Sir Isaac Newton discovered that any two masses m, and m, attract each other with a force that is equal in magnitude and acts in the opposite direction, according to the relationship: Gm, m, F = r2 where F = attractive force (N) G= Universal Gravitational Constant m, = mass of particle – 1 (kg) m, = mass of particle – 2 (kg) r – distance between the center of each particle (m) What are the appropriate units for G, if the preceding equation is to be homogeneous in units?

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.