# How Local time of a sun synchronous orbit is related to Right ascension of ascending node?

My question may sound naive and hence would like to apologise if this question is already answered in same or other form in this forum.
How does Right Ascension Of Ascending Node ( RAAN ) of a sun synchronous orbit earth orbit is related to its local time ? Suppose a spacecraft needs to be injected into a sun synchronous orbit of certain a,e,i and local time t combination from a particular launch site. Now for the same combination of a,e,i and local time t, if the satellite is injected on any other day from the same launch site, the RAAN would differ. Still the desired local time is achieved. As long as rate of change of nodal regression is maintained, does it matter whether the injection RAAN should have any particular value ?

• As "local time" you understand solar time on Earth at point directly below satellite's nadir, right? (because "local time" has also other meanings; in the fundamental meaning it's set through political/regulatory process and only very loosely related to daytime as result of orbital mechanics.)
– SF.
Commented Jun 28, 2017 at 23:11
• @SF by "local time", I meant the equator crossing time of a spacecraft, Commented Jun 29, 2017 at 2:41
• Yes, that's a point in time. But given in time of control center timezone (= on-board clock of the probe)? GMT? Political local time of the country that point of the equator belongs to?
– SF.
Commented Jun 29, 2017 at 8:09
• @SF I think what I meant by local time matches more with your last option. To make it more clear 9:30 am local time in the morning is different from 12pm local time in the afternoon. Commented Jun 29, 2017 at 11:44
• I would understand equator crossing time, LTAN Local Time of Ascending Node, as being the local solar time, not the political local time. Commented Jun 29, 2017 at 11:53

The special property of sun-synchronous satellites is the precession, at pace equal to Earth's orbital period around the Sun (1 year). That means, the satellite's RAAN drifts by a full 360 degrees over the year, and as result, local solar time at the moment of crossing the equator remains constant.

if the satellite is injected on any other day from the same launch site, the RAAN would differ. Still the desired local time is achieved.

No - the RAAN would not differ. The two RAAN values from moments of respective injections would, but if you want the second satellite to achieve the same solar time as the first, your injection RAAN must be equal to RAAN of the first satellite at the moment of the second injection - significantly different from what it was at its own injection time, having drifted to the new value with precession since.

Pictured below are two sun-synchronous orbits (or thereabouts...) differing only by Right Ascension of Ascending Node values - by 90 degrees. This picture remains "true" - unchanged - regardless of time of day or time of year. There's the sunlit side and the night side, and one satellite passes the celestial equator at noon and midnight, the other - at sunrise and sunset (6AM, 6PM) - regardless of whichever country or ocean happens to be below at that moment, and regardless of date.

IF the date was 20th March, the day of Vernal Equinox, then RAAN of first satellite would be 0, second - 90 degrees. At any other day, the angle will differ - at autumnal equinox these values will be 180 and 270 degrees, respectively. That's because the sunlit side of Earth will be facing in exactly the opposite direction of the universe, being on the other side of the Sun. But the orbits will remain in their orientation relative to the direction of Sun and the terminator line.

• thanks for making it straight! So do you mean that local solar time is unique to a particular value of RAAN. In other words, 8:30 local solar time would necessarily have different RAAN than 9:30 local solar time ? Commented Jun 29, 2017 at 13:42
• 8:00 1st January has different RAAN from 9:00 1st January (exactly 15 degrees away; 360/24=15 : 1 hour) . But 8:00 1st February RAAN is about 30 degrees from 8:00 1st Jan ( (360 ~= 365) /12 = 30 : 1 month).
– SF.
Commented Jun 29, 2017 at 14:06
• Also note, this is only for solar local time at crossing the equator. Sun-synchronous orbits have varied (high) inclinations and the local solar time varies in other points of the orbit in a less straightforward manner.
– SF.
Commented Jun 29, 2017 at 14:08
• Thanks once again! But still I am a bit confused ! ( pardon me if I sound very naive ) . So the RAAN on 1st January is differing from RAAN on 1st February at 8:00 for the same solar local time ? Commented Jun 29, 2017 at 14:25
• @user19925: RAAN is defined in relation to "distant stars". Solar time is defined in relation to direction of Sun from given point on surface of Earth at given moment. In half a year, direction of Sun for the same hour shifts by 180 degrees in relation to distant stars (Earth on the opposite side of the Sun). For 12 hours, direction of the Sun shifts by 180 degrees in relation to a point on Earth equator. Compare synodic and sidereal day definitions. Orbital elements are defined in sidereal; solar time is synodic, the quirk of sun-synchronous is maintaining synodic, not sidereal orientation.
– SF.
Commented Jun 29, 2017 at 14:32