Keplers Law: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Keplers Law. Understanding the underlying formula is key to arriving at the correct answer below:

To find the number of years Mars takes to make one revolution around the Sun, we can use Kepler's Third Law, which states:

\[
T^2 \propto r^3
\]

where \( T \) is the orbital period and \( r \) is the average distance from the Sun.

Given:
- Let the average distance of Earth from the Sun be \( r_E \).
- The average distance of Mars from the Sun is \( r_M = 1.5 r_E \).

Using Kepler's Third Law:
1. For Earth:
\[
T_E^2 \propto r_E^3
\]

2. For Mars:
\[
T_M^2 \propto r_M^3 ; T_M^2 \propto (1.5 r_E)^3 = 1.5^3 r_E^3
\]

3. We know \( T_E \) (the period of Earth) is approximately **1 year**:
\[
T_M^2 = 1.5^3 T_E^2
\]
\[
T_M^2 = 1.5^3 \times 1^2 = 3.375
\]

4. Therefore,
\[
T_M = \sqrt{3.375} \approx 1.84 \, \text{years}
\]

Conclusion:
Mars takes approximately 1.84 years to make one revolution around the Sun.