It appears that all spacecraft orbit within different parameters, dependant on altitude, and orientation to earths turn. The ISS synchronizes its orbit every 6 days(same latitude,same time of day) but a 6/365ths of a turn away from the same spot,east to west. After that, it all gets a bit blurred. My guess would be every 72 years, but does anyone know?
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6$\begingroup$ How precisely does "exactly" mean here? $\endgroup$– Russell BorogoveAug 6, 2019 at 16:07
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$\begingroup$ related but different question How long does it take for ISS to travel over all possible places of the world one time? $\endgroup$– uhohAug 6, 2019 at 16:32
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1 Answer
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(I've omitted my original approximate answer.)
It takes 3.00 days, for 46 orbits with apoapsis 394.6 km and periapsis 394.5 km, calculates section 3.2 of Earth Orbits With Repeating Ground Tracks. That paper also explains why a quickly repeating ground track is desirable. If a Soyuz launch is delayed, a new launch window for a similar rendezvous occurs quite soon.
The actual orbit is sometimes higher and more eccentric, for reasons like reducing the fuel consumption of its reboosts. The paper's Fig. 2 shows this during 2015-2016. During the past hour it climbed from 414 km to 429 km. So,
This additional mean orbit height would cause λAN to drift slightly westward after each 3-day cycle.
Practically (for Soyuz planners) it's 3 days. But the orbit is too irregular and unpredictable to predict the next time that it gets within a degree of the zenith at some terrestrial position (see Fig. 2 again).
answered Aug 6, 2019 at 17:10
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1$\begingroup$ You might want to try validating your answer at spotthestation.nasa.gov You may be surprised by the result. $\endgroup$ Aug 6, 2019 at 19:03
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2$\begingroup$ But the assumption of an orbit of exactly 90 minutes is wrong anyway. The ISS orbit height is not constant due to decay and lift operations, orbit period is also not constant. $\endgroup$– UweAug 6, 2019 at 19:11
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$\begingroup$ A circular orbit with a period of 90 minutes has a height of only 282 km. A height of 400 km has a period of 92 minutes and 24 seconds. 410 km and 92 minutes and 37 seconds. $\endgroup$– UweAug 6, 2019 at 19:33
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$\begingroup$ 46 orbits in 3 days or 72 hours would require a period of 93 minutes and 54.782 seconds. But the period of a circular orbit with 394 km height is 92 minutes and 17 seconds $\endgroup$– UweAug 6, 2019 at 20:20
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$\begingroup$ I've just quoted the eminently qualified author's numbers; I unfortunately don't have the WeavEncke software to replicate or tweak his results. $\endgroup$ Aug 6, 2019 at 20:30