NDA 2026
- Exam
- NDA
- Year
- 2026
- Subject
- General Ability
- Chapter
- General Science
NDA 2026 · General Ability · General Science
One year at a planet is 8 times as large as compared to the one...
One year at a planet is 8 times as large as compared to the one year at the Earth. Which one of the following is correct about the planet's orbit?
Options
- AThe semimajor axis of the planet's orbit is same as that of the Earth.
- BThe semimajor axis of the planet's orbit is twice as compared to that of the Earth.
- CThe semimajor axis of the planet's orbit is thrice as compared to that of the Earth.
- DThe semimajor axis of the planet's orbit is four times as compared to that of the Earth.
Correct answer
D. The semimajor axis of the planet's orbit is four times as compared to that of the Earth.
Step-by-step solution
According to Kepler's third law of planetary motion, the square of the time period of revolution is directly proportional to the cube of the semimajor axis of the orbit.
\left(\dfrac{T_p}{T_e}\right)^2 = \left(\dfrac{a_p}{a_e}\right)^3T_p = 8 T_e(8)^2 = \left(\dfrac{a_p}{a_e}\right)^364 = \left(\dfrac{a_p}{a_e}\right)^3\dfrac{a_p}{a_e} = (64)^{1/3} = 4a_p = 4 a_e
The semimajor axis of the planet's orbit is four times as compared to that of the Earth.
Answer: The semimajor axis of the planet's orbit is four times as compared to that of the Earth.
\left(\dfrac{T_p}{T_e}\right)^2 = \left(\dfrac{a_p}{a_e}\right)^3T_p = 8 T_e(8)^2 = \left(\dfrac{a_p}{a_e}\right)^364 = \left(\dfrac{a_p}{a_e}\right)^3\dfrac{a_p}{a_e} = (64)^{1/3} = 4a_p = 4 a_e
The semimajor axis of the planet's orbit is four times as compared to that of the Earth.
Answer: The semimajor axis of the planet's orbit is four times as compared to that of the Earth.