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mum accuracy for azimuth lies along the plane that bisects the angle formed by the baselines; the maximum accuracy for elevation lies along the plane perpendicular to this bisector. Physically, the plane for maximum elevation accuracy occurs when so that an error that occurs in Ro is cancelled when it appears in both p and q. The same statement is true for azimuth also, of course. G RAVITATIONALLY oriented satellites are of interest currently because of the possibility they afford to control orientation in space for long time durations without a continuing power requirement. A major design problem is the provision of adequate damping for rotational oscillations; the theory of physical librations of the moon is a useful guide to the underlying dynamics. Consideration of the interactions between librational and orbital motions leads to a new relationship between masses and orbital distances and reveals a condition on friction terms.Energy dissipation within the moon is directly related to the couple-producing term in the gravitational potential, the sun's effect predominating over the earth's. If the energy of moon's orbital motion around earth is expressed as k*M e M m /-2r and its variation determined by dissipation, the relationship can be written as (1) where the Gaussian constant k 2 has been suppressed as a common factor. Earth, moon, and sun masses are denoted M e , M m , M s ] earth-moon and sun-moon mean distances are represented by r and R-, effects of lunar orientation toward sun and lunar mass asymmetries determine $1, the explicit form of which is given by MacCullagh's formula (see, e.g., Ref.l).Tidal dissipation within the earth due to the proximity of the lunar mass can likewise be related to variation of earth's orbit around sun, givingwhere <£ 2 likewise depends on the differences between earth's principal inertia moments and the earth-moon orientation. Although the two Eqs.(1) and (2) do not form a simultaneous system, it is observed that the products of diagonal coefficients form an equality (M e M m /M s M s ) =(3) as is easily verified by direct substitution of known numerical values for each of the quantities contained in this equation. It should be noted that Eq. (3) has not been deduced from (1) and (2), so that a further relationship is implied between the differential coefficients which they contain:The ratio on the right side of (4) can be evaluated on the basis of orbital considerations (e.g., by requiring the total moment of momentum of earth and moon orbital motions to remain constant). Then the terms on the left relate dissipation within the satellite (moon) to that within the primary. Reciprocity relationships are suggested by the form of (4).Equation (3) recalls the formula given by Laplace for the radius of the "activity sphere" outside of which the sun's attraction is more important than the earth's on the motion of a third body. If the geometric mean of earth and moon masses is replaced by earth mass, in fact, Eq. (3) becomes identical to Laplace's formula (see, e.g., Ref. 2). Th...