Extracting tides from laser altimetry observations: A global approach

Abstract

Measurements of planetary solid body tides provide crucial constraints on the interior structure, and thereby the formation and thermal evolution, of planets and satellites. The tidal Love number h2 describes the radial surface displacement due to tides. On the planet Mercury, a successful measurement of h2 can prove the existence and determine the size of a possible solid inner core. On Jupiter’s moon Ganymede, h2 constrains the thickness of the outer ice shell if a subsurface ocean exists. This dissertation presents a method for the retrieval of h2 from global laser altimetry data sets. Contrary to previous studies, which determine the radial displacement over time at crossover points, this method applies a global approach, simultaneously solving for displacement and the global static topography, parametrized as 2D cubic B-splines on an equirectangular grid. The first step is a validation of the method by studying the Moon. On the Moon, tidal forces cause radial displacements that have a maximum peak-to-peak amplitude of about 25 cm, making their detection very challenging. The Lunar Orbiter Laser Altimeter aboard the Lunar Reconnaissance Orbiter has provided over 7 billion range measurements. The obtained h2 result agrees well with that of a previous study, thereby validating the method. The second step is a determination of the expected retrieval accuracy of Mercury’s h2 from the BepiColombo mission. The analysis of independent synthetic sets of measurements of the BepiColombo Laser Altimeter provides a measure for the uncertainty of h2. The experiment considers errors caused by the unknown properties of Mercury's topography, the performance and misalignment of the instrument, the orbit determination, and uncertainties in the rotational model of Mercury. The detection of a solid inner core is possible under all assumed error cases. Favorable cases enable the determination of its size to roughly 150 km if the core is larger than 800 km. The main error sources are the small-scale topography of Mercury and the misalignment of the instrument. Another application of the method is the determination of parameters describing planetary rotation and librations. On Ganymede, a joint solution for h2 and the amplitudes of selected librations using data collected by the Ganymede Laser Altimeter aboard the Jupiter Icy Moons Explorer will deliver a sufficiently strong constraint on these parameters to prove the existence of a subsurface ocean and give valuable insights on the properties of the outer ice shell. A future application of the method presented in this dissertation to the data that the BepiColombo and Jupiter Icy Moons Explorer missions will collect will yield significant geophysical insights into Mercury and Ganymede.