Heliosynchronous orbit
A Sunsynchronous orbit (sometimes called a heliosynchronous orbit^{[1]}) is a geocentric orbit which combines altitude and inclination in such a way that an object on that orbit ascends or descends over any given Earth latitude at the same local mean 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 and spy satellites) and for other remote sensing satellites (e.g. those carrying ocean and atmospheric remote sensing instruments that require sunlight). For example, a satellite in sunsynchronous orbit might ascend across the equator twelve times a day each time at approximately 15:00 mean local time. This is achieved by having the osculating orbital plane precess (rotate) approximately one degree each day with respect to the celestial sphere, eastward, to keep pace with the Earth's movement around the Sun.^{[2]}
The uniformity of Sun angle is achieved by tuning the inclination to the altitude of the orbit (details in section "Technical details") such that the extra mass near the equator causes the orbital plane of the spacecraft to precess with the desired rate: the plane of the orbit is not fixed in space relative to the distant stars, but rotates slowly about the Earth's axis. Typical sunsynchronous orbits are about 600–800 km in altitude, with periods in the 96–100 minute range, and inclinations of around 98° (i.e. slightly retrograde compared to the direction of Earth's rotation: 0° represents an equatorial orbit and 90° represents a polar orbit).^{[2]}
Special cases of the sunsynchronous orbit are the noon/midnight orbit, where the local mean solar time of passage for equatorial longitudes is around noon or midnight, and the dawn/dusk orbit, where the local mean 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 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, Hinode and Proba2, affording them a nearly continuous view of the Sun.
Sunsynchronous orbits are possible around other oblate planets, such as Mars. But Venus, for example, is too spherical to have a satellite in sunsynchronous orbit. See the article Venus where a flattening coefficient of zero for this planet is cited.
Technical details
Equation (24) of the article Orbital perturbation analysis (spacecraft) gives the angular precession per orbit for an orbit around an oblate planet as
 $\backslash Delta\; \backslash Omega\; =\; 2\backslash pi\backslash \; \backslash frac\{J\_2\}\{\backslash mu\backslash \; p^2\}\backslash \; \backslash frac\{3\}\{2\}\backslash \; \backslash cos\; i\backslash ,$
where
 $J\_2\backslash ,$ is the coefficient for the second zonal term (1.7555 · 10^{10} km^{5} / s^{2}) related to the oblateness of the earth (see Geopotential model),
 $\backslash mu\backslash ,$ is the gravitational constant of the Earth (398600.440 km^{3} / s^{2})
 $p$ is the semilatus rectum of the orbit,
 $i$ is the inclination of the orbit to the equator.
An orbit will be sunsynchronous when the precession rate, $\backslash rho$, equals the mean motion of the Earth about the Sun which is 360° per tropical year (1.99106 · 10^{7} radians / s) so we must set $\backslash Delta\backslash Omega/P=\backslash rho$ where P is the orbital period.
As the orbital period of a spacecraft is $2\backslash pi\backslash \; a\backslash sqrt\{\backslash frac\{a\}\{\backslash mu\}\}\backslash ,$ (where a is the semimajor axis of the orbit) and as $p\; \backslash approx\; a\backslash ,$ for a circular or almost circular orbit it follows that
 $\backslash rho\backslash approx\; \backslash frac\{3J\_2\backslash cos\; i\}\{2a^\{7/2\}\backslash mu^\{1/2\}\}=(360\backslash text\{\xb0\; per\; year\})\backslash times(a/12352\backslash text\{\; km\})^\{7/2\}\backslash cos\; i=(360\backslash text\{\xb0\; per\; year\})\backslash times(P/3.795\backslash text\{\; hrs\})^\{7/3\}\backslash cos\; i$
or when $\backslash rho$ is 360° per year,
 $\backslash cos\; i\backslash \; \backslash approx\backslash \; \backslash frac\{\backslash rho\backslash \; \backslash sqrt\{\backslash mu\}\}\{\backslash frac\{3\}\{2\}\backslash \; J\_2\}\backslash \; a^\{\backslash frac\{7\}\{2\}\}=(a/12352\backslash text\{\; km\})^\{7/2\}=(P/3.795\backslash text\{\; hrs\})^\{7/3\},$
As an example, for a=7200 km (the spacecraft about 800 km over the Earth surface) one gets with this formula a sunsynchronous inclination of 98.696 deg.
Note that according to this approximation cos i equals −1 when the semimajor axis equals 12 352 km, which means that only smaller orbits can be sunsynchronous. The period can be in the range from 88 minutes for a very low orbit (a=6554 km, i=96°) to 3.8 hours (a=12 352 km, but this orbit would be equatorial with i=180°). (A period longer than 3.8 hours may be possible by using an eccentric orbit with p<12 352 km but a>12 352 km.)
If one wants a satellite to fly over some given spot on Earth every day at the same hour, it can do between 7 and 16 orbits per day, as shown in the following table. (The table has been calculated assuming the periods given. The orbital period that should be used is actually slightly longer. For instance, a retrograde equatorial orbit that passes over the same spot after 24 hours has a true period about 365/364 ≈ 1.0027 times longer than the time between overpasses. For nonequatorial orbits the factor is closer to 1.)
Orbits per day  Period (hrs)  Height above Earth's surface 
Maximum latitude 

16  $1\backslash tfrac\{1\}\{2\}$ = 1 hr 30 min  282  83.4° 
15  $1\backslash tfrac\{3\}\{5\}$ = 1 hr 36 min  574  82.3° 
14  $1\backslash tfrac\{5\}\{7\}$ ≈ 1 hr 43 min  901  81.0° 
13  $1\backslash tfrac\{11\}\{13\}$ ≈ 1 hr 51 min  1269  79.3° 
12  $2$  1688  77.0° 
11  $2\backslash tfrac\{2\}\{11\}$ ≈ 2 hrs 11 min  2169  74.0° 
10  $2\backslash tfrac\{2\}\{5\}$ = 2 hrs 24 min  2730  69.9° 
9  $2\backslash tfrac\{2\}\{3\}$ = 2 hrs 40 min  3392  64.0° 
8  $3$  4189  54.7° 
7  $3\backslash tfrac\{3\}\{7\}$ ≈ 3 hrs 26 min  5172  37.9° 
When one says that a sunsynchronous orbit goes over a spot on the earth at the same local time each time, this refers to mean solar time, not to apparent solar time. The sun will not be in exactly the same position in the sky during the course of the year. (See Equation of time and Analemma.)
The Sunsynchronous orbit is mostly selected for Earth observation satellites that should be operated at a relatively constant altitude suitable for its Earth observation instruments, this altitude typically being between 600 km and 1000 km over the Earth surface. Because of the deviations of the gravitational field of the Earth from that of a homogeneous sphere that are quite significant at such relatively low altitudes a strictly circular orbit is not possible for these satellites. Very often a frozen orbit is therefore selected that is slightly higher over the Southern hemisphere than over the Northern hemisphere. ERS1, ERS2 and Envisat of European Space Agency as well as the MetOp spacecraft of the European Organisation for the Exploitation of Meteorological Satellites are all operated in Sunsynchronous, "frozen" orbits.
See also
 Orbital perturbation analysis (spacecraft)
 Analemma
 Geosynchronous orbit
 Geostationary orbit
 List of orbits
 Polar orbit
 World Geodetic System
References
 Sandwell, David T., The Gravity Field of the Earth  Part 1 (2002) (p. 8)
 SunSynchronous Orbit dictionary entry, from U.S. Centennial of Flight Commission
 NASA Q&A
External links
 List of satellites in Sunsynchronous orbit
