Since the dawn of the Space Age, over six thousand satellites have been launched into Earth orbit. The function of determining the orientation of a satellite in orbit, so that it can point its antennas and instruments in the required direction is known as attitude determination. Depending on the nature of the mission, this important function is typically performed by means of optical instruments that determine the orientation of the satellite with respect to known bodies such as the Earth, the sun, and bright stars. Conventional Earth sensors use cameras and telescopes to locate the position of the Earth's horizon and hence to calculate the orientation of the satellite. In the event that a satellite starts to tumble, existing Earth sensors that use optical sensing are severely limited in their ability to reacquire the attitude due to the limited field of view of the instruments. Also, due to this limited field of view, multiple Earth sensor units need to be placed on all faces of the satellite to ensure 4π steradian coverage. Because of the optical sensing principle of existing Earth sensors, constraints are imposed on the positioning of solar panels and antennas so that they do not block the field of view of optical sensors. This thesis describes a novel inertial sensor that uses the Earth's gravity gradient as a reference for attitude determination on-board a satellite in low Earth orbit. Using the gravity gradient for attitude determination makes it possible to realise a single, compact Earth sensor instrument which can be positioned flexibly within the satellite. Due to its 4π steradian field of view, such an instrument can offer added capability as a backup sensor, or act as the main Earth sensor. By using Micro-Electro-Mechanical System (MEMS) technology for the inertial sensor, a target mass of 1 kg and target volume of 1 dm3 can be realised for the entire gravity gradient Earth sensor system. The gravitational force decreases as the square of the distance from the center of the Earth. An elongated object in orbit around the Earth will have slightly different values of gravity acting over the different points in its volume. This gives rise to a small torque, the Gravity Gradient Torque (GGT), on the object. A compact micromachined inertial sensor was designed with an elongated proof mass and compliant spring to measure the GGT, so that the orientation of the proof mass with respect to the normal from the Earth's surface can be determined. Such a sensor on-board a satellite can act as an Earth sensor, and provide information about the satellite attitude with respect to the normal to the Earth's surface. An inertial sensor to measure GGT, which with readout electronics fits within a 1 dm3 volume, has to measure a torque of magnitude 10-15 N.m. Currently, no inertial sensor is capable of such a fine measurement. In addition to the required performance in microgravity, the inertial sensor must be robust enough to be tested on Earth with no special handling, and must survive the vibration and shock of a launch, to be used in space. The readout scheme to measure the displacement due to GGT must also be simple and robust. The designs of two generations of a novel inertial sensor to measure the GGT are presented in the thesis. To be able to measure the GGT with the required accuracy a sensor is designed that has a proof mass 5 cm long, suspended by springs which have widths less than ten microns. The sensor resonant frequency of the inertial sensor is on the order of 1 Hz. A new fabrication process is developed for the sensor, which incorporates hard stops to limit the motion of the proof mass along all the axes, thus making it robust enough for testing without any special precautions. The sensor survives low magnitude vibration tests. A digital electronic readout based on capacitive sensing of the displacement due to GGT, is developed based on commercially available ICs, and allows easy interfacing of the inertial sensor output to a PC or microcontroller. To test the sensor on Earth, a dedicated test setup is developed to replicate the nm-scale motion of the proof mass expected in orbit. The electronic readout is capable of measuring the sub-nm displacements due to GGT. The 2nd generation sensor design with capacitive displacement sensing is the first demonstration of an inertial sensor capable of measuring the GGT in low Earth orbit, and an important step towards realization of a 1 kg, 1 dm3 Earth sensor that uses the gravity gradient of the Earth for attitude determination.