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At what distance does the Earth become indistinguishable from stars and other planets to the naked eye, like the Pale Blue Dot or like Venus or Mars visible from Earth? Dot-like rather than spherical.

As the Tesla Roadster with Starman was launched towards Mars and the main asteroid belt, at what distance would one no longer recognize the Earth and Moon as spherical bodies from the Tesla Roadster?

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    $\begingroup$ @OscarLanzi Dot-like rather than spherical, as written in the question body. When you look on Venus or Mars with the naked eye you don't see whether it's a star or a planet (Mars appears reddish but that's Betelgeuse too), you don't see them as globes but star-like. $\endgroup$
    – LoveForChrist
    Commented Jul 6, 2020 at 9:56
  • $\begingroup$ When I looked at Venus during the last transit before the Sun, I could see it clearly as a small circle. Venus is seen as 9.7 to 66 arcseconds. So my eyes with glasses seem to be better than one arcminute. $\endgroup$
    – Uwe
    Commented Jul 6, 2020 at 10:33
  • $\begingroup$ @Uwe Venus should appear as a crescent aside transits. $\endgroup$
    – LoveForChrist
    Commented Jul 6, 2020 at 10:51
  • $\begingroup$ At bright sunlight the angle resolution of the human eyes is better than at night. So I saw the Venus at transit and minimal distance as a small disk, but in the night at greater distance only as a bright star but not as a crescent. $\endgroup$
    – Uwe
    Commented Jul 6, 2020 at 13:07
  • $\begingroup$ Clearly this is going to depend on the individual. I've encountered people (like @Uwe) who claim that they can spot the planets by eye for Venus, Mars, Jupiter, and Saturn and I've never been able to see any of them as anything but little dots just like stars. $\endgroup$
    – Steve Cox
    Commented Jul 6, 2020 at 15:46

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The visual acuity of a healthy human eye is about 1 arcminute (a full circle is 360°, 1 ° is divided into 60 arcminutes).

A football with a diameter of 220 mm at a distance of about 775 m subtends an angle of 1 arcminute. Or a tiny object of 0.2908 mm at a distance of 1 m.

The Earth diameter is 12742 km. So the distance is 43,8 million km or 0.293 AU as @chrylis -cautiouslyoptimistic notes.

The diameter of the Moon is 3474.8 km, the distance to see it as an arcminute only is 11.9 million km.

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    $\begingroup$ Venus can be a sliver of almost 60 arc seconds tall, and Jupiter can get to almost 50, and yet I'm not sure if either of those is ever noticeably extended, so I think this is an upper limit. Can you see the difference with the naked eye whether Venus is at the other side of the Sun or at the Earths' side? and also Venus' magnitude during inferior conjunction $\endgroup$
    – uhoh
    Commented Jul 6, 2020 at 10:18
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    $\begingroup$ The distance to resolve the continents and clouds of Earth is much smaller than 43 million km. At 4.3 million km the human eye would resolve it as 10 pixels wide and high, $\endgroup$
    – Uwe
    Commented Jul 6, 2020 at 10:28
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    $\begingroup$ Info about distinguishing features on Earth at lunar distance here: space.stackexchange.com/a/41967/6944 $\endgroup$
    – Organic Marble
    Commented Jul 6, 2020 at 13:28
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    $\begingroup$ @uhoh I remember the Venus transit, I have seen Venus noticeably extended as a small black disk before the Sun. But it was at bright sunlight and minimal distance of Venus. $\endgroup$
    – Uwe
    Commented Jul 6, 2020 at 14:42
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    $\begingroup$ This answer is much more intuitive to me expressed as 0.287 au. $\endgroup$
    – chrylis -cautiouslyoptimistic-
    Commented Jul 6, 2020 at 16:30

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