On Fri, May 6, 2022 at 2:43 PM Alan Grayson <agrayson2...@gmail.com> wrote:

> 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.
It does matter for the kinetic energy (1/2)mv^2, although it cancels out
when you equate the gravitational acceleration to the centripetal
acceleration of a circular orbit.

> 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.
That is the trouble. When the energies change it is not clear that anything
can be kept fixed. You do have trouble with things like gravitational PE
near the earth's surface. mgh is hard to halve at a constant height.

  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.
I think we agree that however you cut it,  there are going to be noticeable
changes because we use secondary standards for things like distance and
time -- we do not refer everything to Caesium clocks (even if that is the


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