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@Uwe's comment

No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back.

below the question How far have astronauts been in space? has got me wondering...

Question: What's the closest that an Apollo mission has passed GEO on its way to the moon? Did they end up always going substantially above or below it, or did they pretty much just pass right through due to the Earth's inclination.

It's not a profound question, GEO was a lot less populated fifty years ago of course.

While GEO could be abstracted as a mathematically zero-height line, if you'd like a height by which to define what "through it" means, then let's assume whatever a typical scatter would be in North-South station keeping in the day. Perhaps 1 degree or less?

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    $\begingroup$ Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them. $\endgroup$ – Alex Hajnal Dec 31 '18 at 14:32
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    $\begingroup$ I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles? $\endgroup$ – Rory Alsop Dec 31 '18 at 14:32
  • $\begingroup$ @RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong). $\endgroup$ – Alex Hajnal Dec 31 '18 at 14:39
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    $\begingroup$ @RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers. $\endgroup$ – uhoh Dec 31 '18 at 14:39
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    $\begingroup$ I'm working on getting range data to make best estimate from first 2 orbit data $\endgroup$ – Rory Alsop Dec 31 '18 at 15:13
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Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.

Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.

2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
and traveling at 12,914 feet per second. Crew members keep busy with
housekeeping duties.

This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins

Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
After TLI, which places the spacecraft in a free lunar return trajectory,
the following major events occur prior to LOI:
 (a) Transposition, docking and LM ejection, including SIVB photography
 (b) Separation from SIVB and a CSM evasive maneuver
 (c) SIVB propulsive venting of propellants (slingshot)
 (d) Two series of P23 cislunar navigation sightings, star/earth horizon,
   consisting of five sets at 06:00 GET and five sets at 24:30 GET
 (e) Four midcourse corrections which take place at TLI +9, TLI +24,
   LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
 (f) Passive thermal control (PTC) will be conducted during all periods
   when other activities do not require different attitudes.
 (g) LM inspection and housekeeping
 (h) LOI1, performed at 75:54:28 GET, ends the TLC phase.

There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:

Doff & Stow helmet, gloves and PGA's.

There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.


Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...

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If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.

enter image description here

Graphic from wikipedia.

The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.

The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.

For the calculation I assume the axis of Earth lying in a plane through the centers of Earth and Moon as shown in the graphic. We get the maximal distance in this way. For the actual distance of each Apollo mission we need the individual position of the Moon.

The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.

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    $\begingroup$ I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO. $\endgroup$ – asdfex Dec 31 '18 at 17:04
  • $\begingroup$ A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though) $\endgroup$ – pericynthion Dec 31 '18 at 17:07
  • $\begingroup$ @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle". $\endgroup$ – Uwe Dec 31 '18 at 17:10
  • $\begingroup$ @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission. $\endgroup$ – Uwe Dec 31 '18 at 17:13
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    $\begingroup$ @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this. $\endgroup$ – uhoh Dec 31 '18 at 17:22

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