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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 Jul 6 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 Jul 6 at 10:33
  • $\begingroup$ @Uwe Venus should appear as a crescent aside transits. $\endgroup$ – LoveForChrist Jul 6 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 Jul 6 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 Jul 6 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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