The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are , and , respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then [2018]

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Solution

Q.
The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are $K_{A}$ , $K_{B}$ and $K_{C}$ , respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then [2018]

1 $K_{A} < K_{B} < K_{C}$

2 $K_{A} > K_{B} > K_{C}$

3 $K_{B} < K_{A} < K_{C}$

4 $K_{B} > K_{A} > K_{C}$

Ans.
(2)

Point A is perihelion and C is aphelion.

So, $v_{A} > v_{B} > v_{C}$

As kinetic energy $K = (\frac{1}{2}) m v^{2}$

or $K \propto v^{2}$

So, $K_{A} > K_{B} > K_{C}$

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