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In the question At what time in the Apollo 14 mission did the maneuver shown in this image happen, and what exactly was happening? I've included the image and information below. The caption says that Apollo 14 CM & LEM and the Saturn IV B were "40,000 miles from Earth" at the time, or about 64,000 km. @X's answer estimates this to be at about 03:02:29 into the mission.

Question: How far away can spacecraft be seen with an optical telescope?

note: For the purposes of this question "optical" means near-UV through thermal IR, let's say 0.1 to 30 microns, and "seen" means it's existence and position determined in some way, either via recorded digital or film image, photomultiplier, or even reliable reporting by an experienced visual astronomer.

In a search for information for this answer I received this google books link of Comment: The Relevance of Space, by Arthur Kantrowitz, Bulletin of the Atomic Scientists 197, 4 April 1971, pp 32-33. It includes the image below, I've retyped the caption for easier reading.

enter image description here

Apollo 14 (at arrow tip) is nothing more than a speck in the sky at 40,000 miles from Earth. This picture of the spacecraft was taken by Justus Dunlap of Northwestern University’s Corralitos Observatory, and shows the capsule separating from the S4B rocket. The capsule itself is visible as a pinpoint at the apex of the fan and the fan itself is expanding rocket exhaust.

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    $\begingroup$ duplicate of astronomy.stackexchange.com/questions/22764/…? $\endgroup$
    – JohnHoltz
    Jan 7, 2019 at 13:42
  • $\begingroup$ @JohnHoltz yes, it seems to be, good catch! And there are some very impressive distances there as well There isn't a mechanism to close this as duplicate of a question in another SE site, but it wouldn't be good to build up a second group of answers here either. So maybe if we can keep this question here as a pointer to your question, but close it so answers don't collect here, that would be the best way to go. What do you think? $\endgroup$
    – uhoh
    Jan 7, 2019 at 13:48
  • $\begingroup$ @JohnHoltz oh I was there 15 months ago, time flies. $\endgroup$
    – uhoh
    Jan 7, 2019 at 13:54
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    $\begingroup$ @JohnHoltz Without the ability to close a question on one site as a duplicate on another (only Physics and Chemistry can do this), I think this question should stay open since it is not an exact dupe by the same user and it is firmly on topic here. That said, anyone is welcome to make an answer summarizing and citing the information available on the other post. $\endgroup$
    – called2voyage ♦
    Jan 7, 2019 at 14:04
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    $\begingroup$ @uhoh I don't disagree with anything. I'm simply asking what was the Apollo spacecraft doing when that picture was taken? It can't be TLI, because TLI happened roughly in LEO. 40,000 miles is too far. What's the exhaust from? I don't see why the SIVB would be firing at 40,000 miles altitude. $\endgroup$
    – Star Man
    Apr 26, 2021 at 13:26

3 Answers 3

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See the post Whats the farthest distance a spacecraft has been detected (except by radio) on the Astronomy StackExchange. As of 2019 Jan 7, those answers list observations of OSIRIS-REX at 12 million km, the Rosetta at about 5 million kilometers, and the Gaia at about 1.5 million kilometers (observed "systematically" at the Earth-Sun L2 location).

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  • $\begingroup$ uhoh!! need more digits! or a timestamp for that 12 million km photo. $\endgroup$
    – uhoh
    Jan 12, 2019 at 12:04
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I'd say that currently the answer is "at least 2.2 lunar distances".

According to this source, 2006 RH120,believed to be an Apollo third stage, was "2.2 Lunar Distances", about 890,000 km, away at (re-)discovery; photos are provided at the first link.

Another possibility is J002E3 a.k.a. the Saturn IVB third stage of Apollo 12 which has a similar orbit; photos here.

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  • $\begingroup$ Great start! Those are definitely farther than Hagoromo's last sighting. $\endgroup$
    – uhoh
    Jan 7, 2019 at 5:30
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It's a Toss-Up!

Starman/Roadster with a 1-m telescope LCO at SAAO

According to this expert answer to the question When was the last time that Starman/Roadster was seen? the last time was at 2018-03-19 03:22:33 UTC.

Checking JPL's Horizons ephemeris, the positions and velocities of Roadster and Earth at that time were:

                 x (km)            y (km)            z (km)
Roadster:  -1.57275802e+08,  -2.01095341e+06,  -2.07215013e+06
Earth:     -1.48658778e+08,   5.58303992e+06,  -1.54991786e+04

               vx (km/s)         vy (km/s)          vz (km/s)
Roadster:  -4.37647101e+00,  -3.15569852e+01,  -4.91204263e-01
Earth:     -1.41352231e+00,  -2.98898278e+01,   1.99372867e-03

Subtracting and taking the norm, the distance was about 11.668 million kilometers, or about the same as the "12 million kilometers" in @johnholtz's answer. So as of now, it's a toss up until we get more digits on OSIRIS-REX!

The relative velocity was 3.435 km/sec.

These are the instantaneous positions, I haven't turned on any light-time corrections yet, but at only ~40 seconds that wold only be of order 100 km.

OSIRIS-REx and the Giant Binocular Telescope

According to this expert answer to the question When was the last time that Starman/Roadster was seen? the last time was at 2018-03-19 03:22:33 UTC.

Checking JPL's Horizons ephemeris, the positions and velocities of Roadster and Earth at that time were:

               JD           x (km)            y (km)            z (km)
ORIRIS-REx: 2457997.5   1.53010820e+08,  -5.34072644e+07,   1.03600496e+05
            2457998.5   1.53295992e+08,  -5.10445680e+07,   9.66569193e+04
            2457999.5   1.53545162e+08,  -4.86696737e+07,   8.96856099e+04

Earth:      2457997.5   1.40857392e+08,  -5.44685444e+07,  -1.89302419e+04
            2457998.5   1.41736081e+08,  -5.20747450e+07,  -1.89439071e+04
            2457999.5   1.42574120e+08,  -4.96659225e+07,  -1.89461025e+04

Separation of the two on these three days is then

               JD            r (km) 
Separation  2457997.5       12200293.5
            2457998.5       11606298.6
            2457999.5       11016718.1

which means we need some exact times for the images in the GIF to tell for sure

See more in formation here https://www.asteroidmission.org/lbt-orex-1049-loop-gif-2/

On Sept. 2, 2017, the Large Binocular Telescope on Mt. Graham, Ariz., imaged OSIRIS-REx as the spacecraft approached Earth. This is the first Earth-based view of the spacecraft since its launch on Sept. 8, 2016.

Date Taken: Spet. 2, 2017

Credit: Large Binocular Telescope Observatory

Roadster was last seen by "...K93/Dome C is the central telescope in (this) view...":

enter image description here

...in this image from the south end of the plateau looking North to the SALT telescope (center of the picture) the LCO 1m telescopes are the white domes at the front, left of center.:

enter image description here

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