Supernova gravitation field and Newton

[zankaon]

If a 10 solar mass star explodes, leaving behind a 5 solar mass black hole, and blowing off an idealized spherical symmetrical (5 solar mass) neutrino shell, would the gravitational field (i.e. curvature of manifold) change? http://en.wikipedia.org/wiki/Supernova

p.s. addendum: could Newton have determined that velocity of light was finite?

 

[K.J.Healey]

Depends on where you're talking about. Far outside = still Schwarzschild, inside is a 2 shell system of different mass/energy density/distribution/pressure.

 

[zankaon]

The gravitational field (curvature) of manifold patch, inside of outward expanding idealized spherical shell of matter, would be affected by newly formed 5 solar mass BH only. This is an example of Newton's First Theorem: A body inside a spherical shell of matter is not gravitationally affected by mass of such spherical shell i.e. no gravitational force is felt. So gravitational field has changed for inside of spherical shell of neutrinos. In contrast, a body outside of such spherical shell, would feel gravitational force (i.e. curvature) as if all of mass were concentrated at center of such spherical shell. Thus 10 solar mass gravitational effect. Hence curvature (i.e. gravitational force) has not changed for outside of such shell. The latter is an example of Newton's Second Theorem. See Shell Theorem. http://en.wikipedia.org/wiki/Shell_theory Realistically only about 10% (?) of mass is carried off by neutrino symmetrical expanding shell.

Also the change in distribution of mass would occur over a finite time (finite velocity); hence the gravitational field (i.e. curvature, deformation of manifold) would change over a finite time.

In regards to addendum: if Newton had been exposed to a clear ordinary glass with a spoon, stirrer etc. in it, his analytical mind probably would have surmised that velocity of light was finite; not infinite, since a change in velocity has occurred for a different medium.

 

[Jonathan Scott]

p.s. addendum: could Newton have determined that velocity of light was finite?

The Italian astronomer Cassini noticed that the times of the eclipses of Jupiter's moons seemed to vary by a few minutes depending on whether the Earth was on the near side or far side of its orbit, and published a short paper on this in 1675. The Danish astronomer Ole Roemer refined these measurements and published calculations which meant that one could estimate the speed of light in terms of the Astronomical Unit (roughly speaking the radius of the Earth's orbit) which was not yet determined, but had been given an approximate value by Cassini. That means that it would have been possible for Newton not only to be be aware that the speed of light was finite, but to have a reasonable idea of its magnitude.

 

[zankaon]

In regards to Cassini and Roemer - very interesting. http://en.wikipedia.org/wiki/Ole_R%C3%B8mer