A planet revolves about the sun in elliptical orbit. The areal velocity dAdt of the planet is $$4.0$$×$$1016m2/s$$. The least distance between planet and the sun is $$2$$×$$1012m$$. Then the maximum speed of the planet in $$km/s$$ is

$$dAdt=12r$$ω$$2=vr2$$⇒$$4$$×$$1016=v$$×$$2$$×$$10122$$⇒$$v=4$$×$$104m/s=40km/s$$

Gravitational force and laws

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A planet revolves about the sun in elliptical orbit. The areal velocity $(\frac{d A}{d t})$ of the planet is $4.0 \times 10^{16} m^{2} / s$ . The least distance between planet and the sun is $2 \times 10^{12} m$ . Then the maximum speed of the planet in km/s is

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Solution

$\begin{array}{l} \frac{d A}{d t} = \frac{1}{2} r ω^{2} = \frac{v r}{2} \\ \Rightarrow 4 \times 10^{16} = \frac{v \times 2 \times 10^{12}}{2} \\ \Rightarrow v = 4 \times 10^{4} m / s = 40 k m / s \end{array}$

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