Harry, For your ice covered planet, you may need to indicate if it is rotating or not and then, depending on your frame of reference, address Coriolis forces.
This link addresses the weight at poles vs that at the equator. https://en.wikipedia.org/wiki/Centrifugal_force#Weight_of_an_object_at_the_poles_and_on_the_equator The difference between* centrifugal force* vs the *reactive* centrifugal force[41] <https://en.wikipedia.org/wiki/Centrifugal_force#cite_note-Bowser-41>[42] <https://en.wikipedia.org/wiki/Centrifugal_force#cite_note-Angelo-42> is interesting. https://en.wikipedia.org/wiki/Reactive_centrifugal_force#Difference_from_centrifugal_pseudoforce Andrew _ __ _ On Wed, Jan 22, 2020 at 11:30 PM H LV <hveeder...@gmail.com> wrote: > > 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 >
