Hi everyone,

On this table (https://www.skyscript.co.uk/ra.htm) which converts right ascension to zodiacal longitude, 0 degrees of aries, cancer, libra and capricorn are where we would expect them to be; on the positions of 0, 90, 180 and 270 by right ascension.
But, the rest of the positions are off by several degrees each. Example: we would expect 15 degrees of cancer to be on 105 degrees of zodiacal longitude, but it's actually on 106 deg and 17 min.
How can one explain such disparity?
I tried to look at a scheme of the ecliptic and equator (https://en.wikipedia.org/wiki/Ecliptic# ... liptic.PNG), but the solution still evades me.
I guess that for 0 aries and 0 libra it's easy, as there's an exact overlap. But why for 0 cancer and 0 cap, it's also exact? If in those positions we need to project the ecliptic degrees onto the equator, just like we do with the rest of the non 0 ari/lib positions,?

A definition of Right Ascension, to those interested:
https://www.skyscript.co.uk/glossary/right-ascension

Hi there - this is because of the obliquity of the ecliptic. Degrees of right ascension are measured on the celestial equator, which does not lie on the ecliptic. At 0 Aries and 0 Libra the two circles cross and hence, as you have pointed out, celestial longitude (ecliptic longitude) = right ascension.

At 0 Cancer and 0 Capricorn, the degrees of right ascension (90 and 270) are at right angles to the equivalent degrees of celestial longitude and this means that at these specific degrees, celestial longitude (in absolute longitude) = right ascension .

At all other points on the ecliptic, degrees of longitude will not equal degrees of right ascension because of the obliquity of the ecliptic and one has to perform some spherical trigonometry to find the points of equivalence.

I guess, strictly speaking, it is the projection of degrees of RA (right ascension) at right angles to the celestial equator, that gives rise to the difference with zodiacal longitude. It is only at the solstices that the degrees of celestial longitude (0 Cancer and 0 Capricorn) lie orthogonally to celestial equator.

Essentially, the celestial equator is the plane of the earth's rotation and gives rise to the day and diurnal (primary) motion. The ecliptic is the plane of the Earth's motion around the Sun over the course of the year and gives rise to the annual cycle and secondary motion.

https://en.wikipedia.org/wiki/Ecliptic

Relationship to the celestial equator

Main article: Axial tilt

The plane of Earth's orbit projected in all directions forms the reference plane known as the ecliptic. Here, it is shown projected outward (gray) to the celestial sphere, along with Earth's equator and polar axis (green). The plane of the ecliptic intersects the celestial sphere along a great circle (black), the same circle on which the Sun seems to move as Earth orbits it. The intersections of the ecliptic and the equator on the celestial sphere are the equinoxes (red), where the Sun seems to cross the celestial equator.

Because Earth's rotational axis is not perpendicular to its orbital plane, Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, which is known as the obliquity of the ecliptic.[8] If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes. The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south.[5] The crossing from south to north is known as the March equinox, also known as the first point of Aries and the ascending node of the ecliptic on the celestial equator.[9] The crossing from north to south is the September equinox or descending node.

https://en.wikipedia.org/wiki/Axial_tilt

Best wishes. Ed

Hi there - I hope this makes things a little clearer.
Best wishes. Ed

astralwanderer:

Thanks alot, your post answered almost all of my questions.
I tried to find a definition of "obliquity", but failed in finding a simple one.
If I understand it correctly, it has to do with the fact we're dealing with two (imaginary) planes in space, from which we project points, from one plane to the other.
Is the ecliptic an oval plane or round. Not sure if it's important or not.

Ed's answer and illustration are spot on. The ecliptic and equator are both circles, more specifically great circles, meaning that they have the point of observation (the place of birth, in a nativity) for their centre. So they are concentric (have the same centre) but are inclined to each other. That is what is meant by obliquity. The angle at which they are inclined changes slightly over time but is currently somewhere around 23.45 degrees (23°27′). The points where they intersect are the equinoxes (0° tropical Aries and Libra).

Hi - thanks for the response.

If I understand it correctly, it has to do with the fact we're dealing with two (imaginary) planes in space, from which we project points, from one plane to the other.

This is correct. For the purposes of astronomical/astrological calculations, the planes are effectively thought of as great circles, all points on each circle (ecliptic and equator) equidistant from the central point of both which is taken to be the centre of the earth. Some diagrams might make the great circles look like ovals, but this is just an effect of trying to reduce a 3 dimensional sphere to a 2 dimensional representation.

Obliquity: the angle between the planes of the Earth's equator and the ecliptic. Its present value is approximately 23 degs 26 mins.

Obliquity is a dynamic value and it alters over long periods of time from 21 degs 55 mins to 24 degs 18 mins. This is due to the effects of precession and nutation.

The definition of obliquity is taken from J Mitton (1993) The Penguin Dictionary of Astronomy.

Ed

Martin hi,
I though you'll might want to chime in.

Astral Wanderer (Ed):
Okay, interesting.
So, the ecliptic tilt relative to the celestial equator changes from 21 degs 55 mins to 24 degs 18 mins and back, over the course of 26,000 years?

Trying to find a good vid on YouTube, to see an animation of what we're talking about.

Hi again - broadly speaking, it is a 26, 000 year cycle, but it gets very complex at this point as there are a number of factors/forces interacting to impact on the Earth's position in space.

The precessional cycle is the one of greatest interest to astrologers of course, moving the stars around the zodiac over the course of the full precessional cycle.

Ed