Angles in Right Ascension

[BlueKnight22]

When measured in Longitude, the Ascendant (Asc), Descendant (Dsc), Zenith (Z) and Nadir (N) are all 90 (or 180) degrees apart from each other. The same is true about the set of: Vertex (Vx), Anti-Vertex (Av), South Point (SP) and North Point (NP) (when measured in Longitude).

However, MC and IC are NOT perpendicular to East Point (EP) and West Point (WP) when measured in Longitude. [I’m not sure if we refer to EP & WP as Equatorial Ascendant and Equatorial Descendant when measured in Longitude?]

When measured in Right Ascension (RA), MC, IC, EP and WP are all 90 or 180 degrees apart from each other.

My question, is that, when measured in RA, is the set of Asc/Dsc/Z/N all 90 & 180 degrees apart? Same question for Vx/Av/SP/NP (when measured in RA).
And if they are not, is there a way to calculate these non-perpendicular angles (in RA) using Solar Fire?

[Jim Eshelman]

When measured in Longitude, the Ascendant (Asc), Descendant (Dsc), Zenith (Z) and Nadir (N) are all 90 (or 180) degrees apart from each other. The same is true about the set of: Vertex (Vx), Anti-Vertex (Av), South Point (SP) and North Point (NP) (when measured in Longitude).

However, MC and IC are NOT perpendicular to East Point (EP) and West Point (WP) when measured in Longitude.

This is an astute way of thinking - and understandable given how the terms are often used. It's a great question.

However, the actual longitudes of EP and WP are indeed the ecliptical squares to MC/IC. (BTW, these are the cusps of the Morinus 1st/7th which are openly called Eastpoint and Westpoint.)

The points written on a chart face that are the ecliptical position that is square MC in RA have been called "Eastpoint" etc. for a long time. A little over a year ago, I decided to disentangle this historic awkwardness be rebranding a couple of things - basically, going back to calling the "[ecliptical] squares to MC" EP & WP, then calling the squares to it in RA the same thing with an alpha tagged on the end (to mean, "the same thing, but in Right Ascension." Here's the thread where I worked thouigh all that: viewtopic.php?f=15&t=4659

My question, is that, when measured in RA, is the set of Asc/Dsc/Z/N all 90 & 180 degrees apart? Same question for Vx/Av/SP/NP (when measured in RA).

No. Those points (other than two brief moments a day) aren't equatorial. This was discussed in a long (but I think clear) larger discussion of the angles here:
viewtopic.php?f=15&t=4079
The gist is in this passage (taken here out of context) - but I recommend the whole thread:

Separately, we can measure the minor angles in right ascension (RA) along the celestial equator. Of six minor angles, only two have positions unique from what we have seen above. Zenith, Nadir, Northpoint, and Southpoint all have the same RA as the meridian - of either the MC or IC - therefore, no new angles are introduced by measuring them in RA.

However, the RA of Eastpoint and Westpoint are not shared by any other angles. Their conjunctions are measured in RA. (For convenience, we place in our charts the point of the ecliptic that is exactly square MC in RA to alert us when a planet may be conjunct. We use it not as an ecliptical point but, rather as an inference - a hint - of where a planet would be when it squares MC in RA. One must always go back and check the contact in RA.)

And if they are not, is there a way to calculate these non-perpendicular angles (in RA) using Solar Fire?

The RA of Zenith-Nadir and Northpoint-Southpoint is identical with the RA of MC-IC. There's nothing new to find. This also means that their squares in RA are points already being examined.

Squares to Asc-Dsc in RA are nonsensical. They have nothing to do with the celestial equator.

To answer your explicit question, the celestial longitudes of Asc/Dsc and Z/N are not 90° in RA. The actual Zenith and Nadir, though, are indeed 90° from Asc/Dsc - that is, the horizon - because the Zenith-Nadir axis is the polar axis of the entire horizon.

Don't overrate the importance of RA. It's of relatively minor importance in astrology. Even MC-IC contacts are better measured along the prime vertical, even if the math happens to be simpler along the equator. Note that the true EP and WP (being points on the horizon) are also exactly 90° from MC and IC (being points on the meridian) if measured along the prime vertical, because all points on the horizon square all points on the meridian measured along the PV.

[BlueKnight22]

Thanks Jim, this is very helpful.

So one point I just want to be clear on is that these 3 things:

1) the square to the MC (which is the 1st house cusp in the Morinus house system)
2) the equatorial ascendant
3) the East Point (measured in Right Ascension)

are all basically the same "point" but viewed from 3 different vantage points/perspectives?

[Jim Eshelman]

1) the square to the MC (which is the 1st house cusp in the Morinus house system)
2) the equatorial ascendant
3) the East Point (measured in Right Ascension)

are all basically the same "point" but viewed from 3 different vantage points/perspectives?

The last two are exactly the same - no difference.

The first one is the same point in the following sense: All three are the simultaneous intersection of the horizon, prime vertical, and celestial equator. The literal celestial longitude of this point is your number (1). Your (2) and (3) are the longitude of a point on the ecliptic (zero latitude) that has the same RA.