its total energy must be zero or positive. The escape velocity (\( V_e \)) is the minimum velocity required for the satellite to escape the gravitational field of the planet. This condition can be expressed as:
\[ E \geq 0 \quad \text{(for escape)} \]

3. **Positive Total Energy**:
If the total energy of the satellite-planet system is positive (\( E > 0 \)), it implies that the kinetic energy of the satellite is greater than the gravitational potential energy (in absolute value). This can be expressed as:
\[ K.E. > |P.E.| \]
This means that the satellite has enough kinetic energy to overcome the gravitational attraction of the planet.

4. **Implication of Positive Energy**:
When the energy is positive, the satellite is not bound to the planet anymore. It will move away from the planet and will not return. The satellite will continue to move outward indefinitely unless acted upon by another force.

5. **Conclusion**:
Therefore, when the energy of a satellite-planet system is positive, the satellite will escape the gravitational influence of the planet and move away with a speed greater than the escape velocity.

### Final Answer:
When the energy of a satellite-planet system is positive, the satellite will escape out with speed greater than the escape velocity.

---