A planet revolves about the sun in an elliptical orbit of semi-major axis 2 × 10 12 m . The areal velocity of the planet when it is nearest to the sun is 4 .4 × 10 16 m 2 s - 1 . If the least distance

Question

A planet revolves about the sun in an elliptical orbit of semi-major axis 2 × 10 12 m . The areal velocity of the planet when it is nearest to the sun is 4 .4 × 10 16 m 2 s - 1 . If the least distance between the planet and the sun is 1 .8 × 10 12 m , then the minimum speed of the planet is

TestHub · Accepted Answer

The areal velocity of a planet around the sun is

$\frac{d A}{d t} = \frac{L}{2 m}$ , where $L$ is the angular momentum of the planet around the sun and $m$ is its mass.

$4.4 \times 10^{16} = \frac{m v_{\min} r_{\max}}{2 m}$

$2 \times 4.4 \times 10^{16} = v_{\min} (4 \times 10^{12} - 1.8 \times 10^{12})$

$v_{\min} = 40 km s^{- 1}$

Physics - Gravitation Question with Solution | TestHub

Options:

Doubts & Discussion