Abstract
An analytic method is presented to establish J 2 invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J2 influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.
Similar content being viewed by others
References
Aksnes, K.: 1972, ‘On the use of the hill variables in artifical satellite theory: Brouwer's theory’, J. Astr. Astrophy. 17, 70-75.
Brouwer, D.: 1959, ‘Solution of the problem of artifical satellite theory without drag'. Astronaut. J. 64(1274), 378-397.
Carter, T. E.: 1998, ‘State transition matrix for terminal rendezvous studies: Brief survey and new example'. J. Guid. Nav. Cont.148-155.
Coffey, S. L. and Deprit, A.: 1982, ‘Third order solution for artificial satellites'. AIAA J. Guid. Cont. Dyn. 5(4).
Kapila, V., Sparks, A. G., Buffington, J. M. and Yan, Q.: 1999, ‘Spacecraft Formation Flying: Dynamics and Control’, In: Proceedings of the American Control Conference, San Diego, California, pp. 4137-4141.
Lyddane, R. H.: 1963, ‘Small eccentricities or inclinations in the Brouwer theory of the artificial satellite’, Astronom. J. 68(8), 555-558.
Sedwick, R., Miller, D. and Kong, E.: 1999, ‘Mitigation of Differential Perturbations in Clusters of Formation Flying Satellites’, In: AAS/AIAA Space Flight Mechanics Meeting. Paper No. AAS 99-124.
Xing, G. Q., Parvez, S. A. and Folta, D.: 1991, ‘Implementation of Autonomous GPS Guidance and Control for the Spacecraft Formation Flying’, In: Proceedings of the American Control Conference. San Diego, California, 4163-4167.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schaub, H., Alfriend, K.T. J2 Invariant Relative Orbits for Spacecraft Formations. Celestial Mechanics and Dynamical Astronomy 79, 77–95 (2001). https://doi.org/10.1023/A:1011161811472
Issue Date:
DOI: https://doi.org/10.1023/A:1011161811472