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.
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.
Bruce
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