Technical Details
Equation (24) of the article Orbital perturbation analysis (spacecraft) gives the precession rate of an orbit around an oblate planet as
radians per orbit.
As the orbital period of a spacecraft is and as for a circular or almost circular orbit it follows that such an orbit is sun-synchronous if and only if
where
- is the mean motion of the Earth in its orbit around the Sun
- is the gravitational constant of the Earth
- is the coefficient for the second zonal term
As an example, for a=7200 km (the spacecraft about 800 km over the Earth surface) one gets with this formula a sun-synchronous inclination of 98.696 deg.
The definition of the Local time of the ascending node concept for Sun-synchronous spacecraft is only related to the position of the Sun indirectly through Newcomb's formula which gives the angle between the Greenwich meridian and the Vernal equinox in the form
where is the time in days from a reference epoch that corresponds to mid-night at the Greenwich meridian and is an extremely small coefficient. Nowadays one uses 2000/01/01 00:00:00 corresponding to Modified Julian Day zero. This then means (counting angles in radians) that the angle from Vernal equinox to the direction away from the Sun projected down to the equatorial plane must be approximately
The right ascension of the ascending node for a sun-synchronous orbit increases with precisely this rate
- radian/day
which is the "mean motion" of the Earth in its orbit around the Sun.
The local time of the ascending node in hours is then the constant value
where is reduced modulo to the interval
The local time of the descending node is obtained by adding (or subtracting) 12 hours
The Sun-synchronous 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. ERS-1, ERS-2 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 Sun-synchronous, "frozen" orbits.
Read more about this topic: Sun-synchronous Orbit
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