The sttdies of earth-satellite orbits at R.A.E., between 1957 am 1961 are reviewed historioally in the main text of this Report. The topics covered include prediotion methods, the determination of orbits from observations, orbital theory, and the geophysical information derived from measuring orbital perturbations. Papers written on these topics which have not hitherto been issued as R.A.E. publioations are reprinted in the 38 Appendices to the Report. Their authors and titles are listed on pages 3 to 5·