# Puzzler: Precisely what maximum distance from the Earth did the Apollo 13 astronauts achieve?

tl;dr:

Both this answer and this answer quote Wikipedia to state that the Apollo 13 astronauts reached 404,171 km from Earth. I'm not able to reproduce that value.

According to JPL's Horizons the distance between the center of the Earth and the center of the Moon at the beginning and end of occultation times from here are:

          Event                        UTC        Earth-Moon R (km)
-------------------------  --------------------   -----------------
Lunar occultation entered  1970-Apr-15 00:21:00       404418.652
Lunar occultation exited   1970-Apr-15 00:46:00       404423.901


Just in case I entered something wrong using the Horizons interface, I've double checked the numbers with Skyfield on DE421 and go the same thing except for about 100 meters because the times scales are slightly different due to accumulated leap seconds. Note these distances are not light time or otherwise corrected, they are just the differences in positions.

Let's call the Earth-Moon distance at the midpoint time to be 404 421.3 km, and the equatorial radii of the Earth and The Moon 6378.1 km and 1738.1 km.

Wikipedia's Apollo 13 (quoted in this answer) says:

The flight passed the far side of the Moon at an altitude of 254 kilometers (137 nautical miles) above the lunar surface, and 400,171 km (248,655 mi) from Earth, a spaceflight record marking the farthest humans have ever traveled from Earth.

Wikipedia's List of spaceflight records: Speed and altitude records (quoted in this answer) says:

Farthest humans from Earth

The Apollo 13 crew (Jim Lovell, Fred Haise, and Jack Swigert), while passing over the far side of the moon at an altitude of 254 km (158 mi) from the lunar surface, were 400,171 km (248,655 mi) from Earth. This record-breaking distance was reached at 0:21 UTC on 15 April 1970.

Question: I don't know how to combine the Horizons distances, the radii of the Earth and Moon, and the reported altitude in order to get to 400,171 km. Can someone help?

Secondary item is that the 2nd Wikipedia quote gives the maximum at 00:21 UTC but that seems to be the time of entry into occultation, not the midpoint 12.5 minutes later, that could be a clue, or just an oversight.

• @OrganicMarble max Earth altitude: 404421 - 6378 + 1738 + 254 = 400035, max distance from Earth center: 404421 + 1738 + 254 = 406413 So there's perhaps a 136 kilometer disparity with Wikipedia – uhoh Dec 31 '18 at 1:37
• Wow, that 1970 datestamp is annoying - my programmer brain has been trained to immediately suspect it as wrong/a bug 😂 – Lightness Races in Orbit Dec 31 '18 at 17:06
• @LightnessRacesinOrbit it's less problematic for people who started to program "way back" in the 1900's. – uhoh Dec 31 '18 at 17:18
• @uhoh Alan Shepard on his first mission probably won the US award for spaceflight travel the farthest from the moon.... – Organic Marble Jan 1 '19 at 2:26
• Yeah, I meant the Mercury one. – Organic Marble Jan 1 '19 at 2:36