Tidal deformation of Europa and Phobos: implications on their structure and history M.H.P. Kleuskens Delft, 12 October 2006 Delft University of Technology Faculty of Aerospace Engineering Astrodynamics & Satellite Systems Tidal deformation of Europa and Phobos: implications on their structure and history M.Sc. Thesis Report M.H.P. Kleuskens Delft, 12 October 2006 This document was typeset with LATEX 2ε. The layout was designed by Remco Scharroo c 1993. Astrodynamics & Satellite Systems Faculty of Aerospace Engineering Delft University of Technology Kluyverweg 1, 2629 HS Delft The Netherlands Preface In September 2005, I finished a “sabbatical” year of working for a student choir. From the world of arranging concert halls and rehearsal rooms, I entered back in the world of another passion: science. This M.Sc. thesis work was carried out at the section Astrodynamics and Satellite Systems of the Aerospace Faculty of Delft University of Technology. This chair works mainly on precise orbit determination, Earth observation and Space instrumentation. Recently, planetary science has become a more important subject at this chair. This work is a continuation of previous M.Sc. theses researches about Jupiter’s moon Europa. This report is set up for M.Sc. students or higher on the same subject. For people who are interested in planetary sciences but do not have a technical back- ground, I advice to read the background information of Europa and Phobos, in sections 4.1 and 5.1, respectively. The results in sections 4.6 and 5.5 can be fairly understood without mathematical background. This work would have been impossible to accomplish without the help of a lot of people. The people on the ninth floor of the Aerospace Faculty building created a pleasant atmosphere to work in. I could not have completed this work without the help of fellow students and staff members, who did not only provide help, but moreover encouraged my interest in planetary sciences. In particular, I want to thank my tutor Bert Vermeersen, who always kept the door open for questions, and Luuk van Barneveld, who shared his knowledge about Europa. Next, I want to thank Tony Dobrovolskis for sending me his numerical model of Phobos to make my graphics look more realistic and Ren´ePischel for keeping me up to date about the encounters of Phobos by Mars Express. Furthermore, I thank Terry Hurford for sharing his methods and results on Europa. A special gratitude goes to friends, family and the One above for hearing my stories about tidal deformation over and over again. Marco Kleuskens v Summary Tidal forces are very important in various processes in our solar system. This thesis shows the effects of tidal deformation on the Jovian moon Europa and Martian moon Phobos. It makes use of the normal mode analysis, which was initially developed to model the deformation of the Earth. Grooves and ridges on the surface of Europa show a possibility of a liquid ocean under the icy surface, caused by tidal heating as a result of Europa’s eccentric or- bit around Jupiter. By using an altimeter on an orbital mission to Europa the daily tidal deformation could be measured. The normal mode model is adapted to include internal fluid or low-viscosity layers. The viscoelastic response that is modelled is used to determine the amplitude and phase of the deformation as a function of rigidity, viscosity and thickness of the icy surface. For all realistic sit- uations, the relaxation times of the mantle and the core are too long to contribute to a phase lag with the surface ice layer. Based on surface features, it is suggested that Europa’s rotation is faster than its revolution. In this case, Europa would complete a rotation counter clockwise with respect to Jupiter on the timescale of 104 years. Since the relaxation times of the mantle and the core are on this order of magnitude, it is possible that the tidal bulge of the mantle and core is not aligned with the subjovian point. An altimetry mission could observe the presence of such an offset. This would make it possible to constrain the material and rheo- logical properties of those layers. Furthermore, it could be predicted whether the surface is co-rotating with the mantle or not. In the latter case, only the surface would rotate with respect to Jupiter, while the mantle and core would be locked to Jupiter. Compared to Europa, Phobos is an irregular moon that is about one hundred times smaller, an its orbit is very close to Mars. Moreover, the moon is in a spiral motion that will end on the surface of Mars within 32 million years. But before that will happen, it will have broken up already by tidal forces. Although it is likely to be a captured asteroid, the