Harry, You are touching on an important area that I am also contemplating. Your frictionless, smooth, planet provides a constraint to the motion of a disk on its surface. It is a real (physical) constraint, independent of frame of reference and disk velocity. What about the nuclear hard core or the centrifugal force? The centrifugal force is frame dependent and only provides a virtual potential. I don't know if the nuclear hard core has been adequately defined yet.
However, if your disk is traveling fast enough to not touch the surface and then slows down just enough to touch the surface, then its interaction with a "weight-measuring" device would indicate it to have no weight prior to touch down and a very small weight afterward. In GR, a small deviation from a geodesic (where "weight" would be zero) would result in a small restoring force. Thus, as the disk slows down, its geodesic changes. If the planet surface prevents the alteration of the disk's path to follow the changing geodesic, then it experiences a slight force from the attempt to alter the path to get the disk back to its geodesic. This small force on a measuring device would certainly not correspond to the weight of the disk if it were stationary on the surface. Andrew On Thu, Jan 23, 2020 at 12:01 PM H LV <hveeder...@gmail.com> wrote: > I don`t think it matters if the planet is rotating since the surface is > frictionless. > > Of course measuring a change of weight in the real world that is > exclusively due to the rotation of earth is complicated by many variables. > The link you provided on the reactive centrifugal force could be one of > those variables as well as the coriolis force. If a spring balance is used > to measure weight, wouldn't the length of an unloaded spring be affected by > the rotation? If so they could give the impression of weight change when > the spring is loaded. > > Harry > > > On Thu, Jan 23, 2020 at 8:19 AM Andrew Meulenberg <mules...@gmail.com> > wrote: > >> >> 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 >>> >>
