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What is required for a satellite to remain positioned 400 km above the north pole, thus allowing it to appear essentially stationary relative to the surface of the earth? Could this best be achieved by placing the satellite in a solar orbit with the same period as the earth, only 400 km above the pole?

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    $\begingroup$ You mean, a geostationary orbit is too far from Earth for you? $\endgroup$ – AtmosphericPrisonEscape Sep 9 '17 at 19:31
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    $\begingroup$ @AtmosphericPrisonEscape Geostationary is only over the equator anyway. $\endgroup$ – Loren Pechtel Sep 10 '17 at 2:49
  • $\begingroup$ A solar orbit with the same period as the earth, only 400 km above the pole is not possible, the sun must be in the plane of the orbit and not below. $\endgroup$ – Uwe Sep 10 '17 at 20:24
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Could this best be achieved by placing the satellite in a solar orbit with the same period as the earth, only 400 km above the pole?

No. At least, not without it continuously applying thrust against Earth.

At a distance of only 400km above the surface, Earth's gravity (acceleration toward Earth) will still be nearly that of the value at Earth's surface (9.8 m/s/s).

If you could "magically" place an object geostationary to Earth, 400km straight up from the North Pole and release it there, it won't stay there. Yes, technically, it will be in orbit around the Sun, just like Earth is. But, it won't be in orbit around the Earth, so will respond to Earth's gravity field with a downward acceleration of pretty much 1g.

There is no way for an object to orbit the Earth such that it would appear to be stationary over a pole. There are orbits which allow an object to "linger" at high latitudes, but they are actually in highly inclined, highly elliptical orbits (see Molniya orbit); they can be geosynchronous - appearing in the same region of the sky most of the time, and repeatedly describing the same path in the sky (from the point of view of a "fixed" ground-based observer), but they are by no means geostationary.

About Geostationary Orbits

Gravity follows the inverse-square law; the greater the distance, the smaller the force. At low altitudes such as where the ISS orbits, an object must travel at about 7.6km/s to remain in orbit (completing one orbit about every 90 minutes). The Moon, circling the Earth once a month at a distance of about 239,000 miles, travels in its orbit at about 1km/s. At about 22,000 miles, an object would have to travel about 3km/s, completing one orbit every 24 hours. At just the right speed and distance, the orbit will be synchronous with Earth's rotation. If the orbit is also circular and at zero inclination to the equator, an object in that orbit will appear to be at a fixed point in the sky, always directly over some specific point on the Earth's surface. For more on this, see this question: How do communication satellites remain positioned above a particular region? and this Wikipedia article.

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    $\begingroup$ I suspect that the question asker may not be very familiar with satellites and orbits and thus may benefit from a bit more explanation of geostationary orbits—in particular, why they are only possible at a very specific altitude and only over the equator. Possibly direct them to this question? $\endgroup$ – KRyan Sep 10 '17 at 2:53
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    $\begingroup$ Even if Earth was not exerting any force on the satellite, it would still "crash" - 400km above the pole would put it in an orbit of about the same radius, eccentricity, period, etc, but different inclination. If Earth wasjust a weightless hologram, the satellite would cross through it 3 months later, and appear 400km above the south pole 6 months later - the two orbital planes have a common center (the Sun) and intersect each other, meaning "400km above" on one side of the Sun is "400km below" on the other side. You can't have an orbit just "offset from the center of mass". $\endgroup$ – SF. Sep 10 '17 at 19:32
  • $\begingroup$ The satellite being discussed is not in earth orbit. It is in an orbit around the sun and shadows the earth, following in essentially the same elliptic as they both orbit the sun. The altitude (potentially over either pole) was chosen to minimize atmospheric drag but be close enough to quickly reach any point above 23.5 degrees Lat at SX1 speeds. $\endgroup$ – Jim Sep 12 '17 at 4:10
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4,000,000km but not 400km. Even if you ignore Earth there's no solar orbit that stays 400km above the North pole. It's going to swing back and forth over the course of a year, from 400km above the North Pole to 400km above the South Pole. In practice Earth's gravity would rapidly pull it down.

A million km up it's possible to have a pole-hovering satellite but it's not actually in orbit, but using a solar sail to hover. That can only be done when you're far enough out that the minuscule force of a solar sail is enough to counteract the gravity of the body you are trying to hover over. This actually has a practical use--you could put a TV satellite over the pole to serve customers too far north to be served by the equatorial satellites. The patent has expired, you're free to build one.

Edit: The patent: https://www.google.com/patents/US5183225

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    $\begingroup$ Could you link the patent, if it is online somewhere? $\endgroup$ – Paŭlo Ebermann Sep 10 '17 at 9:09
  • $\begingroup$ @PaŭloEbermann there is a question a long time ago with a link to it. I thing the inventor is also a famous SF writer. I'll go take a look now. $\endgroup$ – uhoh Sep 10 '17 at 20:03
  • $\begingroup$ @PaŭloEbermann I found it below another answer by LorenPechtel! It turns out I asked the same question in comments there that you did here. $\endgroup$ – uhoh Sep 10 '17 at 20:12
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    $\begingroup$ @uhoh I had completely forgotten that I had referred to it before. $\endgroup$ – Loren Pechtel Sep 11 '17 at 3:49
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    $\begingroup$ @Jim Imagine Earth in a circular orbit around the Sun with it exactly in the center of the orbit. Now imagine a point above the North pole. As the Earth goes around the Sun, this point moves in a similar circle, but now the Sun is not at the center. This is not an orbit around the sun. In order for this orbit to be centered on the sun, it would have to be tilted, so after 3 months (90 degrees) it would pass through the Earths' orbit, and after 6 months(180 degrees) it would be above the South pole, assuming it could pass through the Earth. It can't orbit the Earth and stay above the pole. $\endgroup$ – uhoh Sep 11 '17 at 4:48

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