Force: Gravity

Newton's Law of Universal Gravitation Any two objects have a gravitational force upon each other The force of attraction between two masses is proportional to the product of their masses, and inversely proportional to the square of the distance between them

This formula can be modified slightly, by getting rid of the proportional sign, and multiplying by a constant, as in this diagram G = universal constant of gravitation =  6.673 × 10⁻¹¹ N m²/ kg²

The force is always attractive The size of the force is the same on each body The force is tiny unless at least one of the masses involved is huge, i.e. a planet or star

Acceleration Due to Gravity The acceleration experienced by a body in free fall within the gravitational filed of a massive body All bodies fall to earth with the same initial acceleration Air resistance provides an opposing force that reduces the acceleration  On Earth, the acceleration due to gravity is roughly 9.8 m/s²

Relationship Between Acceleration due to Gravity and the Mass and Radius of a PlanetDerivation Based on Newton's law of universal gravitation: F = (GMm)/ d² { G = universal constant, M = mass of planet, m = mass of object, d = distance of object from centre of gravity of planet } Substituting 'mg' for F, since the force is the weight, and weight = mg : mg = (GMm)/ R² { d = radius of planet = R} Divide both sides by m : g = GM/R²

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