PEP includes a detailed mathematical model of the solar system with a large number of adjustable parameters, including some that describe basic laws of nature. For example, we include one parameter expressing the gravitational constant G and another that gives a possible time rate of change in G, in case it turned out not to be a constant. By estimating the latter parameter based on the available data, we can place limits on the rate of change, and thereby restrict the range of allowable theories in physics and cosmology. Similarly, we have parameters that are sensitive to several predictions of the theory of general relativity, and we use those to compare GR against competing theories. Among the phenomena we have used in this work are the Shapiro delay in radio signals passing near the Sun, the "geodetic" (de Sitter) precession of the Earth-Moon system, and the relativistic advance of the planetary perihelia.
An important factor in our work is the principle that "one person's noise is another's signal". For the purpose of studying the fundamental laws of gravitation, the details of planetary topography and the resulting "modulations" of the measured round-trip delay of interplanetary radar signals are merely a nuisance that must be modeled and removed. However, the study of other planets very naturally includes just that sort of mapping. Similarly, as a by-product of our data analysis, we obtain a model of the variations in the Earth's rotation, including corrections to the standard models of precession, nutation, UT1 and polar motion.
The rotation of other planets can also be studied by ground-based radar. Analysis of the bandwidth of the first radar echoes from Mercury and Venus quickly revealed that they are not in 1:1 spin-orbit resonances, as had been widely assumed (and as the Earth's Moon actually is). Instead, Mercury is in a 3:2 resonance, and Venus rotates backwards. Indeed, Venus' rotation rate is close to a resonance with the Earth's orbit. It was only through carefully tracking the relative time delays and Doppler shifts of the echoes from specific, easily identifiable features on the surface of Venus over many years of observations that we were able to show that Venus is not actually in the resonance. We are now attempting to use the same techniques to characterize the rotation of the asteroid Toutatis, which came so near the Earth in 1993 that detailed radar images were obtained, showing a highly irregular, bifurcated shape. Radar studies of near-Earth objects, particularly of newly discovered ones, presents a special challenge because of the rapid motion of such objects across the sky and the need to develop the radar ephemeris from scratch in the typically short time available.