This technique for compensating the gravitational attraction experienced by a test-mass freely floating onboard a satellite is new, and solves an important problem that all gravitational wave missions face. Its application to the geostationary Laser Interferometer Space Antenna (gLISA) mission concept addresses and completely solves an important noise source: the gravity-gradient noise.

Each of these masses must be specified in number, and each of them will have to be characterized in magnitude, shape, and location. For the purpose of answering these questions, and to test quantitatively the validity of the solutions through numerical analysis, perfect knowledge of the Comsat mass distribution is assumed, and the one provided to the innovators by Space Systems Loral is adopted. This allows an estimate both of the gravitational acceleration, and the gravity gradient exerted by the Comsat at the TM nominal location, o.

In order to determine the number of compensating masses to be added onboard the Comsat, the gravitational gradient, (gg)ij, is equal to the second partial derivatives of the gravitational potential, V(r), generated by the Comsat.

In order to identify the location and values of the compensating masses, for simplicity, it is assumed that they are of spherical shape and constant mass distribution. In the coordinate system given by the eigenvectors of the gravity gradient, it is then easy to see that the direction, along which the five masses will have to lie, coincides with the three coordinate axes (x, y, z). In particular, if two pairs of spheres on the x and y axes, respectively, are added and located in such a way to “bracket” point o, it should be possible to compensate both the acceleration and gravity gradient components along these two directions. The remaining mass will instead need to be located on the positive z axis in order to counter-balance the negative z component of the gravitational acceleration from the Comsat.

If the distance to the point o of each compensating mass is fixed, one can then solve for the values of the masses (that simultaneously cancel the acceleration and gravity gradient) by solving a nonhomogeneous linear system of five equations in five unknowns. Note that the closer the compensating masses can be to point o, the lighter their values will result. For a typical Comsat design weighing 3,200 kg, it was found that masses ranging between 7 kg and 13 kg would each need to be located about 25 cm away from point o in order to simultaneously cancel the acceleration and gravity-gradient exerted on the TM by the Comsat.

This work was done by Massimo Tinto of Caltech for NASA’s Jet Propulsion Laboratory. NPO-49599