# Re: John K. Clark

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On Thursday, May 5, 2022 at 10:43:14 PM UTC-6 Alan Grayson wrote:```
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> 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.
> 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

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