"Why can't Hubble see the flags on the Moon" - Great answer!

[SEmert]

Just ran across this nice detailed but concise answer to the question many of us have gotten one time or another at public observing nights.

https://www.quora.com/q/astrophysics1?_ ... _=13841880

Q: Why is it that the Hubble telescope can capture images of other galaxies, but allegedly can’t see the flags on the moon?

A: Angular resolution.

Angular resolution is this thing:

Angular Resolution.jpeg

…where d is the diameter of the thing, D is the distance to the thing and δ is the angle that it takes up in this end of the telescope, eye, whatever. Angular resolution is basically how small δ can be for you to still see it.

Hubble has an angular resolution of about 1/20th of an arcsecond. An arcsecond is 1/3600th of a degree, so Hubble can see things as small as 1/72,000th of a degree.

As a comparison, that’s equivalent to about a standard soccer ball at 90 km away. If you park a soccer ball 90 km from the Hubble, it is about 1/72,000th of a degree across. It is not quite equivalent to a pixel on its sensor chip, but let’s pretend that it is.

Galaxies are huge. They measure tens of thousands of light-years from one end to the other. But if you take a galaxy of 100,000 light-years diameter and 10 billion light-years distance, the galaxy would cover 2.026 arcseconds, or show up as about 400x400 pixels across.

The flags on the Moon are 380 000 km away, and about 0.5 meters square. That means that the flag would cover 0.00027 arcseconds, or be about 0.005x0.005 pixels big. If we pretend that the Moon is completely black, and the flag is completely white, it would increase the brightness value of the pixel it would be in with 0.0025% from black.

The smallest thing on the Moon that the Hubble can see is about 92 metres across. That’s about the size of a soccer field. So an entire soccer stadium on the Moon would be like 2x2 pixels to Hubble.

[defalkner]

That is a good explanation. We may have to simplify it a bit for the general public but it does explain why Hubble, or other large telescopes, can't resolve the flags on the Moon.

[Ron Schmit]

I always share that football field fact, and then encourage them to go to the Lunar Reconnaissance Orbiter (LRO) website where they can see the landing sites photographed from just 50 miles up: https://www.nasa.gov/mission_pages/LRO/ ... sites.html

Don't worry, deniers will jump at the chance to tell you the pictures are Photoshopped!!

[Dave Venne]

A demonstration I used to do in Intro Astronomy was much like Comparison 3 in this PDF. I would use dots on a whiteboard in a large lecture hall, and move them closer and closer together until only only the front half of the class could see two distinct dots. The ratio of the dot separation to the mid-class distance became a sort of "resolving power" that could be compared to the ratio of flag size and the distance to the Moon. It's then easy to show that the two numbers are different by much more than the ratio of the Hubble Objective diameter to pupil size.

This actively involves the students and avoids math beyond simple ratios.