Thetwin probe method, proposed by Bertotti and Colombo (1972) to get rid of nongravitational forces in interplanetary space, can be applied to a near-Earth orbit to eliminate the atmospheric drag. Two equal pairs of probes, each pair consisting of two passive, small and dense spheres of equal surface and different masses, are flown on a circular orbit at an altitude of about 300 km. Each pair determines the motion of an ideal point which feels only the gravitational forces. They are separated by a distanced of (100÷200) km and are tracked from a spacecraft or the Space Shuttle, flying at the same altitude. The relative motion of the two ideal points is reconstructed and yields a measurement of the fine structure of the Earth gravitational field, corresponding to a harmonic orderl∼a/d (a is the radius of the Earth). The tracking can be done by laser ranging to the four spheres, covered by corner reflectors; Doppler ranging is more convenient for higher values ofl and can also be used. The accuracy in the compensation of the nongravitational forces and in the measurements one needs for a givenl are discussed in detail.