The first amazement at hearing of the successful launching of the Russian Earthsatellite in October may have been followed in the reader's mind by some bewilderment at its rapid and seemingly erratic progress over all the world's capitals, large cities and outlying island groups. One supposed that a mathematical prediction would be possible but hesitated to attempt anything so complex. Yet, with some simplifying assumptions which must in any case be rather closely approximated by any near satellite that can continue to rotate in orbit, the problem is not difficult and lends itself to graphical treatment. The construction here proposed will give a good insight into the behaviour of such satellites and provide reasonably accurate predictions for a day or two ahead.