perigee and apogee calculations off by a few minutes - skyfield

Question

I'm trying to calculate perigee and apogee (or apsis in general given a second body such as the Sun, and planet, etc)
from skyfield import api, almanac
from scipy.signal import argrelextrema
import numpy as np
e = api.load('de430t.bsp')
def apsis(year = 2019, body='moon'):
apogees = dict()
perigees = dict()
planets = e
earth, moon = planets['earth'], planets[body]
t = ts.utc(year, 1, range(1,367))
dt = t.utc_datetime()
astrometric = earth.at(t).observe(moon)
_, _, distance = astrometric.radec()
#find perigees, at day precision
localmaxes = argrelextrema(distance.km, np.less)[0]
for i in localmaxes:
# get minute precision
t2 = ts.utc(dt[i].year, dt[i].month, dt[i].day-1, 0, range(2881))
dt2 = t2.utc_datetime() # _and_leap_second()
astrometric2 = earth.at(t2).observe(moon)
_, _, distance2 = astrometric2.radec()
m = min(distance2.km)
daindex = list(distance2.km).index(m)
perigees[dt2[daindex]] = m
#find apogees, at day precision
localmaxes = argrelextrema(distance.km, np.greater)[0]
for i in localmaxes:
# get minute precision
t2 = ts.utc(dt[i].year, dt[i].month, dt[i].day-1, 0, range(2881))
dt2 = t2.utc_datetime()
astrometric2 = earth.at(t2).observe(moon)
_, _, distance2 = astrometric2.radec()
m = max(distance2.km)
daindex = list(distance2.km).index(m)
apogees[dt2[daindex]] = m
return apogees, perigee
When I run this for 2019, the next apogee calculates out at 2019-09-13 13:16. This differs by a few minutes from tables such as John Walker's (13:33), Fred Espenak's (13:32), Time and Date dot com (13:32).
I'd expect difference of a minute as seen above in the other sources for reasons such as rounding vs truncation of seconds, but more than 15 minutes difference seems unusual. I've tried this with de431t and de421 ephemeris with similar results.
Whats the difference here? I'm calculating distance of the center of each body, right? What am I screwing up?

Answer 1

After a bit more research and comparing skyfield output to the output of JPL's Horizons, it appears that Skyfield is correct in its calculations, at least against the JPL ephemeris (not surprise there)
I switched the above code snippet to use the same (massive) de432t SPICE kernel used by HORIZONS. This lines up with HORIZONS output (see below, apogees reported by various sources marked), the Moon begins moving away (deldot or range-rate between the observer (geocentric Earth) and the target body (geocentric Moon) goes negative
Ephemeris / WWW_USER Fri Sep 13 17:05:39 2019 Pasadena, USA / Horizons
*******************************************************************************
Target body name: Moon (301) {source: DE431mx}
Center body name: Earth (399) {source: DE431mx}
Center-site name: GEOCENTRIC
*******************************************************************************
Start time : A.D. 2019-Sep-13 13:10:00.0000 UT
Stop time : A.D. 2019-Sep-13 13:35:00.0000 UT
Step-size : 1 minutes
*******************************************************************************
Target pole/equ : IAU_MOON {East-longitude positive}
Target radii : 1737.4 x 1737.4 x 1737.4 km {Equator, meridian, pole}
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : High-precision EOP model {East-longitude positive}
Center radii : 6378.1 x 6378.1 x 6356.8 km {Equator, meridian, pole}
Target primary : Earth
Vis. interferer : MOON (R_eq= 1737.400) km {source: DE431mx}
Rel. light bend : Sun, EARTH {source: DE431mx}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2
Atmos refraction: NO (AIRLESS)
RA format : HMS
Time format : CAL
EOP file : eop.190912.p191204
EOP coverage : DATA-BASED 1962-JAN-20 TO 2019-SEP-12. PREDICTS-> 2019-DEC-03
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar elongation ( 0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate ( 0.0=NO )
*******************************************************************************
Date__(UT)__HR:MN delta deldot
***************************************************
$$SOE
2019-Sep-13 13:10 0.00271650099697 0.0000340
2019-Sep-13 13:11 0.00271650100952 0.0000286
2019-Sep-13 13:12 0.00271650101990 0.0000232
2019-Sep-13 13:13 0.00271650102812 0.0000178
2019-Sep-13 13:14 0.00271650103417 0.0000124
2019-Sep-13 13:15 0.00271650103805 0.0000070
2019-Sep-13 13:16 0.00271650103977 0.0000016 <----- Skyfield, HORIZONS
2019-Sep-13 13:17 0.00271650103932 -0.0000038
2019-Sep-13 13:18 0.00271650103670 -0.0000092
2019-Sep-13 13:19 0.00271650103191 -0.0000146
2019-Sep-13 13:20 0.00271650102496 -0.0000200
2019-Sep-13 13:21 0.00271650101585 -0.0000254
2019-Sep-13 13:22 0.00271650100456 -0.0000308
2019-Sep-13 13:23 0.00271650099112 -0.0000362
2019-Sep-13 13:24 0.00271650097550 -0.0000416
2019-Sep-13 13:25 0.00271650095772 -0.0000470
2019-Sep-13 13:26 0.00271650093778 -0.0000524
2019-Sep-13 13:27 0.00271650091566 -0.0000578
2019-Sep-13 13:28 0.00271650089139 -0.0000632
2019-Sep-13 13:29 0.00271650086494 -0.0000686
2019-Sep-13 13:30 0.00271650083633 -0.0000740
2019-Sep-13 13:31 0.00271650080556 -0.0000794
2019-Sep-13 13:32 0.00271650077262 -0.0000848 <------ Espenak, T&D.com
2019-Sep-13 13:33 0.00271650073751 -0.0000902
2019-Sep-13 13:34 0.00271650070024 -0.0000956
2019-Sep-13 13:35 0.00271650066081 -0.0001010
$$EOE
Looking at Espenak's page a bit more, his calculations are based on Jean Meeus' Astronomical Algorithms book (a must have for anyone who plays with this stuff). Lunar ephemeris in that book comes from Jean Chapront's ELP2000/82. While this has been fitted into DE430 (among others),
Sure enough, when using that ELP2000 model to find the maximum lunar distance today Sept 13 2019. You get 2019-09-13 13:34. See code below.
Meeus based his formulae on the 1982 version of Ephemeride Lunaire Parisienne and the source code below leverages the 2002 update by Chapront, but is pretty much what those other sources are coming up with.
So I think my answer is, they are different answers because they are using different models. Skyfield is leveraging the models represented as numerical integrations by the JPL Development ephemeris while ELP is a more analytical approach.
In the end I realize it's a nit-pick, I just wanted to better understand the tools I'm using. But it begs the question, which approach is more accurate?
From what I've read, DE430 and its isotopes, have been fit to observational data, namely Lunar Laser Ranging (LLR) measurement. If just for that LLR consideration, I think I'll stick with Skyfield for calculating lunar distance.
from elp_mpp02 import mpp02 as mpp
import julian
import pytz
import datetime
def main():
mpp.dataDir = 'ELPmpp02'
mode = 1 # Historical mode
jd = 2451545
data = dict()
maxdist = 0
apogee = None
for x in range(10,41):
dt = datetime.datetime(2019, 9, 13, 13, x, tzinfo=pytz.timezone("UTC"))
jd = julian.to_jd(dt, fmt='jd')
lon, lat, dist = mpp.compute_lbr(jd, mode)
if dist > maxdist:
maxdist = dist
apogee = dt
print(f"{maxdist:.2} {apogee}")