An estimate is fine. But if possible, I am looking for a reference that I can cite.
This is the beginnings of a partial answer, I'm happy if someone takes over or adds to it.
Why not do all six missions instead of just one?
Using scripts from these 1, 2 I've plotted the distance between the Earth and Moon centers as the think black line, then the thick color bars are those distances minus the Earth radius, plus the Moon's radius plus a far-side altitude of 183 km.
The lengths of the bars are the aproximate total mission lengths and so we'll have to add in the times of each ingress and egress of passing behind the Moon.
I'm not sure where to find these but if someone can point me in the right direction I can scrape the numbers and add them here.
from skyfield.api import Topos from skyfield.api import Loader import numpy as np import matplotlib.pyplot as plt from skyfield.api import load loaddata = Loader('~/Documents/fishing/SkyData') # avoids multiple copies of large files ts = loaddata.timescale() # include builtin=True if you want to use older files (you may miss some leap-seconds) eph = loaddata('de421.bsp') earth, moon, venus = [eph[x] for x in ('earth', 'moon', 'venus')] apollos = [(10, 1969, 5, 18, 26), (11, 1969, 7, 16, 18), (12, 1969, 11, 14, 24), (13, 1970, 4, 11, 17), (14, 1971, 1, 31, 40), (15, 1971, 7, 26, 38), (16, 1972, 4, 16, 27), (17, 1972, 12, 7, 19)] # https://en.wikipedia.org/wiki/Apollo_program timez_apollo =  for n, year, month, d_start, d_stop in apollos: times = ts.utc(year, month, range(d_start, d_stop+1)) timez_apollo.append(times) days = 1 + np.arange(5*365.2564+1) times = ts.utc(1969, 1, days) years = days/365.2564 t_1969 = times.tt earthpos, moonpos = [x.at(times).position.km for x in (earth, moon)] r = np.sqrt(((moonpos - earthpos)**2).sum(axis=0)) Rmoon, Rearth = 1737., 6378. alt = 183. fig = plt.figure() ax1 = fig.add_subplot(1, 1, 1) ax1.plot(years, r, '-k', linewidth=0.5) for timez in timez_apollo: yearz = (timez.tt - t_1969) / 365.2564 earthpoz, moonpoz = [x.at(timez).position.km for x in (earth, moon)] r = np.sqrt(((moonpoz - earthpoz)**2).sum(axis=0)) d = r + Rmoon + alt - Rearth ax1.plot(yearz, d, linewidth=2.5) ax1.set_xlim(0.2, 4.0) ax1.set_ylim(357500, 405500) ax1.set_ylabel('km') ax1.set_title('Earth Moon and Apollo far-side orbit to Earth surface distances') ax1.set_xlabel('years since 1969-01-01') plt.show()