Can a very powerful telescope show a person standing on the moon from the side rather than from directly overhead?

Question

If we had a very powerful telescope with say a 150-meter diameter, placed in orbit around earth, would it be possible to get a side view rather than a top view of a person standing on the moon?

Answer 1

Yes.

The person just has to be standing somewhere near the limb of the moon. That is near the edge of the apparent disc of the moon.

We see everything near the limb of the moon from the side, at all times. This is because the moon is (roughly) a sphere. It's not flat.

Answer 2

Yes, but only just. The best-case (called "diffraction-limited") angular resolution of a telescope (i.e. the smallest detail it can make out) is given by $$ \theta = 1.22 \frac{\lambda}{D} $$ Where $\lambda$ is the wavelength of light you're observing in (say, 500nm for visible light) and $D$ is the diameter of the telescope. With a 150m diameter, this is $4 \times 10^{-9}$ radians.

Multiply that by the distance to the moon (400,000km) to get the smallest resolvable detail: 1.6m, only just big enough to see an astronaut. They would appear as a tiny white dot.

This is an absolute best-case scenario — luckily, real space telescopes tend to get pretty close to the diffraction limit.

Answer 3

would it be possible to get a side view rather than a top view of a person standing on the moon

It's kind of possible to do both at the same time. Simply wait for the person to be at the lunar terminator. As seen from the moon, the sun will be so low on the horizon that the shadow of the person can get really long:

Your powerful telescope will not be able to resolve the head from above, but might resolve a few pixels of the shadow.

This is also the reason why you see different craters on the moon every day : you don't see the ones in the shadow, you don't see much detail at all when they're completely sunlit, but you see very crisp details of the craters that are along the terminator.

This "wall" on the moon is only visible during a few hours every month, for example, when the incoming light has just the correct angle:

Answer 4

No, assuming you want to see that the thing you are observing is a human as opposed to a rock.

Steve R beat me to this answer based on the diffraction limit of a telescope. To distinguish between a human and a rock, the telescope would need to be able to have a resolution of 20 centimeters, the size of a human head. Using the Raleigh criterion for the resolution of a telescope, $$\theta \approx 1.22 \frac{\lambda}{D}$$ where $\theta$ is the angular resolution of the telescope, $\lambda$ is the wavelength of the electromagnetic radiation being received (I'll use 600 nanometers), and $D$ is the diameter of the mirror.

Using the small angle approximation, if $d_1$ is the distance between the telescope and the object of interest, and $d_2$ is the size of the object, we want $$\theta d_1 < d_2$$ or $$d1 < \frac{d_2 D}{1.22 \lambda}$$

Plugging in the numbers ($d_2 = 20\,\text{cm}$, $D = 150\,\text{m}$, $\lambda = 600\,\text{nm}$) yields a distance between the telescope and subject of no more than 41000 km. That's orbiting the Moon rather than the Earth.

Answer 5

Summary:
To see someone "from the side" you need to view them side on. This occurs, as others have noted, when they are "on a limb" - where limb is the whole circle edge at full moon. The edge on terrain in the images below shows the principle. Other answers indicate how refraction sets a limit to the smallest size of an image which can be viewed.

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You can see the equivalent now.

Look at good quality high resolution images of the Moon.
Look at the edges of the disk - you'll see they are rough, not smooth. That's the lunar lanscape seen side on. You can see some mountains / large craters quite clearly.

Here you can find A "lower res" version of the highest resolution available. The full resolution version is 11022 x 11022 pixels - but it costs money.

This is a crop of the top left and bottom left corners of a medium resolution showing side on detail.

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Answer 6

Using an orbit that get close to the Moon regularly can be an option and you can take photos while they are close together, but that still have a huge impact on the orbit in a long run.

But at least once you'll be able to do such picture. I guess you can go quite close to the Moon without any harm to the telescope as it doesn't have real atmosphere, but this will change the telescope's orbit totally.

L2 Lagrange point seems much closer to Moon than the Earth, but I guess it's still not close enough.

    

    ^{The Lagrange points for the Earth-moon system. Credit: David A. Kring, LPI-JSC Center for Lunar Science and Exploration}