User:Matrix41/sandbox

Description
A sun-synchronous orbit (sometimes incorrectly called a heliosynchronous orbit) is a special case of a polar orbit which combines altitude and inclination in such a way that a satellite on that orbit passes over any given point of the Earth's surface at the same local solar time. The unique property of the sun-synchronous orbit requires the satellite's ground track to have one local time on its ascending half and another local time (12 hours away) on its descending half. The two local times remain the same for the entire mission. The sun-synchronous orbits are often referred to by the local time of the ascending node (ie 6 AM orbit, 10 AM orbit, etc).

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). For example, a satellite in sun-synchronous orbit might cross the equator twelve times a day each time at approximately 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.

Basic Characteristics
The uniformity of sun angle is achieved by tuning natural precession of the orbit to one full circle per year. Because the Earth rotates, it is slightly oblate (the equator is slightly longer than it would be for a perfect sphere), and the extra material near the equator causes spacecraft that are in inclined orbits to precess: the plane of the orbit is not fixed in space relative to the distant stars, but rotates slowly about the Earth's axis. The speed of the precession depends both on inclination of the orbit and also on the altitude of the satellite; by balancing these two effects, it is possible to match a range of precession rates. Typical Sun-synchronous orbits are about 600–800 km in altitude, with periods in the 96–100 minute range, and inclinations of around 98° (ie slightly retrograde compared to the direction of Earth's rotation: 0° represents an equatorial orbit and 90° represents a polar orbit). The sun-synchronous orbit has a nodal regression rate equal to the Earth's mean rate of revolution around the sund of 0.985 deg/day (360 deg in 365.24 solar days).

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, at the same local solar time for each location, and begin again at the first longitude every fifteenth passage, once per day.

Two Types of Sun-Synchronous Orbits
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.

Dawn/Dusk Orbit
Riding the terminator is useful for active radar satellites as the satellites' solar panels can always see the Sun, without being shadowed by the Earth. It is also useful for some satellites with passive instruments which need to limit the Sun's influence on the measurements, as it is possible to always point the instruments towards the night side of the Earth. The dawn/dusk orbit has been used for solar observing scientific satellites such as Yohkoh, TRACE and Hinode, affording them a nearly continuous view of the Sun. Additionally, the dawn/dusk orbit orbit has been used in all-sky observations in which the boresight of the satellite observes tangentially to the Sun line-of-sight. This observing technique has been used by the COBE and WISE satellites.

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As the satellite's altitude increases, so does the required inclination, so that the usefulness of the orbit decreases doubly: first because (for an Earth-observing satellite) 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.

Given the relation between altitude and inclination, it is impossible to have a sun-synchronous satellite (in near-circular orbit) at inclination lower than 96 degrees, or altitude above 6000 km.

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

Technical details
A sun-synchronous orbit is a retrograde orbit (that is, a spacecraft in such an orbit will move opposite to the Earth's spin direction). Because of this, the node precession rate is positive (in the same direction as the Earth's spin) and a good approximation of the precession rate is


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

where
 * $$\omega_p \,$$ is the precession rate (rad/s)
 * $$a \,$$ is the Earth's equatorial radius (6.378 137 Mm)
 * $$r \,$$ is the satellite's orbital radius
 * $$\omega \,$$ is its angular frequency ($$2\pi$$ radians divided by its period)
 * $$i \,$$ its inclination
 * $$J_2 \,$$ is the Earth's second dynamic form factor (1.08&times;10&minus;3).

This last quantity is related to the oblateness as follows:


 * $$J_2 = \frac{2 \varepsilon_E}{3} - \frac{a^3 \omega_E^2}{3 G M_E}$$

where
 * $$\varepsilon_E \,$$ is the Earth's oblateness
 * $$\omega_E \,$$ is the Earth's rotation rate (7.292115&times;10&minus;5 rad/s)
 * $$G M_E \,$$ is the product of the universal constant of gravitation and the Earth's mass (3.986004418&times;1014 m3/s2)