A comet of mass 1 0 8 kg travels around the Sun in an elliptical orbit. When it is closest to the Sun it is 2.5 × 1 0 11 m away and its speed is 2 × 1 0 4 m s - 1 . Find the change in kinetic energy w

Question

A comet of mass 1 0 8 kg travels around the Sun in an elliptical orbit. When it is closest to the Sun it is 2.5 × 1 0 11 m away and its speed is 2 × 1 0 4 m s - 1 . Find the change in kinetic energy when it is farthest from the Sun and is 5 × 1 0 10 m away from the Sun

TestHub · Accepted Answer

From the conservation of angular momentum,

$v_{1} r_{1} = v_{2} r_{2}$

$\Rightarrow v_{2} = \frac{2 \times 1 0^{4} \times 2.5 \times 1 0^{11}}{5 \times 1 0^{10}} = 1 0^{5} m s^{- 1}$

Change in kinetic energy is,

$Δ K E = \frac{1}{2} \times 1 0^{8} [{(1 0^{5})}^{2} - 4 \times 1 0^{8}] = 48 \times 1 0^{8} J$

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