Question

An artificial satellite revolves around earth in circular orbit of radius r with time period of orbit T. The satellite is made to stop in the orbit which makes it fall into earth. Time of fall of the satellite onto earth is given by

• A. $\sqrt3\frac{T}{6}$
• B. $\frac{\sqrt2}{8}T$
• C. $\frac{T}{\sqrt3}$
• D. $\sqrt\frac{2}{3}\frac{T}{\pi}$

Answer 1

Answer: (B)

$\frac{\sqrt2}{8}T$

Answer 2

On stopping, the satellite will fall along the radius r of the orbit which can be regarded as a limiting case of an ellipse with semi major axis equal to $\frac{r}{2}$ Using Keple's third law $T^2 \infty r^3$ time of fall = $\frac{T}{2} = \frac{T}{2 \sqrt{8}} = \frac{\sqrt{2}T}{8}$