Newton's Law of Universal Gravitation

Consider two masses `m₁` and `m₂` separated by centre-to-centre distance `r`. The gravitational force is: F = Gm₁m₂/r² where: `F` = gravitational force `G` = universal gravitational constant `m₁, m₂` = interacting masses `r` = distance between their centres If either mass increases while all other quantities stay unchanged, gravitational force increases. For example: If `m₁` doubles: **F doubles**

Force varies as: **F ∝ 1r² Therefore: if distance doubles: F becomes F/4 if distance triples: F becomes F/9**

Gravitational force acts along the line joining the centres of the two masses. The forces on the two bodies have equal magnitude and opposite direction, in agreement with Newton’s third law.

**G ≈ 6.67 × 10⁻¹¹ N m² kg⁻²** It is called universal because the same gravitational law applies to masses throughout the universe in the Newtonian model.

**F = Gm₁m₂/r²**