Question

If a graph is plotted between $T^2$ and $r^3$ for a planet, then its slope will be

• A. $\frac{4{\pi }^2}{GM}$
• B. $\frac{GM}{4{\pi }^2}$
• C. $4\pi GM$
• D. $zero$

Answer 1

The correct option is A $\frac{4{\pi }^2}{GM}$

Time period of a planet is given as
$T^2=\frac{4{\pi }^2}{GM}{r}^3$
This is of the form $y=mx$ where $m$ is the slope of the line.
Hence, the slope of graph of $T^2$ against $r^3$ is $\frac{4{\pi }^2}{GM}$