Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20th century. However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings, asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.

Short-Period and Long-Period Effects of Weak Gravitational Waves

We compute the long-term orbital variation of a test particle orbiting a central body acted upon by normal incident of plane gravitational wave. We use the tools of celestial mechanics to give the first order solution of canonical equations of long-period and short-period terms of the perturbed Hamiltonian of gravitational waves. We consider normal incident of plane gravitational wave and characteristic size of bound—two body system (earth’s satellite or planet) is much smaller than the wavelength of the wave and the wave’s frequency nw is much smaller than the particle’s orbital np. We construct the Hamiltonian of the gravitational waves in terms of the canonical variables (l,g,h,L,G,H)?and we solve the canonical equations numerically using Runge-Kutta fourth order method using language MATHEMATICA V10. Taking Jupiter as practical example we found that there are long period perturbations on ω,Ωand i?and not changing with revolution and the short period perturbations on a, e and M?changing with revolution during the interval of time (t−t0 ) which is changing from 0→4π.

Numerical Studies of Resonance and Secular Effects of Gravitational Waves

This work deals with the numerical solution of the gravitational waves effects on the orbital elements of the planets in case of commensurability between the wave’s frequency ng and the planet’s mean motion np. Taking Mercury and Pluto as practical examples for low frequency and high frequency, the variations of the orbital elements of Mercury due to resonance of gravitational wave are different and small than the perturbation on Pluto. The amount of changing in the orbital elements under the effects of gravitational waves is different from planet to planet according to the planet’s mean motion np. For low frequency ng, the secular variation in orbital elements will be negative (i.e. decreasing) in the inclination, semi-major axis and the eccentricity (i, a, e) like as Pluto. For high frequency ng like Mercury, the secular variation in all the orbital elements will be positive (i.e. increasing). The perturbation on all the orbital elements of two planets is changing during each revolution except the eccentricity e of Mercury and the mean anomaly M of Mercury and Pluto during the time.

Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits

For certain values of semi-major axis and eccentricity, orbit plane precession caused by Earth oblate is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Many forces cause slow changes in the inclination and ascending node of sun-synchronous orbits. In this work, we investigate the analytical perturbations due to the direct solar radiation pressure and gravitational waves effects. A full analytical solution is obtained using technique of canonical Lie-transformation up to the order three in (the oblateness of the Earth). The solar radiation pressure and gravitational waves perturbations cause second order effects on all the elements of the elliptic orbit (the eccentricity, inclination, ascending node, argument of perigee, and semi-major axis) consequently these perturbations will cause disturbance in the sun-synchronism. Also we found that the perturbation or the behavior of gravitational waves almost the same as the perturbation or the behavior of solar radiation pressure and their coupling will incorporate the sun-synchronism through the secular rate of the ascending node precession.

The secular effect of gravitational radiation damping on the periastronadvance of binary stars in second order perturbation theory

The second order perturbation effect of gravitational radiation damping on the periastron advance of binary stars is studied.The second order analytic solution is obtained based on the first order theory in the 2014 article by Li.Theoretical results show that secular variation exists in the periastron advance of binary stars in the second order theory,but secular variation does not exist in the first order perturbation theory.Numerical results for two compact binary stars(PSR J0737–3039 and M33 X-7)are given,demonstrating the theoretical significance even though the effect is very small.