We experience gravity every waking moment, so it’s hard to recognize just how strange the gravitational ‘force’ actually is. Push a toy sailboat, a rowboat, and a yacht with the *same* amount of force (effort). What happens?

The smaller the boat, the faster it moves. Physicists would say the acceleration (change in velocity over time e.g. from the boat not moving at all to moving somewhat) is inversely proportional to the mass of the boat. This is Newton’s famous second law force = mass * acceleration. This isn’t actually what he said which you’ll find at the end.

So in every force except gravity, the bigger the force the more the acceleration. In Galileo’s famous experiment (which Wikipedia says might actually not have occurred), he dropped 2 objects of different masses from the leaning tower of Pisa and found that they hit the ground at the same time, so the acceleration of both due to the ‘force’ of gravity is the for all objects regardless of their different masses.

This implies that gravity is a force that adjusts itself to the mass of the object it is pushing on to produce the same acceleration. Weird, but true.

General relativity says, that the motion must be considered not just in space and time, but in 4 dimensional space-time where space can become our conventional time and vice versa. Here all paths are as straight as possible — because the 4 dimensional space-time we inhabit has an intrinsic curvature, produced by the masses found within it.

What Newton said: “The change of motion is proportional to the motive force impressed and is made in the direction of the straight line in which that force is impressed” By motion Newton means what we call momentum — mass * velocity.

The change in momentum is of course a change in velocity — which is what acceleration actually is. Note that mass is assumed constant regardless of how fast the object is moving. This isn’t even true in special relativity (which doesn’t include gravity — that’s what general relativity is all about).

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“Matter tells space how to curve. Space tells matter how to move.” – John Wheeler.