The Evolution of the Dust Screen Near the Inner Photogravitational Libration Point of the Sun-Earth System ALEXANDER VSHIVTSEV*, VICTOR ORLOV** Summary: The equation of the motion of the dust particles in the photogravitational circular restricted three-body problem with the account of Poynting- Robertson effect have been derived and numerically studied for the motion near the inner libration point in the Sun-Earth system. The general properties of this motion have been established. The schemes of the some particles trajectories are given. The use of the dust screen to decrease the solar radiation incident on Earth was found unreal. The realization of such a screen is possible in case of the regular refreshment of dust in the libration point. Recently the problem of diminishing the Earth's insolation and of avoiding it's overheating due to the greenhouse effect attracted attention of many researchers [1-3]. Thus, M. Mautner [1] suggested to use a space screen in the form of a film or dust belt in orbit around the Earth. J. Early [2] gave the idea of thin glass shield built from lunar material and located near the inner Lagrange point L] of the Sun-Earth system. In the present paper the possibility of dust screen existence near L[ are examined. The equation of the motion Let us examine two bodies S and J which have spherical symmetric distribution of the masses and are revolving on the circular orbits around the common inertia center O. Let Mj and M2 be the masses of the bodies S and J accordingly, ® is the angular velocity of the rotating. Let us examine the motion of the particle P with a very small mass m in the rotating barycentric coordinate system (i.e. the center of gravity is at 0,0,0). The axis X is directed from S to J, the axis is Y to the apex of the body J, the axis Z completes the system to the right one. Let the distance of the point P from the bodies S and J and the barycenter O be Rp R2, Rq accordingly. Then, let's assume (x,yz) to be the coordinates of the particle P, (xj,0,0,) the coordinates of S and (x2,0,0,) the coordinates of J in our system. If a is the constant distance between S and J then * The faculty of mathematics, Udmurt State University, Krasnogeroyskaya 71, 426034 Izhevsk, Russia) ** Astronomical Institute, St. Petersburg University, Russia
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