Harry, I'm glad that people are reexamining models of the motion of trapped "bodies" on the surface of a "sphere".
Your comment about the varying weight density of the stone may touch on the explanation of the Goos-Hanchen and Imbert-Federov effects on total internal reflection at the optical level. https://en.wikipedia.org/wiki/Goos%E2%80%93H%C3%A4nchen_effect https://en.wikipedia.org/wiki/Imbert%E2%80%93Fedorov_effect I consider these effects to be important in the total-internal-reflection, bound-photon, model of the electron. Andrew _ _ _ On Fri, Jan 24, 2020 at 8:36 PM H LV <hveeder...@gmail.com> wrote: > Andrew, > > Andrew, > > This is amazing. I have been pondering what puts the curl into a curling > stone for over 15 years and this week my intuition has been bolstered by > letting the entire surface of a planet be a curling rink and reading about > the work of Eötvös. The physics of curling is a controversial area of > physics with competing theories. However, I don't think anyone has > considered what effect the rotation of the planet might have on the weight > of the stones as they move. > > I don't know about GR but some interesting things would happen if the disc > also spins as it slides over the surface like a curling stone on ice. > The weight-density of the disk will vary around it even if it is of > uniform mass-density. This because the contact velocity also varies around > the stone do to combination of its orbital and spin motion. If the surface > is frictionless but supple (not perfectly rigid) the reactionary force > around the disk will vary and be a maximum where the weight density is a > maximum which will result in a orbit that isn't a great circle. > Alternatively if the surface is perfectly rigid but does have friction this > could generate some non-circle paths as well before the disk comes to rest. > > Harry > > On Fri, Jan 24, 2020 at 2:06 PM Andrew Meulenberg <mules...@gmail.com> > wrote: > >> 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 >>>>> >>>>
