35,790km geostationary height + 6,378.4km equator radius = 42,168.4km, (= 6.611 * Earth radius). Various simple fractional day orbits have orbit heights as factors of equator radius, also as factors of the geostationary orbit radius (shown now here as a 3 line table with orbit periods, and both radii ratios):
.1day 1/8 0.2, 1/4, 0.3, 3/8, 0.4, 1/2, 0.6, 5/8, 0.7, 3/4, 0.8, 7/8, 0.9, 1day
1.43 1.65 2.26 2.62 2.96 3.44 3.59 4.17 4.71 4.84 5.21 5.46 5.70 6.05 6.17 6.61
.216 .250 .342 .397 .448 .520 .543 .630 .712 .731 .789 .826 .862 .915 .933 1.00
Satellites orbiting Earth for viewing or communicating with any polar regions, thus best in orbits passing over the poles, instead of orbiting around the equator, would each have been easily given some orbit period which was some exact simple fraction of 1 day, (such as maybe 3/8 or maybe 3/10), which would have been refined into orbits which would never within each whole day's orbit pass too badly close by any one of the 1 day orbit geostationary cable lifts. Best for such satellites might be 10, 8, 5, or 4 exact orbits/day.
Also, fixing orbiting satellites into these perfectly timed orbits meant that more than one could very safely share the same orbit height, conveniently passing over a pole at different times during each day. You could have some signals between them & you aimed differently during the day, somewhat like we usefully keep telescope aiming directions being slowly properly turned throughout each night. Extremely fine orbit refinements could occasionally be done by suitably opening and tilting a wide enough reflector for Sol's light, to then slowly exploit the very weak reflected light pressure.
How far from the equator might be safe to avoid being in any path of any equator orbiting satellite? Much of France is about 600km wide by 750km high (373mi by 466mi). Thus all geostationary cable lifts anchored at least 500km from the equator are nicely at least France's width safely away from the equator. That distance safely cleanly becomes almost 1.2% of each common geostationary orbit radius.
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