Gravitational wave - Binaries (Orbital lifetime)

Description

Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light. They were first proposed by Henri Poincaré in 1905 and subsequently predicted in 1916 by Albert Einstein on the basis of his general theory of relativity. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton’s law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)—showing one of the ways the methods of classical physics are unable to explain phenomena associated with relativity.

Gravitational waves carry energy away from their sources and, in the case of orbiting bodies, this is associated with an inspiral or decrease in orbit.Imagine for example a simple system of two masses — such as the Earth–Sun system — moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the x–y plane.

Generally, the rate of orbital decay can be approximated by the shown formula solved for the time (t).

Related formulas

Variables

tOrbital lifetime (s)
cSpeed of light
GNewtonian constant of gravitation
r0initial distance between the orbiting bodies (m)
m1mass of body 1 in the binary system (kg)
m2mass of body 2 in the binary system (kg)