Question

If orbital radius of geostationary satellite decreases, gravitational potential energy

• A. Increases
• B. Decreases
• C. Remains same

Hint:

Always remember that bound systems have negative potential energy.
A decrease in orbital distance makes the system more tightly bound, thus lowering the potential energy further (making it more negative).

Answer 1

The Correct Option is B

To determine how the gravitational potential energy of a geostationary satellite changes with a decrease in its orbital radius, we need to understand the concept of gravitational potential energy in the context of satellites.

The gravitational potential energy \(U\) of an object in the gravitational field of a planet is given by the formula:

\(U = -\frac{G \cdot M \cdot m}{r}\)

• \(G\) is the gravitational constant.
• \(M\) is the mass of the Earth.
• \(m\) is the mass of the satellite.
• \(r\) is the orbital radius from the center of the Earth to the satellite.

The negative sign indicates that gravitational potential energy is always negative, and it increases (becomes less negative) as the distance \(r\) increases. Conversely, as the radius \(r\) decreases, the value of \(-\frac{G \cdot M \cdot m}{r}\) becomes more negative, indicating that the gravitational potential energy decreases.

Conclusion: When the orbital radius of a geostationary satellite decreases, the gravitational potential energy decreases.