Question

# A planet revolves is an elliptical orbit around the sun. The semi-major and semi-minor axes are $$a$$ and $$b$$, then the time period is given by.

A
T2b3
B
T2[a+b2]3
C
T2a3
D
T2[ab2]3

Solution

## The correct option is C $$T^2 \propto a^3$$ Using Kepler's $$2$$nd law,  $$A= \dfrac{L}{2m} T$$  where $$A= \pi ab$$ Also, $$b^2= a^2(1-e^2)$$Now, at aphelion  $$\theta= 0$$  thus  $$a(1-e)= \dfrac{L^2}{GMm^2(1+e)}$$$$\implies \dfrac{L^2}{m^2}= a(1-e^2)GM$$Thus, from  $$\dfrac{L^2}{4m^2}= \dfrac{\pi^2 a^2b^2}{T^2} \implies T^2 \propto a^3$$Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More