orbit is almost circular. Furthermore, it has a large crater and a remarkable pattern of grooves. The origin of Phobos and its grooves lead to many paradoxes, and have driven a discussion between scientists for decades. This study sheds a new light on various arguments by adopting the normal mode analysis. Although the technique is linear and not accurate for an ellipsoidal figure, it gives new insight in the history of the moon. By simulating the orbital decay, an average viscosity of 4 × 1019P a would deform Phobos to its present shape. It is therefore plausible that the shape of Phobos is mainly caused by tidal deformation. Unfortunately, the impact that caused the main crater on Phobos and the tidal forces cannot be excluded not confirmed as the cause for the grooves. vii Contents 1 Introduction 1 2 Potential theory 3 2.1 Gravity . 3 2.2 Centrifugal potential . 5 2.3 Tides . 6 2.4 Variation in tidal potential due to eccentricity . 8 3 Normal mode analysis 13 3.1 Rheology . 14 3.2 Matrix propagation technique . 15 3.3 Convolution . 24 3.4 Stress . 27 4 Europa 31 4.1 Introduction . 31 4.2 Tidal potential of Jupiter, Io and Ganymede . 35 4.3 Normal mode analysis for fluid layers . 39 4.4 Validation of the method . 47 4.5 Sensitivity to changes in Europa’s rheology . 54 4.6 Results . 57 5 Phobos 63 5.1 Introduction . 63 5.2 Theories about Phobos . 68 ix x Contents 5.3 Normal mode analysis for a homogeneous sphere . 71 5.4 Determining material properties by the deformation . 75 5.5 The causes of the grooves . 81 6 Conclusions and recommendations 87 A Data of moons 89 A.1 Europa . 89 A.2 Phobos . 90 B Mathematical tools 91 B.1 Spherical coordinates . 91 B.2 Spherical harmonics . 91 B.3 Fourier series . 94 Bibliography 99 Chapter 1 Introduction The Dutch interest in planetary exploration is growing rapidly. Industry, techno- logy institutes and scientists cooperate in the Netherlands Platform for Planetary research to ensure a good position in future planetary missions. Different groups of scientists are involved in this research. While geologists and biologists try to connect detailed processes on planets to the processes on Earth, geophysicists deal with the structure of planets on global scales and provide a valuable contribution to the knowledge about planets. This M.Sc. thesis deals with tidal deformations of moons in our solar system, in particular the Martian moon Phobos and the Jovian moon Europa. These moons differ in many aspects: first, Phobos is a tiny, irregular rocky moon while the shape of Europa is more similar to our Moon. Second, their parental planets are an earthly planet and a gas giant, respectively. Their connection is the fact that their their surface features are most probably the result of extreme tidal forces. On Europa, tidal heating by its eccentric orbit could melt the icy upper layers and could form an ocean in the subsurface. The most important clue is the fact that the Europan surface is covered with ridges and cracks. The presence of a liquid or slush water layer, together with the tidally driven reopening of cracks and water convection make Europa one of the most plausible places outside the Earth for sustaining life. The goal of this thesis is to assess whether it is possible to predict the inner structure of Europa by observing the tidal deformation. In particular, the presence of an ocean in the subsurface and the rheology of the surface are of interest. The effect by tides of other Jovian moons and the possible non-synchronous rotation of Europa is taken into account. All these relationships can put constraints on the instruments and the orbit of a future mission to Europa. A study to a Europa mission itself is not covered in this thesis, but is described in detail in e.g. [Weimar, 2005]. Although many UFO believers think life exists on or even inside Phobos, the opposite is more plausible. The small, irregular rock has not sufficient gravity to sustain an atmosphere. Surface features show evidence of a tumultuous history. Phobos has many craters of which the diameter of the largest one, Stickney, is almost half the size of the total diameter of Phobos. Furthermore, the surface is covered with a fine structure of grooves that follow a remarkable pattern. Not only the past was severe, the future brings an inevitable, disastrous end. Due to tidal friction the orbit of Phobos decays, which increases the tidal forces even 1 2 Introduction more and will eventually cause a collapse on the surface of Mars. Before this will happen, the increasing tidal forces will disrupt Phobos. Learning more about the background and origin of Phobos can indirectly provide new information about the creation of our solar system.