# Are ascending node of sun, the point of intersection of prime meridian and equator and center of earth all collinear?

I did a bit of googling but couldn't find the exact answer, so are the following 3 points collinear or not ?

1_center of earth

2_ascending(or descending) node of sun

3_point of intersection of prime meridian and equator(point of zero longitude on equator).

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No. They can align at some special times, though. Why do you think they should be collinear? – Cheeku Jul 20 '14 at 23:46
its not possible, all these points are stationary w.r.t to earth,, so they all remain collinear or never get aligned, they can't be aligned at some times and not at other times, – Salman Azmat Jul 21 '14 at 5:12
The ascending node of the sun is not stationary w.r.t the earth. The earth rotates, so the prime meridian rotates, meaning that the intersection of it and the equator also rotates. The vernal equinox, which is the ascending node of the sun, is fixed in the sky (at least on small timescales), and hence it does not rotate. – Takku Jul 21 '14 at 16:01
oh, right, I meant to ask that at the time when sun passes through vernal equinox does these points get aligned ? – Salman Azmat Jul 21 '14 at 16:19
@SalmanAzmat: Not exactly. During either equinox there is a moment when the line between center of earth and the sun aligns with the equator (as opposed to just crossing it twice daily), and if it happens the sun is in zenith above prime meridian at that moment, your conditions will be satisfied. But depending on precision you allow, that may be a very short time window. It's all about how precisely you want that to be. Each equinox the line crosses the prime meridian within about 0.25 degree of latitude, or about 27 kilometers from equator. Some years it's less, some - more. – SF. Jul 22 '14 at 13:54

Not exactly.

During either of the equinoxes there is a moment when the line between center of earth and the sun aligns with the equator (as opposed to just crossing it twice daily). This doesn't coincide with prime meridian in any way though; it may happen at any meridian whatsoever that happens to coincide with the line.

Of course if it happens the sun is in zenith above prime meridian at that moment, your conditions will be satisfied. But depending on precision you allow, that may be a very short time window. It's all about how precisely you want that to be.

Near Equinox Earth tilts by about 0.25 degree of latitude per day, meaning that is the maximum angle by which the line will be off from equator while crossing the prime meridian on the same day as when Equinox happens. 0.25 degree of latitude is about 27 kilometers, so this is the maximum error. Of course on some years, that will be much less, it's just that Earth tilt is correlated with length of year, zenith line crossing of prime meridian is correlated with time of day, and time of day is not really correlated with length of year.

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Actually, if you allow for precession and nutation, this can never happen, since the only time the celestial equator and earth's equator were perfectly in sync was Jan 1 2000, and there was no equinox on that day. – barrycarter Oct 9 '14 at 1:25
@barrycarter: Could you explain? The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. That seems to imply they are always in sync, since one is defined by the other. Did you mean the ecliptic plane? In that case, it intersects the equator plane, and during equinoxes the intersection line happens to pass the Sun (or, if you nitpick at inexactness of the Ecliptic - the Sun passes the Earth equator plane twice a year.) At these moments Earth center, the Equator and the Sun are colinear, but the meridian is entirely random. – SF. Oct 18 '14 at 21:38
Woops, my mistake. I was assuming the J2000 celestial equator, and the earth's equator as it is today, in 2014. If you choose the J2014.today celestial equator, then, yes, by definition, the celestial equator and the earth's equator are in the same plane (I happen to be working on a program about precession, so J2000 is sort of fixed in my mind <G>) – barrycarter Oct 19 '14 at 2:04
@barrycarter: In fact, I meant the momentary celestial equator for given equinox day - the moment when the point on Earth where the Sun is in zenith crosses the Earth's equator. – SF. Oct 20 '14 at 0:47
Yes, you're right, I'm wrong, I'm sad :) – barrycarter Oct 20 '14 at 1:26