6 Kepler's Third Law of planetary motion for the period of a circular orbit around the Earth is given by the formula, $$t = 2 \pi \sqrt { \frac { r ^ { 3 } } { G m } }$$ where,
\(t\) is the time taken for one orbit
\(r\) is the radius of the circular orbit
\(m\) is the mass of the Earth
\(G\) is a gravitational constant. Use dimensional analysis to determine the dimensions of \(G\)
\includegraphics[max width=\textwidth, alt={}, center]{ce05dedd-515b-49e2-92f3-f5ec22bab4be-08_2491_1755_173_123}