Question

A satellite is revolving round the earth in an orbit of radius r with time period T. If the satellite is revolving round the earth in an orbit of radius $r+\Delta r(\Delta r<<r)$with time period $T+\Delta T(\Delta T<<T)$ then:

• A. $\frac{\Delta T}{T}=\frac{3}{2}\frac{\Delta r}{r}$
• B. $\frac{\Delta T}{T}=\frac{2}{3}\frac{\Delta r}{r}$
• C. $\frac{\Delta T}{T}=\frac{\Delta r}{r}$
• D. $\frac{\Delta T}{T}=-\frac{\Delta r}{r}$

Answer 1

The correct option is A $\frac{\Delta T}{T}=\frac{3}{2}\frac{\Delta r}{r}$

$T^2\propto r^3$
$2T\Delta T\propto 3r^2\Delta r$
$\frac{2\Delta T}{T}=\frac{3\Delta r}{r}$
$\frac{\Delta T}{T}=\frac{3\Delta r}{2r}$