# If a graph is plotted between t^2 and r^3 for a planet then its slope will be:

If a graph is plotted between T2 and r3 for a planet then its slope will be (4π2/GMs), where Ms is the mass of the sun.

Explanation:

Time period of a planet around the Sun, to complete revolution, is:

$$T=\frac{2 \pi r}{v}=\frac{2 \pi r}{\sqrt{\frac{G M_{S}}{r}}}=\frac{2 \pi r^{3 / 2}}{\sqrt{G M_{S}}}$$

Now by squaring the time period we get;

T2 = 4π2r3/GMs

Thus, the slope between the graph T2 and r3 is 4π2/GMs.