The Universal Gravitational Constant ($G$) is defined by Newton's Law of Gravitation: $F = G \frac{m_1 m_2}{r^2}$.

1. Rearranging for G: $G = \frac{F \times r^2}{m_1 \times m_2}$

2. Dimensional Analysis: Force ($F$) = Mass $\times$ Acceleration = $[M] \times [LT^{-2}] = [MLT^{-2}]$ Distance ($r$) = $[L]$

• Mass ($m$) = $[M]$

3. Substituting Dimensions: $[G] = \frac{[MLT^{-2}] \times [L]^2}{[M] \times [M]}$ $[G] = \frac{[ML^3T^{-2}]}{[M^2]}$ $[G] = [M^{1-2} L^3 T^{-2}] = [M^{-1}L^3T^{-2}]$