Electromagnetic Formation Flight Progress Report: November 2002 Submitted to: Lt. Col. John Comtois Technical Scientific Officer National Reconnaissance Office Contract Number: NRO-000-02-C0387-CLIN0001 MIT WBS Element: 6893087 Submitted by: Prof. David W. Miller Space Systems Laboratory Massachusetts Institute of TechnologyINTRODUCTION Description of the Effort The Massachusetts Institute of Technology Space Systems Lab (MIT SSL) and the Lockheed Martin Advanced Technology Center (ATC) are collaborating to explore the potential for an Electro-Magnetic Formation Flight (EMFF) system applicable to Earth-orbiting satellites flying in close formation. Progress Overview At MIT, work on EMFF has been pursued on two fronts: the MIT conceive, design, implement and operate (CDIO) class, and the MIT SSL research group. Recent work in the MIT CDIO class includes the finalizing of the design for a planar EMFF test bed. The class will be holding its Critical Design Review (CDR) on December 5, 2002, and the final hardware design presented in their CDR will be described in the December progress report. Recent work in the MIT SSL has focused on investigating specific applications of the EMFF in Low Earth Orbit (LEO), particularly with regards to managing angular momentum accumulation in LEO due to periodic disturbances. The following report discusses in detail the use of EMFF to manage angular momentum buildup, specifically due to the Earth’s magnetic field and due to its oblateness about the equator, also known as the J2 perturbation. Results of these analyses indicate that EMFF could serve well in this application, replacing the use of thrusters to correct for J2 accelerations, and thus removing an array’s dependence on non-renewable fuel supplies. These results are promising, as they suggest yet another application in which EMFF may be quite useful.ANGULAR MOMENTUM MANAGEMENT 1. Overview EMFF has the property that all the forces generated by the electromagnets are internal to the system. Excluding any disturbance interactions with the Earth's magnetic field, EMFF cannot apply any external forces to the formation. This prevents EMFF from having the ability to change the inertial position of a formation. It also prevents changes in the total system angular momentum. While reaction wheels are used to temporarily store angular momentum changes in a formation, they are not able to change the total system angular momentum. In an ideal situation, this would not be an issue, since the angular momentum of the system would remain constant. However, disturbance forces cause unwanted torques on a satellite formation and cause a net gain in its system angular momentum. If left unchecked, the reaction wheels will eventually saturate and become useless. These disturbance torques must be accounted for, and methods for removing this unwanted angular momentum are suggested in this report. 2. Earth’s Magnetic Field One disturbance source that is immediately apparent is the Earth's magnetic field. Whenever any of the EMFF electromagnets are energized, they interact with the Earth's magnetic field. This disturbance will manifest itself as disturbance forces and torques on the satellite formation. These disturbance forces and torques will cause a net gain in the angular momentum of the satellite formation. In order to characterize this effect, the Earth can be thought of as one large electromagnetic dipole. This is the same simplification technique used in previous studies, where interactions (forces and torques) between the electromagnets on different spacecraft are modeled as functions of the product of the magnetic dipole strengths. One novel way of canceling the disturbance torques and forces due to the Earth's magnetic field is to reverse the polarity of every spacecraft dipole at the same time [Hashimoto et al. 2002]. Since the electromagnetic forces are functions of the product of the dipoles, the inter-spacecraft forces are unchanged. However the disturbance forces and torques due to the Earth's dipole have switched sign, thus canceling out the disturbance forces. This polarity switching could be done at a low frequency; the dipoles would switch only when the accumulated angular momentum becomes large, or the switching could also be done at a relatively high frequency, essentially preventing any angular momentum build-up. Since we have the ability to apply a net torque to the satellite formation in one direction or the other, the Earth's magnetic field could be utilized to remove the overall net angular momentum of the system. If the system were gaining angular momentum due to some other disturbance torque, the Earth’s magnetic field could be used to reduce the system angular momentum. Also, since the inter-spacecraft forces are once again products of the magnetic dipole strengths, we can selectively turn up one satellite's dipole strength and reduce the other spacecraft’s dipole strength. The inter-satellite forces and torques would remain unchanged, butthe magnetic disturbance force would be focused on one specific satellite. Thus individual satellites could be targeted for momentum exchange. 3. LEO and the J2 Disturbance Satellite formations in Low Earth Orbit (LEO) are subjected to variations in the Earth's gravitational potential. The largest variation is known as the J2 gravitational potential constant. The J2 term refers to the fact that the Earth is not round, but has a mass bulge around the equator. This mass bulge has three main effects on the satellite formation: it changes the orbital period of the satellite, it causes the formation to separate in the cross-track direction, and it causes the formation as a whole to rotate about its own angular momentum vector. One effect of the J2 geopotential is that it causes a satellite's orbital angular momentum vector to precess about the vector coincident with the North Pole. The rate of this precession is dependent primarily on the satellite inclination and altitude. Except for a couple of specific geometry formations, satellite formations usually have satellites with slightly different inclinations and altitudes and thus different rates of precession of the orbital angular momentum vector. The different rates of precession cause the formation to drift apart, since their orbital planes are not aligned anymore. Internal forces can be used to counteract these differential J2 forces. In order to counteract these