Question

How does the orbital period of a satellite change as its distance from the Earth's center increases?

• A. $T \propto r$
• B. $T \propto r^2$
• C. $T \propto r^{3/2}$
• D. $T \propto \frac{1}{r}$

Hint:

Remember: Kepler’s 3rd Law → $T^2 \propto r^3$.

Answer 1

The Correct Option is C

Concept: The motion of satellites follows Kepler’s third law of planetary motion.
Step 1: Kepler’s third law.
\[ T^2 \propto r^3 \]
Step 2: Deriving the relation.
Taking square root on both sides: \[ T \propto r^{3/2} \]
Step 3: Understanding the result.
As the distance from Earth increases, the orbital period increases more than linearly.
Step 4: Evaluating the options.

• $T \propto r$ $\rightarrow$ Incorrect
• $T \propto r^2$ $\rightarrow$ Incorrect
• $T \propto r^{3/2}$ $\rightarrow$ Correct
• $T \propto \frac{1}{r}$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, $T \propto r^{3/2}$.