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