On Thursday, May 5, 2022 at 10:43:14 PM UTC-6 Alan Grayson wrote:
> On Thursday, May 5, 2022 at 9:05:47 PM UTC-6 [email protected] wrote: > >> >> >> On 5/5/2022 6:04 PM, Bruce Kellett wrote: >> >> On Fri, May 6, 2022 at 10:45 AM Brent Meeker <[email protected]> wrote: >> >>> If the mass-energy of the Sun is halved, then for the Earth to continue >>> in the same orbital path, it's mass-energy must also be halved. The >>> period, a year, will go up by a factor of sqrt(2). Will the SI definition >>> of the second also go up by sqrt(2)? I think so. But if the Earth is >>> slower in the same orbit, the measurements of the speed of light by stellar >>> aberration will change. >>> >> >> The problem I see is that orbital mechanics depend on the product of the >> masses, not the ratio, so if the energy (and masses) halve, the orbits must >> change. For example, the energy of the earth in orbit is the sum of the >> gravitational and potential energies: >> >> E_T = KE +PE = I/2 mv^2 - GMm/r = GMm/(2r) - GMm/r = -GMm/(2r), >> >> where M is the mass of the sun, m is the mass of the earth, and r the >> earth-sun distance. We note that the total energy is negative. If the total >> energy is to halve, the radius must change since Mm/(2r) is divided by 4, >> not 2. In other words, the radius of the orbit must also halve. If the KE >> simply halves, the velocity will remain the same. But if the orbit changes, >> the velocity must change also. >> >> >> To a good approximation the mass of the Earth doesn't matter. Whatever >> it's mass, it can continue in the same radius orbit if the Sun's mass is >> halved and it's speed is reduced by a factor of 1/sqrt(2). There's more >> than one way to halve the energy and you're trying do it changing r and >> keeping v the same...which would certainly be noticeable to move closer to >> the Sun. The way I see it is to keep the same orbital path at a lower >> speed...which is measureable by the change in stellar abberation, event if >> atomic clocks tick slower because of the energy change. >> >> >> >> The problems are magnified when we consider the potential energy of a >> mass lifted from the surface of the earth: >> PE = mgh. Now g = GM/(r^2), so it halves along with the mass m. So mgh is >> reduced by a factor of 4 unless the height doubles in order for the PE to >> change only by a factor of two. I think these effects would be very >> noticeable, so the idea that one can halve the energy in a branch without >> causing any changes within the branch is just a nonsense. >> >> The idea that the SI definition of the second will also change to >> compensate other changes is as silly a notion as one could imagine. >> >> >> It's determined by the energy difference of two levels of the cesium >> atom. Why wouldn't it change? >> >> Brent >> > > Thanks for these replies. I intuited that Clark's scenario must be wrong > since after not too many splits, gravity is gone and so will closed orbits. > AG > Not that it matters, but Sean will be moving to JohnS Hopkins on July 1, 2022. In my quest for perfection, I looked up references to that university, and the first one, which I posted, got it WRONG, leaving out the S at the end of "John". AG -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/12d01a6f-2e6a-466e-a83a-2995443a829dn%40googlegroups.com.
