As a binary system start producing gravitational waves even before merge should the stars start losing mass while still orbiting each other? But is this really difficult to understand as just orbiting shouldn't take away material from the stars?
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
Stars falling on each other, as is the case with any two masses attracted to each other, change potential energy, which has a 1/r dependence, to kinetic energy, analogous mathematically to the change in potential energy to kinetic energy of two opposite charges falling on each other.
In the case of electromagnetism , Maxwell's equations show that the acceleration relative to each other produces electromagnetic waves,from the kinetic energy of the objects. Gravitational waves are analogous to the electromagnetic waves, the gravitational theory , General Relativity, is much more complicated .
The basic point is that the gravitational waves from the in-falling stars come from their kinetic energy, not from their invariant mass.
$\begingroup$
$\endgroup$
The energy radiated away by gravitational waves is taken from the energy of the orbit, not from the rest masses of the two stars.
The total energy (sum of kinetic and potential energy) of a bound, circular orbit is $-GM_1M_2/2a$, where $a$ is the separation of the two stars. This energy becomes more negative when gravitational waves are produced, by decreasing $a$.
