On Mon, Jan 13, 2020 at 10:15 AM H LV <[email protected]> wrote: > This is an illustration from Newton's Principia of his famous cannon > thought experiment. It shows how a cannonball fired horizontally from a > mountain top (assuming no air resistance) will orbit the Earth without > falling to the ground if it is fired with sufficient speed. > https://imgur.com/gallery/dzSLWaa > > Now imagine an ice covered planet which is perfectly smooth, with no > mountains or valleys. On the surface rests a curling stone of a given > _weight_. If the curling stone is propelled horizontally with sufficient > speed it will orbit the planet while sliding over the surface. At this > velocity it will be in free fall so its weight will be effectively zero. > The question is does the weight of the curling stone gradually increase as > the horizontal velocity gradually decreases or does the curling stone > resume its full weight for any velocity less than the orbital velocity? > > Harry >
To answer my own question... the classical prediction is the weight of the stone should increase, because the centrifugal force is decreasing in the frame of reference of the stone. However, if gravity in General Relativity is not a force then a corresponding a centrifugal force does not arise. Therefore, if GR is true, the weight of the stone should jump to its full weight for any value less than the orbital speed. (Actually I think there is argument to be made that even Newtonian gravity is not a force and is just an acceleration). Harry
