Rock-Around Orbits

The ability to observe resident space objects (RSOs) is a necessary requirement for space situational awareness. While objects in a Low-Earth Orbit are easily ob- servable by ground-based sensors, diffculties arise when trying to monitor objects with larger orbits far above the Earth's surface, e.g. a Geostationary Orbit. Camera systems mounted on satellites can provide an eff ective way to observe these objects. Using a satellite with a speci c orbit relative to the RSO's orbit, one can passively observe all the objects that share the RSO's orbit over a given time without active maneuvering. An orbit can be defi ned by ve parameters: semi-major axis, eccentricity, right ascension of ascending node, inclination, and argument of perigee (a; e; ; i; !). Using these parameters, one can create an orbit that will surround the target orbit allowing the satellite in the Rock-Around Orbit (RAO) orbit to have a 360 degree view of RSOs in the target orbit. The RAO orbit can be applied to any circular or elliptical target orbit; and for any target orbit, there are many possible RAO orbits. Therefore, diff erent methods are required to narrow down the selection of RAO orbits. These methods use distance limitations, time requirements, orbit perturbations, and other factors to limit the orbit selections. The first step is to determine the range of RAO semi-major axes for any given target orbit by ensuring the RAO orbit does not exceed a prescribed maximum al- lowable distance, dmax from the target orbit. It is then necessary to determine the eccentricity range for each possible RAO semi-major axis. This is done by ensuring the RAO still does not exceed dmax but also ensuring that the RAO orbit travels inside and outside of the target orbit. This comprises one half of the rock-around motion. The final step is to determine the inclination of the RAO orbit. Only a small inclination different from that of the target orbit is required to complete the rock-around motion while the maximum inclination is found by making sure the RAO orbit does not exceed dmax. It is then important to consider orbit perturbations, since they can destroy the synchronization between the RAO and target orbit. By examining the e ffects of the linear J2 perturbations on the right ascension of ascending node and argument of perigee, the correct semi-major axis, eccentricity, and inclination can be chosen to minimize the amount of fuel required for station keeping. The optimal values can be found by finding the Delta v needed for di fferent combinations of the variables and then choosing the values that provide the minimum Delta v. For any target orbit, there are multiple RAO orbit possibilities that can provide 360 degree coverage of a target orbit. Even after eliminating some of them based on the methods already described, there are still many possibilities. The rest of the elimination process would then be based on the mission requirements which could be the range of an on-board sensor, the thruster or reaction wheel controls, or any other number of possibilities.