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The rate of loss of orbital energy is simply the rate at the external force does negative work on the satellite as the satellite traverses an infinitesimal circular arc-length ds, spanned by some infinitesimal angle dθ and angular rate ω.
The orbit has decayed since the binary system was initially discovered, in precise agreement with the loss of energy due to gravitational waves described by Albert Einstein's general theory of relativity. [2] [10] [11] [12] The ratio of observed to predicted rate of orbital decay is calculated to be 0.997 ± 0.002. [12]
The specific orbital energy associated with this orbit is −29.6 MJ/kg: the potential energy is −59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg. Compared with the potential energy at the surface, which is −62.6 MJ/kg., the extra potential energy is 3.4 MJ/kg, and the total extra energy is 33.0 MJ/kg.
The rate of losing energy (averaged over a complete orbit) is given by [14] = (+) / (+ +) where e is the orbital eccentricity and a is the semimajor axis of the elliptical orbit. The angular brackets on the left-hand side of the equation represent the averaging over a single orbit.
Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.
In particular, the predictions for energy loss due to gravitational waves appear to match the theory. As a result of energy loss due to gravitational waves, the common orbit (roughly 800,000 kilometers [500,000 miles] in diameter) shrinks by 7 mm per day. The two components will coalesce in about 85 million years.
A space vehicle's flight is determined by application of Newton's second law of motion: =, where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement.
Stellar dynamics is the branch of astrophysics which describes in a statistical way the collective motions of stars subject to their mutual gravity.The essential difference from celestial mechanics is that the number of body