Sun-synchronous orbit

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This article is about a class of orbits about the Earth. For a class of orbits around the sun, see heliosynchronous orbit.

A sun-synchronous orbit (also rarely called a heliosynchronous orbit) is a geocentric orbit which combines altitude and inclination in such a way that an object on that orbit passes over any given point of the Earth's surface at the same local solar time. The surface illumination angle will be nearly the same every time. This consistent lighting is a useful characteristic for satellites that image the earth's surface in visible or infrared wavelengths (e.g. weather, spy and remote sensing satellites). There is, of course, a yearly oscillation of the actual solar time of passage because of the eccentricity of the Earth's orbit (see analemma).

For example, a satellite in sun-synchronous orbit might cross the equator twelve times a day each time at 15:00 local time. This is achieved by having the orbital plane of the orbit precess (rotate) approximately one degree each day, eastward, to keep pace with the Earth's revolution around the sun.

This is possible for a range of altitudes (typically 600–800 km, for periods in the 96–100 min range) because the Earth's equatorial bulge causes a satellite's orbit to precess at a rate which depends on the orbit's inclination (about 98° for the aforementioned altitudes), allowing one to pick an inclination that will cause just the right amount of precession (360° per year). Variations on this type of orbit are possible; a satellite could have a highly eccentric sun-synchronous orbit, in which case the "fixed solar time of passage" only holds for a chosen point of the orbit (typically the perigee). The orbital period chosen depends on the desired revisit rate; the satellite crosses the equator at the same solar time on every passage, but it will usually be at a different longitude since the Earth rotates underneath it. For example, an orbital period of 96 min, which divides evenly into the Earth solar day (15 times) means the satellite will cross at fifteen different longitudes on consecutive orbits, looping back to the first longitude every fifteenth passage, once per day.

Special cases of the sun-synchronous orbit are the noon/midnight orbit, where the local solar time of passage for equatorial longitudes is around noon or midnight, and the dawn/dusk orbit, where the local solar time of passage for equatorial longitudes is around sunrise or sunset, so that the satellite rides the terminator between day and night. Riding the terminator is not useful for passive imaging satellites, but is useful for active radar satellites; the advantage of being on the terminator is that the satellites' solar panels can always see the Sun, without being shadowed by the Earth.

As the satellite's altitude increases, so does the required inclination, so that the usefulness of the orbit decreases doubly: first because the satellite's photographs are taken from ever farther away, and second because the increasing inclination means the satellite won't fly over higher latitudes. A sun-synchronous satellite designed to fly over the continental United States, for example, would need its inclination to be 132° or less, which means an altitude of ~4600 km or less.

Sun-synchronous orbits are possible around other planets, such as Mars.

[edit] Technical details

For a sun-synchronous orbit, the precession is retrograde (that is, opposite to the Earth's spin direction) in order to slow the apparent movement of the satellite around the Earth to match the Earth's rotation. A good approximation of the precession rate is:

$\omega_p = -\frac{3 a^2}{2 r^2} J_2 \omega \cos i$