CONSTRAINING THE INTERIOR STRUCTURE OF PLANETS IS A BASIC GOAL OF PLANETARY SCIENCE THAT ADVANCES OUR UNDERSTANDING OF THEIR FORMATION AND EVOLUTION. SEISMOLOGY OFFERS ONE OF THE MOST DIRECT WAYS TO PROBE THE INTERIOR OF A PLANET; HOWEVER IT IS CURRENTLY ONLY AVAILABLE FOR THE EARTH AND THE MOON. FOR OTHER PLANETS IN THE SOLAR SYSTEM WE MUST RELY ON OTHER TECHNIQUES. GRAVITY AND TOPOGRAPHY DATA ARE AVAILABLE FOR MANY PLANETS IN THE SOLAR SYSTEM AND JOINT ANALYSIS OF THESE DATA CAN CONSTRAIN THEIR INTERIOR STRUCTURE. THIS APPROACH HAS BEEN USED TO CONSTRAIN THE CRUST PARAMETERS OF TERRESTRIAL PLANETS AND ICY SATELLITES; HOWEVER IT SUFFERS FROM AN INHERENT NONUNIQUENESS IN THE INVERSION PROCESS. THE DEGENERACY CAN BE REDUCED BY ASSUMING THAT THE TOPOGRAPHY IS SUPPORTED BY A SPECIFIC ISOSTASY MECHANISM. OUR FIRST GOAD IS TO DEVELOP A NOVEL PHYSICAL ISOSTASY MODEL BASED ON MINIMIZATION OF ELASTIC ENERGY. IN ADDITION TO PROVIDING A NEW PHYSICALLY REASONABLE APPROACH TO ISOSTASY THE MODEL WILL BE GENERAL ENOUGH TO BE APPLICABLE TO ARBITRARY CRUST THICKNESSES AND COMPRESSIBLE INTERIORS. AN ALTERNATIVE METHOD FOR CONSTRAINING THE INTERIOR STRUCTURE IS TO COMPARE THE LOCATION AND ORIENTATION OF TECTONIC FEATURES TO THOSE PREDICTED BY A SPECIFIC MODEL. THERE ARE TWO ASPECTS OF STRESS AND TECTONICS MODELS THAT CAN BE EXTENDED. FIRST CURRENT MODELS ARE RESTRICTED BY ASSUMPTIONS ON LITHOSPHERE THICKNESS LOAD SIZE OR GEOMETRY AND COMPRESSIBILITY. SECOND MULTIPLE PROCESSES (E.G. MASS LOADING DESPINNING TRUE POLAR WANDER AND ORBIT MIGRATION) CAN GENERATE TECTONIC PATTERNS SIMULTANEOUSLY WHILE CURRENT MODELS ONLY CONSIDER TECTONIC PATTERNS DUE TO A SINGLE PROCESS IN ISOLATION. OUR SECOND OBJECTIVE IS TO DEVELOP A GENERAL STRESS AND TECTONICS MODEL THAT IS APPLICABLE TO (1) MASS LOADING WITH ARBITRARY SIZE OR GEOMETRY (2) ARBITRARY LITHOSPHERE THICKNESSES AND COMPRESSIBLE INTERIORS AND (3) ROTATIONAL AND ORBITAL PERTURBATIONS. FINALLY OUR LAST GOAL IS TO CONSTRAIN THE INTERIOR STRUCTURE OF TITAN ENCELADUS DIONE PLUTO AND MARS; AND THE PROCESSES CAPABLE OF GENERATING TECTONIC PATTERNS ON THESE PLANETS BY COMPARING THE PREDICTIONS OF OUR NEW MODELS WITH GRAVITY TOPOGRAPHY AND TECTONIC PATTERNS OBSERVATIONS. INTERIOR STRUCTURE MODELS MUST TAKE RIGOROUS ACCOUNT OF ALL THE UNCERTAINTIES GIVEN THE INHERENT NON-UNIQUENESS. WE WILL ACCOMPLISH THIS BY PROVIDING THE PROBABILITY DISTRIBUTIONS OF ALL THE INTERIOR STRUCTURE PARAMETERS USING BAYESIAN PROBABILITY THEORY. THE PROPOSED RESEARCH WILL ADVANCE OUR UNDERSTANDING OF PLANETARY INTERIOR STRUCTURES AND PROCESSES CAPABLE OF GENERATING TECTONIC PATTERNS. IT WILL ALSO PROVIDE NOVEL MODELS FOR ISOSTASY AND TECTONICS THAT ARE GENERAL ENOUGH TO BE APPLICABLE TO ANY PLANET OR SATELLITE WITH A SOLID SURFACE MASS LOADING WITH ARBITRARY SIZE OR GEOMETRY ARBITRARY CRUST THICKNESSES AND COMPRESSIBLE INTERIORS AND ROTATIONAL AND ORBITAL PERTURBATIONS (E.G. DESPINNING TRUE POLAR WANDER NON-SYNCHRONOUS ROTATION AND ORBIT MIGRATION). THIS IS SIGNIFICANT BECAUSE CURRENT MODELS ARE RESTRICTED BY ASSUMPTIONS ON CRUST THICKNESS LOAD SIZE OR GEOMETRY COMPRESSIBILITY AND THE INABILITY TO TREAT MULTIPLE STRESS GENERATING PROCESSES SIMULTANEOUSLY. THE PROPOSED STUDY SUPPORTS THE OBJECTIVES OF THE SOLAR SYSTEM WORKINGS PROGRAM AND NASA OVERALL BY DEVELOPING A GREATER UNDERSTANDING OF THE DYNAMICS AND PHYSICAL PROCESSES RESPONSIBLE FOR SHAPING PLANETARY BODIES IN THE SOLAR SYSTEM. THIS WORK WILL BE OF DIRECT RELEVANCE TO THE GOALS OF THE SOLAR SYSTEM WORKINGS PROGRAM AS IT DIRECTLY ADDRESSES TWO BULLETS IN THE APPENDIX C.3 OF THE ROSES 2016: INTERIOR STRUCTURE AND LITHOSPHERES.