Answer to Question #139013 in Field Theory for Max

Question

Suppose we have made a model of the Solar system scaled down in the ratio but of materials of the same mean density as the actual materials of the planets and the Sun. How will the orbital periods of revolution of planetary models change in this case?

Answer 1

Solution

Time period can be given as

$T=\frac{2\pi R^{\frac{3}{2}}}{\sqrt{\gamma m_s}}$

$T\propto \frac{R^\frac{3}{2}}{\sqrt{m_s}}$

If scaled down ratio is $\eta$ then then $R^\frac{3}{2}$ Will be scaled by $\eta^\frac{3}{2}$ And $\sqrt{m_s}$ wil be scaled down as same ratio as the $R^\frac{3}{2}$ .

So time period will remain unchanged.

So time period will be

$T=\frac{2\pi R^{\frac{3}{2}}}{\sqrt{\gamma m_s}}$