Chapter 7, Problem 33A

To determine

The change in the ratio $\frac{T^2}{r^3}$ if the mass of the Sun were doubled.

Answer to Problem 33A

No change

Explanation of Solution

Introduction:

Kepler’s Third Law,

  ${\left(\frac{T_A}{T_B}\right)}^2={\left(\frac{r_A}{r_B}\right)}^3$

Where $T_A$ and $T_B$ are the periods of the planets A and B around the Sun, and $r_A$ and $r_B$ are their average distances from the Sun.

As can be seen from above mentioned Kepler’s law, the ratio $\frac{T^2}{r^3}$ always remains constant and is independent of the mass of the Sun.

Conclusion:

Thus, the ratio $\frac{T^2}{r^3}$ will not be changed if the mass of the Sun were doubled.