On Thursday, May 5, 2022 at 9:05:47 PM UTC-6 meeke...@gmail.com wrote:

> On 5/5/2022 6:04 PM, Bruce Kellett wrote:
> On Fri, May 6, 2022 at 10:45 AM Brent Meeker <meeke...@gmail.com> 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. 

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