# Luna artificial satellite eclipses

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

• Possible duplicate of Picture of equipment left on the Moon? Jan 20 '19 at 19:28
• No. Just like the lunar landers are too small to see from Earth, satellites shadows are too small. Jan 20 '19 at 19:29

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°. 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.

• Is "perigee" appropriate off Earth? "Periapsis" maybe? Jan 20 '19 at 21:04
• @OscarLanzi Thanks, I edited it to periselene instead, which refers specifically to the moon. Jan 20 '19 at 23:03