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

  • $\begingroup$ 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

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°.

enter image description here

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.

| improve this answer | |
  • 1
    $\begingroup$ Is "perigee" appropriate off Earth? "Periapsis" maybe? $\endgroup$ – Oscar Lanzi Jan 20 '19 at 21:04
  • 2
    $\begingroup$ @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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.