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Recently, I have been going out to observe the ISS when it is within sight of my location. I have noticed that the ISS, based on the time that I have to observe the space station during any given transit, moves at a fairly constant speed across the sky, depending on the degree of elevation and maybe some other factors related to the seeing conditions.

My question relates to the different course the space station takes when traversing over my location. There may be as long as several weeks when the ISS is not within viewing parameters for my location. Why does the course across the sky vary from time to time?

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I recommend you to take a look at Wikipedia about the ISS's orbit: Wikiepdia - ISS: Orbit

There is also a very interesting video that I think will answer to your question: ISS Orbit animation

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The iss is orbiting around the earth, but even as it does so, the earth is rotating, and the orbital rate of the iss is not aligned to the rotation of the earth. The effect is that the track that the iss takes changes with each orbit.

Roughly the Iss move back about 10 degrees with each orbit, though this amount varies, as the Iss is not in a stable orbit wrt the earth, over long periods of tim.

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To a first-order approximation, the ISS (as all satellites do), orbits in a fixed plane around the planet. As the orbital period is about 90 minutes, and observational conditions that allow viewing usually last longer than that, you might expect that if you could see it at one time, you would be able to in the future.

There are two major effects that change the relationship of the orbit with respect to twilight locations on the earth. The first is the orbit of the earth around the sun. If the plane of the orbit were fixed, this would change where the orbit encountered twilight with a yearly cycle.

The stronger effect though is precession. At the altitude of the ISS, the non-spherical mass of the earth causes the plane of rotation to move (about 5 degrees a day). So it takes a bit more than 2 months to precess all the way back around. Depending on your latitude, you should have two good periods of viewing during the full precession.

This means that for periods of weeks or so, the ISS will be passing overhead during unobservable times (middle of the day/middle of the night). As the orbit continues to precess, it will begin to pass overhead closer to twilight and you'll have opportunities for viewing based on the specifics of the orbit.

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