The planet Mars has two satellites, Phobos and Deimos, in nearly circular orbits. The orbit radii of Phobos and Deimos are 9.38 x 10³ km and 23.46 x 10³ km, respectively. The mass of Mars is 6.42 x 10²³ kg, that of Phobos is 9.63 x 10¹⁵ kg, and that of Deimos is 1.93 x 10¹⁵ kg. Find the center of gravity and the center of mass of the two satellite system using the center of Mars as the origin when

(a) The satellites are in opposition (i.e., on exactly opposite sides of Mars),

(b) The satellites are in conjunction (i.e., in line on the same side of Mars).