Rankers Physics
Topic: Gravitation
Subtopic: Keplers Law

The mean distance of mars from sun is 1.5 times that of earth from sun. What is approximately the number of years required by mars to make one revolution about sun ?
2.35 years
1.85 years
3.65 years
2.75 years

Solution:

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.

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