Bill Cunningham wrote:

How can I convert astrological data like 14 CAN 28 into RA and
declination?

It's fairly straightforward spherical trignometry, once you've
'translated' the astrological notation into conventional terms. Note
that the above position has only one coordinate, ecliptic longitude,
so it will only give a true result for the Sun's location or some
other point on the ecliptic, i.e. having zero latitude. For all other
objects you're only dealing with the *projection* of its position
onto the ecliptic. Some astrological ephemerides include latitude
data for the planets &c. but most astrologers seem happy enough to
work in only one dimension, plotting everything right on the ecliptic.

At any rate, where A is right ascension, D is declination, L is the
ecliptic longitude (of a point on the ecliptic), and E is the
obliquity of the ecliptic:

A = atn(sinL * cosE / cosL); D = asn(sinL * sinE).

Watch your signs in the first formula, because the arctangent yields
two solutions 180° apart, while most calculators &c. only give one of
them, usually in quadrant I or IV (or perhaps I or II).

For the example above, first write L = 14 Cancer 28 = 3*30° + 14°28'
= 104°28'. If the obliquity of the ecliptic is taken to be 23°26' (it
varies slightly over time -- this value is good for epoch 2000.0),
then A = atn(+0.8884/-0.2498) = 105°42' = 7h02.8; D = asn(0.3851) = +22°39'.

For a nonzero latitude the formulas are a bit more complicated, but
no more difficult to apply.

--
Odysseus