Assuming that the plane of the ecliptic is not at a tangent to the center of the Milky Way galaxy, on what calendar date each year is the Earth closest to the galactic core?
I also assume this date will change over time, as the Sun orbits the core, and as Earth’s orbit around the Sun precesses, so to be more specific, when is “Closest-to-the-Core Day” 2004? Also, how quickly does CTTC Day change (in years-per-calendar day), and in which direction (forward or backward on the calendar)?
17 Jun 2004, around noon US time.
As you may know, the plane of the galaxy and the ecliptic intersect in two places, on opposite sides of the sky: Sagittarius and Taurus (roughly). It just so happens that the galactic core - the radio source Sgr A - is in Sagittarius. The ecliptic passes within about five degrees of it. When the Sun is closest to the antipodal point of Sgr A, the Earth will be closest to it. The antipodal point is near the border of Taurus and Aurigae, and sometime during the day on 17 Jun is when the Sun passes by.
Your other question is trickier. We rotate around Sgr A in the direction of (roughly) Cygnus. From our point of view, if we hold the ecliptic fixed, Sgr A will appear to move along the galactic equator in opposite direction, toward Orion and Monoceros. The sun passes by this way a little later in the year, so the CTTC day is getting later. It takes roughly 220 Million years to orbit the galaxy, so if the galactic core and the ecliptic were aligned, the date would be getting later by 1/220Million of a year (0.14 seconds) per year. However, because they’re tilted by an angle of 62.6°, we have to multiply by the cosine of this angle, so it’s only 0.066 seconds per year. At this rate, it will be 1.3 million years (220 million / (365 cos(62.6°)) before CTTC is midday 18 Jun. This rate is not constant, and these calculations will only work as long as Sgr A is near the ecliptic.
I should tell you that there are bigger effects than rotation around the core that cause shifts in the date. Precession is the big one that comes to mind.
Boy did I screw that up. I got Sgr A confused with the antipodal point! As Sgr A moves away from Cygnus, the antipodal point will move closer to Cygnus, going through Auriga toward Perseus. So instead of getting later, CTTC will get earlier, by the amount I gave before. In about 1.3 Myr it would occur midday on 16 Jun, if galactic rotation were the only factor.
Achernar wrote:
Thanks. I mentioned precession in my OP, and figured it’d be a factor. At the very least, would precesison make CTTC Day change more slowly or more quickly?
Right now, I’ve got to wait some 4.5 million years or so before CTTC Day falls on my birthday for even a fraction of a second, I’d like to see it speeded up a bit. 
And personally, I’d like some more secular days off work. How much of a hassle will it be to get CTTC Day turned into a Federal holiday? And another one, six months later (“Rim Day?”).
My Galactic Celestial Mechanics expertise is a little rusty. However, since the sun (and other stars) revolve around the galactic center more like an old phonograph record (speed increases with distance from the center) than like the planets around the sun (Kepler like), is there precession in the sun’s orbit?
When I said precession, I meant precession of the Earth’s axis, which happens with a 26,000-year period - much faster than galactic rotation. This causes everything to shift by about 20 minutes per year. It used to be, a few thousand years ago when Zodiac horoscopes were invented, that the sun passed through Taurus in May. But now, as is seen by my earlier post, the sun is passing through Taurus in June. This is because of precession.
The Sun’s orbit around Sag A is really not like a phonograph record in the sense that there are interactions with clumpy matter nearby that cause the orbit to change radially quite substantially as the galaxy rotates about itself.
The galactic rotation is something of an average effect, the average velocity of the stars in our region is in the tangential direction to an orbit about the center, but the peculiar velocities of individual stars (including our own) are subject to random aberrations.
Luckily, we don’t live in an ellipitcal galaxy, because in those babies stars don’t really have a preferred direction at all!
Achernar wrote:
Well, that effect is fantastically larger than any effect from the Sun’s orbit around the core. Before CTTC Day shifts by a full 24 hours due to the solar orbit, it’ll go through the entire calendar 50 times due to precession. And if I’m reading correctly, precession changes the date in the opposite direction, by one full day every 71.2 years. So I only have to wait 25,703 years for CTTC Day to be on my birthday. (Well, if I read it wrong, I only need wait about 297 years.)
I think you read it right, but another way of looking at it is, you just missed it. It was 285 years ago (71.2 x 4).