Question 368: Gravitation

Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is

Accepted Answer

The orbital velocity near the surface of the earth
$$\mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$$
At an altitude $$\frac{R}{2}$$, the orbital velocity
$$\mathrm{V}^{\prime}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}+\frac{\mathrm{R}}{2}}}=\sqrt{\frac{2 \mathrm{GM}}{3 \mathrm{R}}} \quad 	herefore \frac{\mathrm{V}^{\prime}}{\mathrm{V}}=\sqrt{\frac{2}{3}} \quad 	ext { or } \quad \mathrm{V}^{\prime}=\sqrt{\frac{2}{3}} \mathrm{~V}
$$

Answer

$$\frac{3}{2}$$V

Answer

$$\sqrt{\frac{3}{2}}$$V

Answer

$$\sqrt{\frac{2}{3}}$$V

Answer

$$\frac{2}{3}$$V

Gravitation

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is

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