Discrepancy transforming `SkyCoord` to `AltAz`

Description

I have come across a discrepancy that I cannot explain when converting SkyCoord (RA/Dec) to AltAz. In short, I get slightly but significantly different results using the equation of celestial navigation (as described here) and SkyCoord.transform_to.

Expected behavior

SkyCoord.transform_to should match the trigonometric result from the celestial navigation equation.

Actual behavior

There is a small difference between results.

Steps to Reproduce

1. Use the online celestial to horizon coordinates calculator available here to convert location + time + RA/Dec to an Alt/Az:

(Note that this calculator uses your local time as an input, rather than the observer’s).

This result is consistent with what I get using my own implementation of the celestial navigation equation.

1. Use astropy to do the same calculation:

from datetime import datetime
from astropy import units as u
from astropy.time import Time
from astropy.coordinates import AltAz, EarthLocation, SkyCoord

location = EarthLocation(lat=0 * u.deg, lon=0 * u.deg)
skycoord = SkyCoord(ra=0 * u.deg, dec=0 * u.deg)

# Time at longitude = 0 == UTC
time = Time(datetime(2021, 1, 1, 0, 0), scale="utc", location=location)

altaz_frame = AltAz(obstime=time, location=location)
altaz = skycoord.transform_to(altaz_frame)
print(altaz.alt.to_value("deg"), altaz.az.to_value("deg"))

# Prints: -10.59990770524396 270.1166107257178

Is there an explanation for this difference? Thanks!

System Details

macOS-10.16-x86_64-i386-64bit Python 3.8.5 (default, Sep 4 2020, 02:22:02) [Clang 10.0.0 ] Numpy 1.20.1 astropy 4.2.1 Scipy 1.6.2 Matplotlib 3.4.2

[mkbrewer]

Since the problem here is with the calculator rather than Astropy and there has been no further discussion on this issue for nearly three weeks, I believe that this issue should be closed.

[mkbrewer]

There is also the fact that the calculator uses UTC rather than UT1 to calculate sidereal time.