Abstract
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.
Highlights
It is well known that the sun-synchronous orbits are useful for remote sensing mission, because the illumination of the sub satellite point is nearly constant on each successive pass
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
Since the relativistic generator W2*r depends on the angle variables ( L,G, H, g ), the solar radiation pressure generator W2*s depends on ( L,G, H, L4, g, h,l4 ) ; the generator of their joint effects W2*rs depends on ( L,G, H, L4, g, h,l4 ), and the generator of joint effect of solar radiation pressure and gravitational waves W2*sw depends on ( L,G, H, L4w, g, h,l4w ) we found that there is long-period perturbation in all elements of the orbit due to the relativistic effect, the solar radiation pressure effect, and the joint effect of solar radiation pressure and gravitational waves, except the semi-major axis
Summary
It is well known that the sun-synchronous orbits are useful for remote sensing mission, because the illumination of the sub satellite point (the point where a straight line drawn from a satellite to the center of the Earth intersects the Earth’s surface) is nearly constant on each successive pass. Since a sun-synchronous orbits follows the Sun, so the solar pressure perturbations cannot be neglected, if the orbit is un-shadowed, long period occur in all the orbital elements except semi-major axis [1] [2]. For certain value of semi-major axis and eccentricity orbit plane precession caused by oblateness is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Semi-analytical theory of the mean orbital motion due to the effect of gravitational waves is investigated by [6]. The solution is obtained up to order three and two in secular and periodic terms respectively assuming the effect of direct solar radiation pressure and the gravitational waves of the same order of magnitude and equal to the order of. J (the second order zonal harmonic of the geo potential i.e. 10−6)
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