We propose to develop a compact tensor superconducting gravity gradiometer (SGG) for obtaining accurate gravimetric measurements from planetary orbits. A new and innovative design, based on three decades of development with support from NASA, gives a potential sensitivity better than 10^(-3) E Hz^(-1/2) in the measurement band of 1 mHz to 0.1 Hz for a device miniaturized to a baseline just over 10 cm. Significant advances in the technologies needed for space-based cryogenic instruments have been made in the last decade. These technologies include cryocoolers, spacecraft architectures, and cryogenic amplifiers. The use of a cryocooler will alleviate the previously severe constraint on mission lifetime imposed by the use of liquid helium, enabling mission durations in the 5-10 year range. After the tensor SGG is demonstrated, we plan to submit a follow-on proposal to integrate and test the SGG with a flight-like cryocooler. The original SGG, fully developed in the 1990's, had mechanically suspended test masses, which limited the sensitivity at 1 mHz to ~ 10^(-2) E Hz^(-1/2) with a baseline nearly 20 cm. Magnetic levitation gives a number of advantages. The resulting magnetic spring is much more compliant than a mechanical spring, enabling construction of a more compact tensor SGG with higher sensitivity, as required for planetary missions. Magnetic spring gives two degrees of freedom to each test mass. Hence a tensor gradiometer can be constructed with only six test masses, rather than twelve, which further simplifies the design and compactifies the instrument. As a result, the 10^(-3) E Hz^(-1/2) sensitivity can be achieved with a device miniaturized by an order of magnitude in volume and mass from the existing device. With our intended 10^(-3) E Hz^(-1/2) sensitivity of the miniaturized gradiometer, it is anticipated that the present resolution of the global gravity field from decades of Doppler tracking data (L ~ 90 for Mars, where L is the maximum degree of gravity coefficients) could be substantially improved by using SGG data (L ~ 220) from a single spacecraft only within 100 days. It would be even better than the expected resolution of the gravity model (L ~ 180) using satellite-to-satellite tracking (SST) from two co-orbiting spacecraft. The more sensitive measurements from the SGG should also enable mapping the regional scale of seasonal gravity variations every month or every season. Further, the multiple-axis measurement of the gradiometer will give a better east-west resolution of gravity over SST. The development of a single-axis SGG with levitated test masses started in 2012 with a small amount of support from NASA's Earth Science Division. Without provision to measure linear and angular accelerations in the other two axes, the common-mode rejection ratio (CMRR) in this device will be limited to 10^5, which does not permit demonstration of the full sensitivity of the new SGG. Under this PICASSO program, we will expand this instrument to three axes and apply residual balance to improve the CMRR by a factor of 10^3 to 10^8, with a goal to advance the TRL from 3 to 4. Light superconducting test masses will be levitated against Earth's gravity and connected to superconducting circuits to detect all six components of the gradient tensor. We will also study the effect of the cryocooler vibration on the SGG by simulating the same vibration environment in the cryostat as from a cryocooler by use of a shaker. In addition to the hardware development, we will examine scientific applications of time-variable high-resolution global gravity field solutions anticipated from the planetary SGG mission. We will also develop a theoretical error model of the new instrument, which will then be used to define spacecraft control requirements.