Re: Gravity Question


OG wrote:
"Martin Brown" <|||newspam|||@nezumi.demon.co.uk> wrote in message
news:1156839414.327802.195560@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

OG wrote:
"Mark McIntyre" <markmcintyre@xxxxxxxxxxx> wrote in message
news:enl6f21njsb4a9qmg0h86g2to4td4dik47@xxxxxxxxxx
On Mon, 28 Aug 2006 20:03:29 GMT, in uk.sci.astronomy , "Pete"
<petenfay@xxxxxxxxxxxxxxxx> wrote:

If the Sun vanished in an instant would all the orbiting objects
instantly
fly off into the universe or would they fly off one by one starting
with
the
nearest one to the Sun. Newtonian gravity or special relativity?

Neither. Only GR can handle this question.

I agree. Newtonian mechanics and special relativity do not mix well.
The crucial point here is that unless gravity acts instantaneously in
the Newtonian world view we would see the planets spiralling into the
sun since they would always feel a retarding force from the place where
the sun was a time R/c ago (where R is the planets orbital distance
from the sun). This is demonstrably not the case. The force or gravity
is always exactly a radial one.

SR is not sufficient to handle gravitation reliably.

My
understanding is that it is propagated at a maximum speed of c; so
everything would head off at a tangent to its orbit only as the
information
that the Sun no longer existed reached them. i.e. their movement changed
at
the moment that it became evident the sun had disappeared. The tricky
part
would be confirming whether this actually happened or not.

We can rule this out because in Newtonian dynamics the planets behave
exactly as if the force of gravity is propogated instantaneously.

We can certainly rule out Newtonian dynamics, but we knew that already.

The GR interpretation is that space-time itself is curved so that
nothing moves between the sun and planet to acheive this result.
Planets follow a natural shortest path. If you were able to make the
sun disappear totally you would violate so many other laws of physics
that all bets are off.

Thought experiment
If we had a very massive particle and its antiparticle close together but
kept apart (exercise for the reader); at sufficient distance from their
barycentre they would (to first order measurements) distort space as though
a single mass, and the motion of a test particle would be evidence of the
mass of the pair.

So far so good. But there are some minor practical problems with this
scenario. You have just described a form of gamma ray burster - one of
the most violently luminous objects known in the universe. They make a
supernova explosion look like a picnic!

Now let the two particles annihilate each other producing a spherical shell
of Gamma rays which move out at speed c. The question being asked above is
when does the test particle's 'natural path' change from curving around the
' central mass' to movement in a 'straight' line.

It never really gets the chance. The total annihilation of two solar
mass objects into energy will create a flash of gamma rays so bright it
will illuminate the nearest stars with a flux roughly equivalent to
standing next to a nuclear weapon detonation. If my quick back of the
envelope calculation is right...

The planest would be turned to plasma or possibly at such short range
quark soup before they had any chance to respond. And even if they were
indestructible ideal test planets the forces from the outgoing radition
shockwave would be enormous.

My understanding of GR is that its the mass/energy metric that determines
the curvature of the metric, so the curvature at the location of the test
particle doesn't change until the gamma rays propagate to the distance of
the test particle; i.e. while the energy is 'inside' the orbit, the orbit is
as if the mass is at the centre, but as soon as the energy is outside the
orbit, the space is flat within the sphere.

I agree. But it is the time taken for the mass-energy to get out of the
enclosing orbit that makes the difference. The critical question would
be did a gravity wave detector on the Earth stop registering gravity
waves 8 minutes before it was turned into plasma or not.

My instinct is that changes in the gravitational field have to
propogate at light speed. I believe it was experimentally measured by
Ed Formalont et Al at NRAO in 2002.

http://www.newscientist.com/article.ns?id=dn3232

Ergo - the situation as described in the OP would be as though gravity
propagates at speed c.

Changes in gravity do in GR. But to make classical mechanics work you
must have an instantaneous gravitational central force. It is when you
try and mix ideas from the two differnt world views that you have
potential for confusion.

http://www.newscientist.com/article/mg17723774.600-how-fast-is-gravity.html

Answers the OP question in reasonable form but you need a New Sceintist
subscription to access the full article, The summary still isn't bad
though.

I would be very scared of any aliens with the technology to make suns
disappear magically without any trace. Shades of an intergalactic David
Copperfield trick anyone?

Regards,
Martin Brown

.