Right. - Bodies accelerate and fall towards a gravity field (vacuum) with the same speed..
This happens even though the pull of gravity affects the canon ball with much greater attraction than it effect the football.
The cause of this factum is it self really a mystery, - we have no idea of why this is so.
Intuitive we would expect that the canon ball would fall faster, - but it’s not what happens.
Imaging a football and a canon ball falling down to earth from let say only 1 meters height.
Its not “space enough” for believing that the cause of these bodies both fall with the same speed, (on that short distance) is due to curvature of space.
Both bodies follow a straight line and are not affected of the curvature of space. – So how can the curvature of space in this particular example be the cause of gravity? - It’s simple make no sense.
What we do know is that it requires more force to lift a canon ball to 1 meter height as it require to lift a football to same height.
The canon ball will in this position have greater potential energy. If we accelerate the football and the canon ball up to both 100 MPH (1 meter above the surface of earth) the canon ball still will have greater potential energy.
Let’s say that that the size of the canon ball and the football is the same, wind resistance is therefore also the same.
If we should be able to explain gravity based on curvature of space, - the football as well as the canon ball (moving with 100 MPH) would hit the earth’s surface simultaneously, - but this is not what happens.
The explanation is of course, - the canon balls have greater potential energy proportion to the earth. – It is this FORCE involved that pull down the canon ball first.
So based on simple everyday’s observation gravity seems to be a FORCE. – On the other hand we can not close our eyes for the fact that the curvature of space ALSO seems parts of the gravity phenomena.
But attempt to implement this aspect in a complete and coherent way is: 'the end of the known road'; - from here we are forced into philosophically considerations.
So far we have not been able to archive any kind of coherent understanding to why we can say we have two independent (and both pretty good) theories for the same gravity phenomena. Common for these 2 theories is that we do not understand on the one hand why space curves, and on the other hand from where does the 'well known' FORCE come from, and how does it occour.
Well, - it seems to be a broad hint build in, - matter must be responsible / the origin for this force, - Could this force also be responsible for space to curve? – Or why do space curve? - What does 'curvature of space' really mean? - I mean think about a game-roulet, - it is something physical we know - but this is not the way space is? - What is space? - What's its nature?