Precise measurements of the Doppler shift of radar waves reflected from Moon disclose unexpectedly large discrepancies-averaging about 0.6 centimeter per second-between the radial velocities and the predictions based on the Eckert-Brown lunar ephemeris. These residuals have a rapidly changing component corresponding to a relatively large, variable, and unexplained discrepancy in radial acceleration of about 10(-4) centimeter per second, per second, in magnitude and about 1 day in period.