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

Step 1: Understanding the Concept:
Gravitational potential energy is the energy possessed by a mass due to its position in a gravitational field.
For a satellite orbiting the Earth, the potential energy is always negative, which indicates that it is a gravitationally bound system.
Step 2: Key Formula or Approach:
The formula for the gravitational potential energy $U$ of a satellite of mass $m$ orbiting a planet of mass $M$ at an orbital radius $r$ is given by:
\[ U = -\frac{GMm}{r} \] Step 3: Detailed Explanation:
In this formula, the gravitational constant $G$, the mass of the Earth $M$, and the mass of the satellite $m$ are all positive constants.
When the orbital radius $r$ decreases, the denominator becomes smaller, which makes the magnitude of the fraction $\frac{GMm}{r}$ larger.
However, because of the negative sign in the formula, an increase in the magnitude means the actual value of the potential energy becomes more negative.
Becoming more negative corresponds to a mathematical decrease in the total value.
Step 4: Final Answer:
The gravitational potential energy decreases.