Markus Schwarz wrote:
Markus Schwarz wrote:
when simulating the orbit of stars in a galaxy, do retardation effects need to be taken into account? The time dependent gravitational field of a accelerating mass can only propagate at the speed of light, and would take about a year (on average) to reach the nearest star. A similar reason would also apply to the solar system (distance sun-neptune 4 light hours). As far as I know, these retardation effects are not taken into account. Does anyone know the reason why?
Stars orbit the center of the galaxy in more-or-less elliptical orbits, hence they are constantly accelerated. And since the size of a galaxy extends over 100 light years, I wonder if one should take retardation effects into account as well.
I am think along the lines of classical electrodynamics: the Coulomb field of an electric field is static and extends infinitely in space (with decreasing magnitude, of course). But once the charge accelerates, the information that the location of the charge has changed can only propagate at the speed of light. This means that an observer always detects the retarded field of the charge.
The Newtonian gravitational field of a star behaves in the same way as the Coulomb field of an electric charge. Even though the time dependence is described by Einstein's equations instead of Maxwell's, by causality, the effect of an accelerating source can only propagate at the speed of light.
The Earth responses gravitationally to where it thinks
the Sun is now and NOT
to where the Sun was sitting 8 minutes ago. If the Earth responded gravitationally to where the Sun was sitting 8 minutes ago then the Earth would be constantly accelerated forward and spiral out of the Solar System. The Earth doesn't seem to do that.
The classic example of retarded Einsteinian gravitational interaction is what happens if the Sun were to suddenly disappear. As you probably already know: the Earth would continue to orbit (in a helical ellipse
) to the old (moving!
) position of the Sun for 8 minutes until a powerful gravitational signal finally reaches the Earth at which point the Earth would fly off into space along a straight line.
The Einsteinian gravitational field of a star behaves in the same way as the Maxwell field of an electric charge in that one sometimes
has to take into account 1) relativistic effects and/or 2) the propagation of waves.
However, the vast majority of many-body gravitational simulations are 1) highly non
relativistic and 2) the propagation of gravitational waves in them is negligible. Inaccuracies in the calculations come rather from dynamic computer algorithm digital approximations such as round off error and chaos.