Sensitivity and antenna pattern for an interplanetary laser trilateration network

An array of laser transponders, moving along orbits centered on Venus, Earth, and Mars, could provide significant new information about the distribution of mass in the solar system and beyond. In this report we begin an analysis of the sensitivity and effective antenna pattern for such a device. While the main source of changes in the lengths of the three legs of the Venus-Earth-Mars triangle is motion along the nearly circular heliocentric orbits of those bodies, measurable perturbations can be caused by other masses, either inside or outside the triangle. Our main focus here is on sources which are close to the ecliptic plane, and farther from the Sun than Jupiter. We present results on simulations of the ability of the transponder array to measure accelerations, and use that to describe the ability of the array to characterize sources of perturbing mass. Measurements of time-of-flight for short laser pulses between pairs of detectors directly constrains distance between them. Fitting a quadratic model to a daily collection of range measurements yields an estimate of the average daily difference in accelerations at those points, projected onto the baseline between them. Range measurements along a single baseline, with 1 ​cm accuracy, and a 1 ​Hz sampling cadence, will yield acceleration sensitivity of 10−15 ​m/s2, for each daily acceleration normal point. We consider two different types of sources: one is an isolated point mass, and the other is a sinusoidal variation in mass density along a circular arc. In both cases, we are able to characterize the performance of the transponder array. Simultaneous projections of acceleration differences onto the 3 baselines, at a single epoch, provide unique values for the mass and position of a single point source. Characterization of distributed sources requires a range of baseline orientations.