Paper Title
Secular Long Periodic and High Frequency Semi Major Axis Time Rates of Change Due to Emission of Gravitational Radiation

Abstract
For a two-body system, we derive expressions for the secular, long periodic and high frequency effects caused on to the semi-major axis of the secondary body due to the emission of gravitational waves. This is possible by considering the time rate of change of the total energy of the system, and substituting for the energy loss due the emission of gravitational waves. Next, we convert the time rate of change of the semimajor axis as a function of the orbital elements using standard a celestial mechanics approach, where the inverse powers or the orbital radial vector r is written as a function of the orbital elements with the help of the eccentricity functions G(e). We apply our result to Mercury/Sun system, and the secular time rate of change of the semi-major axis has been found to be the order -1.66010-12 m/y. In the case where the primary is a super massive black hole (SBH) the secular semimajor axis time rate of change of the secondary of eccentricity 0.9 is equal to -23 m/y. In the case of Mercury/Sun, this secular change is an extremely small and it cannot be easily detected by today’s Earth based technology. The secular rate change related to the SBH, can be probably detected by a future space technology. Therefore, such two-body system where the primary has mass equal to that of the Sun does not really constitute a good candidate for observing the quadrupole radiation effects on the semimajor of the orbital body. On the other hand, SBH will constitute better candidates if new space-based technologies are to be in effect in the nearest future.