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The secular effects of the electric induction drag on the orbit of a charged satellite moving in the ionosphere are examined by the method of average values. The first solutions are obtained under the assumption of non-rotation of the Earth; the second solutions are obtained assuming rotation of the Earth. In the first case the semi-major axis exhibits secular variation, but the other orbital elements exhibit no secular variation. In the second case both semi-major axis and eccentricity exhibit secular variation, but the other orbital elements exhibit no secular variation. It can be shown that the semi-major axis is contracted due to the action of the electric induction drag if the satellite has enough charge in the ionosphere. The eccentricity is decreased gradually with time, but its variation is very small for the case of a rotating Earth. An example is presented in which the secular effects of the electric induction drag on the orbits of a charged satellite are calculated. The numerical results are given in Table 1 and a discussion of them is presented in Table 2.
Linsen Li (Tue,) studied this question.