On Mon, Jan 13, 2020 at 12:21 PM H LV <[email protected]> wrote: > > > 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 >
Just a follow up. Since a body sitting at the equator is moving faster than the same body near the pole it should weigh less due to the greater centrifugal force caused by the Earth's rotation. Until recently I don't think anyone had tried to measure this predicted effect and it was just taken for granted to be true. (There have been tests on the equivalence of inertial mass and gravitational mass but this is a different test). However arguments between Flat-Earthers and Anti-Flat earthers have resulted in amateur empirical investigations of the matter. Flat Earther's contend the weight should be constant since they hold the earth is flat and does not rotate. The results so far seem to be open to interpretation. I am not a Flat- Earther but it is interersting how this fringe community has turned it into an empirical question. Harry
