## Extract

So long as the rocket and satellite are in essentially the same orbit, their rates of change of period are simply as the ratios of their frontal areas divided by their masses. Very early in their common life, when their periods were both about 96.2 min, their rates of change of period were about – 0.0042 and — 0.0028 min/period, respectively, i. e. as 1-5:1. Taking their masses as 450 and 84 kg, their frontal areas must thus be as 8:1. The ratio of their ‘seen’ areas, however, as computed from the brightness, is far greater. The rocket has been observed as of zero magnitude, or even brighter, at a distance of 500 km; at this distance, a sphere of albedo 0.6 must have a projected area of 1.07 x 10^{6} cm^{2}, if its brightness (averaged over all phases) is to be zero apparent magnitude. The projected area of the satellite, taking it as a sphere of 30 cm radius, is 2827 cm^{2}, or 378 times less, and it follows that the rocket’s ‘seen’ area is 47 times its frontal area. The rocket is thus a long thin object travelling end-first; it cannot have been tumbling, even in its early life, since these observations were made then. So large a ratio as 47 is difficult (unless the rocket is a tube open throughout its length), and so large a total area also involves a very thin wall. We can reduce them both somewhat if we suppose that there was an approach to specular reflexion in some directions, with very little light in others; and in fact the brightness was very variable in some cases. It is, however, rather difficult to believe that the average brightness, taken over all directions, can have been as much as two magnitudes fainter than we have supposed, and thus the area seen cannot well be as small as 1.6 x 10^{5}. If we take it as 2.4 x 10^{5}, and assume the rocket is a cylinder of radius *r* and length *l*, then if, *l*/2*r* = 15 we have *r* = 63 cm and *l* = 1890 cm. The frontal area at zero yaw is then only 4.4 times that of the satellite, but yaws averaging about 10° would bring it up to the correct figure. Actual tumbling still seems out of the question; it would involve a frontal area comparable with the ‘seen’ area, and a drag several times greater than that observed.

## Footnotes

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- Received May 7, 1958.

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