In connection with ambiguity of the decision of return problems of gravimetry (RPG) very sharply there is a question on existence of absorption of a gravitational field (GF) by a substance. For definition of various factors as measures of absorption of a field some variants of direct problems of gravimetry (DPG) for sphere are solved. They are solved under formulas in which the field element under integral is increased on an exhibitor with an indicator in the form of distance product between a point of measurement of a field and an element of weight, its density and linear density factor (LDF) of absorption of the field, the taken for linear or nonlinear model in the first or second degree. For decision of RPG we theoretically received formulas of DPG which are equal to the experimental values of gravity which are measured on a pole or an equator. These equations are solved rather of LPG depending on the chosen model of absorption. In linear model for each density, more measured without field absorption, we have one positive value LPG which grows with increase in density of a planet and decreases with increase of its radius. In nonlinear model for any density of minor planets it is received three positive values of LPG and for big – only one that confirms the possibility of existence of the phenomenon of field absorption.

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