EC said: "Gravity is tricky. Its force is proportional to the two masses, yet the acceleration is equal for any two bodies. If F did not = Mass*Accel., this would not be true. The greater mass creates a greater force, that cannot if the force is as the mass, be greater per unit mass, for any body"
Nothing strange really.
The force of gravity between two bodies = G*M*m/(R*R) (Eq. 1)
Where G is a constant, M is the mass of the larger body, m the mass of the smaller body and R the distance between their centres.
Also, F = m*a. according to Newton. So acceleration is F/m.
So the accelaration of the smaller body towards the larger body is arrived at by taking the first equation for F above and dividing it by m to give:
a = G*M/(R*R), to get the acceleration of the smaller body.
The mass of the small body disappears from the equation for acceleration, thus all bodies relative to any given M (earth) and distance (relative to the centre of the earth) will give the same acceleration. In other words, the inertia of a body cancels the effect of the larger force of gravity when acceleration is calculated.
On the moon, where M is smaller, the acceleration is smaller. At the top of Everest, where R is greater than at sea level, acceleration of a body is less than at sea level.
So nothing really mysterious at all. |
