Separation between moon and target not reversible

Description

When I want to compute the distance between the moon and an object I get two different value based on which reference I use (the moon of the object)

Expected behavior

It should be exactly the same

Actual behavior

The separation between the moon and the target is different.

Steps to Reproduce

import astropy.units as u
from astropy import coordinates as c
import astropy.time as TIME

##get a position on earth
obs = c.EarthLocation.of_site('Keck Observatory')

##and a time
start_time = '2018-01-23T01:01:05.813'
starttime = TIME.Time(start_time, format='isot', scale='utc')

##get the moon information
moon = c.get_moon(starttime, location=obs)

##and get a target
RA = 97.00
DEC = 4.9
c1 = c.SkyCoord(RA, DEC, frame='fk5', unit='deg')

##and compute the separation
moon_sep = moon.separation(c1)
moon_sep2 = c1.separation(moon)

if you print moon_sep and moon_sep2 you will get 86.05756420797839 and 30.615793847554087.

By the way, if I create a SkyCoord object manually from the moon coordinates:

c2 = c.SkyCoord(moon.ra.value, moon.dec.value, frame='fk5', unit='deg')
sep = c1.separation(c2)
sep2 = c2.separation(c1)

I get: sep = sep2 = 86.05242730221599 which is slightly different from one of the previous value but this time the reference does not matter.

System Details

Linux-5.9.16-1-MANJARO-x86_64-with-glibc2.33 Python 3.9.2 (default, Mar 3 2021, 20:02:32) [GCC 7.3.0] Numpy 1.21.2 astropy 4.3.1 Scipy 1.7.1 Matplotlib 3.4.3

[astrom-tom]

I did not really find anything so I allowed myself to post it there. In any case, if this is a known behavior I guess it would be useful to mention it in the webpage about separation here

[pllim]

I feel like similar questions have been asked several times. I vaguely remember the explanation being something about frame of reference. Either that, or that is no moon! Maybe @adrn could clarify for real.