Many spacecraft use such orbits, e.g. the US Air Force surveillance satellites of the DMSP series (successfully adapted to carry science sensors), or the series of French Earth-resources spacecraft SPOT. The next generation following DMSP, named NPOEES and essentially dedicated to research, also uses such orbits. The space shuttle avoids polar orbits, because flying through the aurora
exposes astronauts to radiation and creates other problems. But for studying
the aurora, Birkeland currents, polar rain and other phenomena related to the
distant magnetosphere, such orbits are very useful. For instance, although
the DMSP spacecraft (above) were designed for military needs, scientists have
also equipped them with magnetometers, particle detectors and other
instruments, which have provided a great amount of scientific information.
In fact, although the DMSP mission was originally conceived as a project of the US Air Force, its scientific usefulness has been so widely recognized, that its follow-up will be a joint mission of the USAF, NOAA (National Oceanic and Atmospheric Administration, successor to the US Weather Bureau) and NASA. Known as the National Polar-orbiting Operational Environmental Satellite System or NPOESS ("en-poss") for short, the satellites of that mission, to be launched in the first decade of the 21st century, will carry a sophisticated complement of scientific instruments.
The Earth is not an exact sphere but bulges slightly at its equator. Any orbit passing exactly above the geographic poles is symmetrically affected by the bulge and its plane stays fixed relative to the stars.
Relative to the Sun, however, the orbital plane will slowly rotate. The reason is that the Earth itself orbits the Sun, so that the Sun's position in the sky, relative to the distant stars, slowly rotates around the Earth, one circuit per year. (The 12 constellations through which the Sun passes on that journey were named by the ancients and are known as the zodiac.) If the orbital plane of the polar satellite points at the Sun now, in three months' time the Sun's motion across the sky would make that plane perpendicular to the Sun's direction.

An inclined orbit, whose northermost point is not the north pole but falls short by (say) 1000 km, will be affected asymmetrically by the Earth's bulge, and as a result its orbital plane would slowly rotate around the Earth's axis. With a suitable inclination, about 8 degrees off the polar orbit, that motion matches the slow motion of the Sun across the sky. If the satellite then starts near a noon-midnight orbit, it will always pass near noon and near midnight. A noon-midnight "Sun-synchronous" orbit was actually used by some DMSP satellites.
A different choice was made for MAGSAT, orbited 1979-80 to survey the
Earth's own magnetic field near its surface. Magnetic fields from the
magnetosphere are a disturbing factor in such a mission, a factor that strongly depends on the orientation of the orbit relative to the Sun's direction. By placing the
satellite in a sun-synchronous orbit near the dawn-dusk plane (90 degrees to the
noon-midnight plane described earlier), not only was the interference kept small, but because the orbit's orientation relative to the Sun did not change, the disturbance also stayed more or less the same throughout the mission.
On the other hand, the Dynamics Explorer (DE) mission of 1981 used two polar
spacecraft, one in a low orbit to intercept the aurora (among other things) and
a second one in an elongated orbit to observe auroral acceleration and also to
take pictures of the entire auroral oval from a distance. To ensure the best
chance for the two spacecraft to intercept the same auroral electron beam at
different altitudes, it was decided that both orbits would always share the same plane. They were therefore made to pass over the geographical poles: with
any other choice the Earth's bulge would have rotated the planes at different
rates and they would have soon drifted apart.
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