Solunars by Aldebaran Sidereal Academy

We feel that we may therefore safely use the longitude of the minimum of 1872.6 taken from the table number III published with the curve of Figure 1 in 1929. The corresponding heliocentric longitude for the former date, and not corrected for precession, is 289ª.8.

RingsOfSaturn22 wrote: Sun Nov 05, 2023 12:55 pm This question is for Jim or anyone who might know the answer.

When we have sidereal periods of a celestial body, we are told that it is a measure of the orbit in relation to a "distant star".

Then, this further leads into how are they coming up with heliocentric longitudes? These seem to be based on the vernal point as a point of reference — thus, they have precession built in already.

I'm inclined to believe these heliocentric longitudes are being found based off of geocentric observations done in right ascension, and then they are just using equations to convert them into heliocentric.

If current heliocentric longitudes do indeed have precession built in, what would be the equation to correct for this?

I'm assuming the equation would also have to consider the tilt of the various orbits to one another.

Jim Eshelman wrote: Sun Nov 05, 2023 1:10 pm

RingsOfSaturn22 wrote: Sun Nov 05, 2023 12:55 pm This question is for Jim or anyone who might know the answer.

When we have sidereal periods of a celestial body, we are told that it is a measure of the orbit in relation to a "distant star".

That's a very casual way of saying it, probably phrased for a popular audience.

Jim Eshelman wrote: Sun Nov 05, 2023 1:10 pm

I'm inclined to believe these heliocentric longitudes are being found based off of geocentric observations done in right ascension, and then they are just using equations to convert them into heliocentric.

No, the process of calculating geocentric longitudes starts with calculating heliocentric longitudes and then adjusting for parallax. I think, for calculation speed, the actual calculations are now done from mammoth catalogues of calculated helio X, Y, Z coordinates rather than from root formulae, but in any case it goes helio first and then converted. (The only other way you could do it is with something that was ultimately heliocentric anyway, like Ptolemaic epicycles.)

Optical, radar, laser, and spacecraft observations were analyzed to determine starting conditions for the numerical integration and values of fundamental constants such as the planetary masses and the length of the astronomical unit in meters. The reference frome for the basic ephemerides is the ICRF; the alignment onto this frame has an estimated accuracy of 1-2 milliarcseconds.

Although the directions of the ICRS coordinate axes are not defined by the kinematics of the Earth, the ICRS axes (as implemented by the ICRS and Hipparcos Celestial Reference Frame) closely approximate the axes that would be defined by the mean Earth equator and equinox of J2000.0 (to within 0.1 arcsecond).

RingsOfSaturn22 wrote: Sun Nov 05, 2023 2:11 pm For this question, I was referring to the actual initial observations, not calculations that come afterwards. For instance, when NASA compiled

...doesn't most of the observational data used to create the calculations come from geocentrically based things (including the satellites)? What is the reference point that they use for such observations?

Although the directions of the ICRS coordinate axes are not defined by the kinematics of the Earth, the ICRS axes (as implemented by the ICRS and Hipparcos Celestial Reference Frame) closely approximate the axes that would be defined by the mean Earth equator and equinox of J2000.0 (to within 0.1 arcsecond).

So to me, it sounds like they are not using a "distant object" or even precession free space, since the reference system itself keeps wrapping back around to the vernal point. They mention a "frame bias" multiple times, and have pages upon pages of equations in Section B to correct for this. I was hoping I wouldn't have to use such complicated equations to fix this, haha.

I'm not clear what you mean by "reference point." If you mean coordinate systems, astronomers routinely use RA and declination (or altitude-azimuth that are then converted to equatorial coordinates). Positions are calculated as if viewed from Earth's center.

RingsOfSaturn22 wrote: Sun Nov 05, 2023 3:29 pm For some time, I've been wondering how astronomers even 200 years ago were getting their observed measurements. I mean, we base everything on the vernal point for our reference systems; yet, the vernal point is not anything you can see in the sky. I haven't heard it often detailed what exactly is done to ascertain you have proper coordinates. Maybe measurements from a sun dial or similar type device were used to ascertain the angle difference from the equinox on a particular day and then you gain your bearings from there?

No, it's way easier and more precise than that. You're relying too much on what could be visually determined from Earth (which btw is a good demonstration of why ancient people often never cared about the equinoxes and took millennia to bother to calculate them).

It's all math: The equinoctial points are the two points where the ecliptic intersects the celestial equator. Visual observation went into (and, at very minute adjustment levels, probably still goes into) figuring out how to calculate these things in the first place, but - once those were identified - it's just a matter of calculating where the two great circles intersect. In fact, there's no need to do that any more since there has long been a single equation for calculating the rate of precession across time. (I used to calculate the SVP from formula on a programmable calculated but threw away the notebooks with those formulae 20-30 years ago. There's around somewhere on the Internet.)

Or use a particular star that you know the hour angle of? There has to be something that you can use to independently verify that the calculations are correct.

That one is simple and is observational. (I did it in college and amateur astronomers do it a million times a night.) You see the star and measure the RA distance from the meridian.

I'm not clear what you mean by "reference point." If you mean coordinate systems, astronomers routinely use RA and declination (or altitude-azimuth that are then converted to equatorial coordinates). Positions are calculated as if viewed from Earth's center.

For celestial coordinates, we use the vernal equinox as a reference point.

I don't now who you mean by "we." I certainly don't. It's irrelevant to the zodiac.

But I suspect you mean that it's a factor used in the process of converting equatorial coordinates to ecliptical coordinates, so I think I answered it.