Dynamical limits on dark mass in the outer solar system

Abstract

Simplified model solar systems with known observational errors are considered in conducting a dynamical search for dark mass and its minimum detectable amount, and in determining the significance of observed anomalies. The numerical analysis of the dynamical influence of dark mass on the orbits of outer planets and comets is presented in detail. Most conclusions presented are based on observations of the four giant planets where the observational errors in latitude and longitude are independent Gaussian variables with a standard deviation. Neptune's long orbital period cannot be predicted by modern ephemerides, and no evidence of dark mass is found in considering this planet. Studying the improvement in fit when observations are fitted to models that consider dark mass is found to be an efficient way to detect dark mass. Planet X must have a mass of more than about 10 times the minimum detectable mass to locate the hypothetical planet. It is suggested that the IRAS survey would have already located the Planet X if it is so massive and close that it dynamically influences the outer planets. Orbital residuals from comets are found to be more effective than those from planets in detecting the Kuiper belt. 35 refs.