[net.physics] A Thought Experiment

srk@teddy.UUCP (02/02/86)

Here is a thought experiment which occurred to me many years ago but which I
have never heard a good explanation for so I still find it intriguing - perhaps
some net-people can shed some light on this:

Assume there are two stars, A and B, of equal mass.  They are close enough to
have significant gravitational attraction, but far enough apart that it takes
light a week or two to travel from one to the other.  They are not in mutual
orbit but are approaching each other head on.  This is obviously not a stable
situation!

Star B undergoes supernova - a substantial part of its mass is converted to
energy and radiated away (at least let's assume it's substantial).  It is a
fast supernova, and it is all over before any light from the event reaches
star A.

At a safe distance, equidistant from both A and B, is an observer who decides
to measure these two stars immediately after the light from the supernova
passes his planet (he was watching a soap opera at the time...).  He measures
the mass and acceleration of both stars.

What will he see?

In particular, will he observe an acceleration of A towards B that is
inconsistent with the mass he measures for B?

If he keeps watching, will he see A decelerate slightly for no apparent reason?

This is because he is observing light which B emitted after its explosion and
light which A emitted before it could have been affected by the explosion.

On the other hand, if the observer's measurements are all consistent, doesn't
this imply that A was affected by the supernova sooner than possible?

						-- Stephen Klein

						...!decvax!genrad!panda!srk

gwyn@brl-tgr.UUCP (02/04/86)

> At a safe distance, equidistant from both A and B, is an observer who decides
> to measure these two stars immediately after the light from the supernova
> passes his planet (he was watching a soap opera at the time...).  He measures
> the mass and acceleration of both stars.
> 
> What will he see?

How does he measure the mass and/or acceleration?

One correct answer is, whatever he measures will be consistent
with the general theory of relativity.

franka@mmintl.UUCP (Frank Adams) (02/04/86)

In article <2026@teddy.UUCP> srk@teddy.UUCP writes:
>Assume there are two stars, A and B, of equal mass.  They are close enough to
>have significant gravitational attraction, but far enough apart that it takes
>light a week or two to travel from one to the other.
>
>Star B undergoes supernova - a substantial part of its mass is converted to
>energy and radiated away.  It is a fast supernova, and it is all over before
>any light from the event reaches star A.
>
>At a safe distance, equidistant from both A and B, is an observer who decides
>to measure these two stars immediately after the light from the supernova
>passes his planet (he was watching a soap opera at the time...).  He measures
>the mass and acceleration of both stars.
>
>What will he see?
>
>In particular, will he observe an acceleration of A towards B that is
>inconsistent with the mass he measures for B?

Right.  Until there is time for light to get from B to A, and then to him,
he will see A accelerate towards B based on B's old mass.

Actually, A will accelerate towards B at B's old mass until a significant
fraction of the mass blown off of B is further away from B than A is.
The mass doesn't cease to exist when it stops being part of a star.
(This last is assuming that the mass lost by B is distributed evenly
in all directions.  If it is not, A may accelerate faster or slower, though
it will require a sizable fraction coming near it to make much difference.
A will still be completely unaffected until light from B has time to reach
it.)

Frank Adams                           ihpn4!philabs!pwa-b!mmintl!franka
Multimate International    52 Oakland Ave North    E. Hartford, CT 06108

ethan@utastro.UUCP (02/05/86)

In article <2026@teddy.UUCP>, srk@teddy.UUCP writes:
> 
> Assume there are two stars, A and B, of equal mass.  They are close enough to
> have significant gravitational attraction, but far enough apart that it takes
> light a week or two to travel from one to the other.  They are not in mutual
> orbit but are approaching each other head on.
> 
> Star B undergoes supernova - a substantial part of its mass is converted to
> energy and radiated away (at least let's assume it's substantial).  It is a
> fast supernova, and it is all over before any light from the event reaches
> star A.
> 
> At a safe distance, equidistant from both A and B, is an observer who decides
> to measure these two stars immediately after the light from the supernova
> passes his planet (he was watching a soap opera at the time...).  He measures
> the mass and acceleration of both stars.
> 
> What will he see?
> 
The gravitational field will propagate changes in its structure at the speed
of light.  To do this problem in gory detail would require GR, but we can
simply use a modified form of Newton's law in which the field disturbances
propagate at the speed of light to get a rough idea of what goes on.

If the distribution of mass and radiation around star B remains spherically
symmetric then the perceived gravitational field due to B will be the mass
and *energy* interior to the position of the observer.  Once the radiation
(and other ejecta) start to pass the radius of the observer then she will
perceive a drop in the gravitational force due to B.  Assuming A is farther
away than she is, she will notice that A is reacting to more mass than she
is and will conclude (correctly) that there is a distribution of energy/mass
surrounding B a significant amount of which is between the radius of the
observer and the radial distance to A.  After some time the acceleration of
A will drop and she will conclude (correctly) that the ejected mass and
radiation has continued to move outward.
-- 
"These are not the opinions    Ethan Vishniac
 of the administration of      {charm,ut-sally,ut-ngp,noao}!utastro!ethan
 the University of Texas,      ethan@astro.UTEXAS.EDU
 but they are the opinions     Department of Astronomy
 of your favorite deity, who   University of Texas
 is in daily communication 
 with me on this (and every 
 other) topic. 

matt@utastro.UUCP (Matt Wood) (02/06/86)

In article <2026@teddy.UUCP>, srk@teddy.UUCP writes:
> Assume there are two stars, A and B, of equal mass.  They are close enough to
> have significant gravitational attraction, but far enough apart that it takes
> light a week or two to travel from one to the other.  They are not in mutual
> orbit but are approaching each other head on.  This is obviously not a stable
> situation!
> 
> Star B undergoes supernova.
> 
> At a safe distance, equidistant from both A and B, is an observer who decides
> to measure these two stars immediately after the light from the supernova
> passes his planet (he was watching a soap opera at the time...).  He measures
> the mass and acceleration of both stars.
> 
> What will he see?
> 
While the supernova is bright, it will shine about as brightly as the rest
of the stars in the galaxy.  A "safe distance" from such an event is about
10 light years, so if the stars a one light week apart, 
he'd probably see a single point of light.
Now if we assume that we've got this great shielding on our ship and could
get in close (~1 light year, this would give us good angular resolution),
then roughly one year and 1 month after the explosion we'd see this shell
of gas racing towards us at ~30,000 km/s.  

Seriously though, Ethan Vishniac gave you the theoretically-"correct"
answer that I'll bet you were looking for, that ejecta already past
star A will no longer affect the mechanics of the system.  In fact,
since after a year we'll observe the ejecta to be well past star A,
we might note that A is no longer accelerating at all
noticably, unless B left behind a newborn neutron star.

-- 
		Matt A. Wood 
		Astronomy Dept, University of Texas, Austin TX 78712  
		{allegra,ihnp4}!{ut-sally,noao}!utastro!matt	(UUCP)
		matt@astro.UTEXAS.EDU.				(Internet)

dgary@ecsvax.UUCP (D Gary Grady) (02/07/86)

In article <2153@brl-tgr.ARPA> gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) writes:
>One correct answer is, whatever he measures will be consistent
>with the general theory of relativity.

What a pity!  If it weren't, the observer would surely get a publication
out of it!  :-)
-- 
D Gary Grady
Duke U Comp Center, Durham, NC  27706
(919) 684-3695
USENET:  {seismo,decvax,ihnp4,akgua,etc.}!mcnc!ecsvax!dgary