An artificial satellite of mass m is revolving in a circualr orbit around a planet of mass M and radius R. If the radius of the orbit of satellite be r, then period of satellite is
`T= (2pi)/(R ) sqrt((r^3)/(g))`
Justify the relation using the method of dimensions.

Explanation

To justify the relation \( T = \frac{2\pi}{R} \sqrt{\frac{r^3}{g}} \) using the method of dimensions, we will follow these steps:

### Step 1: Identify the dimensions of the left-hand side (LHS)
The left-hand side of the equation is the period \( T \). The dimension of time \( T \) is given by:
\[ [T] = M^0 L^0 T^1 \]

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