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