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Have we been able to see the shadow on the Moon's surface of any artificial satellites that orbit the Moon?

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  • $\begingroup$ Possible duplicate of Picture of equipment left on the Moon? $\endgroup$ – Hobbes Jan 20 '19 at 19:28
  • $\begingroup$ No. Just like the lunar landers are too small to see from Earth, satellites shadows are too small. $\endgroup$ – Hobbes Jan 20 '19 at 19:29
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The short answer is no.

Any artificial satellites around the moon is too small and too far away to cast a shadow. The angular diameter of the sun from the moon is approximately 0.5°.

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This means that a satellite has to have an equal or greater angular diameter observed from the moon than the sun. The formula for angular diameter is:

$$\delta =2\arctan({\frac{d}{2D}})$$

where $\delta$ is the angular diameter, $d$ is the diameter of the object, and $D$ is the distance from the object to the observer. Using the Lunar Reconnaissance Orbiter as an example, it has a periselene of around 20 km.

Substituting $\delta=0.5$ and $D=20 km$:

$$0.5° =2\arctan({\frac{d}{40km}})$$ $$\tan(0.25°) = \frac{d}{40km}$$ $$d = 40km \cdot \tan(0.25°) = 0.175km = 175m$$

Unless you can find a 175 meter wide artificial satellite around the moon, I'm afraid we won't be seeing shadows anytime soon.

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    $\begingroup$ Is "perigee" appropriate off Earth? "Periapsis" maybe? $\endgroup$ – Oscar Lanzi Jan 20 '19 at 21:04
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    $\begingroup$ @OscarLanzi Thanks, I edited it to periselene instead, which refers specifically to the moon. $\endgroup$ – QiLin Xue Jan 20 '19 at 23:03
  • $\begingroup$ Great answer! This diagram (found in this answer) may also be helpful here. en.wikipedia.org/wiki/File:Solar_eclipse_types.svg $\endgroup$ – uhoh Jan 20 '19 at 23:19

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