On Wed, Jan 22, 2020 at 4:46 PM H LV <hveeder...@gmail.com> wrote: > > > On Mon, Jan 13, 2020 at 12:21 PM H LV <hveeder...@gmail.com> wrote: > >> >> >> On Mon, Jan 13, 2020 at 10:15 AM H LV <hveeder...@gmail.com> 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 >
So it seems Eotvos in the first decade of the 1900s used Earth's rotation and centrifugal force to explain observed differences in some weights on ships moving in opposite directions. Until now I was only familiar with his work on the equivalence of gravitational and inertial mass in 1889. see https://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_effect
