Why we can see unimaginably distant galaxies from Earth, but not the moon landers
Recent Correspondent: We know where the guys langed on the Sea of Tranquility (and the other missions too of course, not just 11), and though small, they left behind a lander and moon rover etc. So, I assume with a big enough telescope (and we have some monsters) we could just hunt around a bit, and actually *see* where we landed - right?
Me: Sorry, it's a good thought, but the landers and so on that we left behind are waaay too small to be seen by any telescope on earth or in orbit.
Recent Correspondent: I must say I am surprised. We have these scopes that appear to be able to see tiny little planets in other galaxies. I know that is a big object, but it is a shit load further away. I figured the size vs distance would be on the side of the lander...
When I replied, I was just repeating what I've read lots of places. I've never seen anyone actually demonstrate that it's true. So I am endeavoring to do so now. There are a couple of things to clear up here. The first is the discovery of extrasolar planets around other stars, and the second is whether size vs. distance is on the side of the moon landers, or the unimaginably distant galaxies.
Part 1: Extrasolar planets
We have not seen tiny little planets in other galaxies. There is a literally vast confusion of scale here. The most distant extrasolar planet discovered to date, OGLE-2005-BLG-390Lb, is only 21,000 light years away. On one hand, that is a hell of a long way away. Our ancestors were hunting down the last mainland mammoths when light from that planet's primary was barely halfway here. On the other hand, it's nothing. The Milky Way is estimated to be about 100,000 light years across, so OGLE-2005-BLG-390Lb is only a fifth of the way across our own galaxy. The closest major galaxy to the Milky Way--excluding our dwarf satellite galaxies, like the Magellanic Clouds--is the Andromeda galaxy, which is 2.5 million light years away. It is the most distant object that you can see with the naked eye, which is pretty cool, because the photons that fall into your unaugmented retina left Andromeda when our ancestors were banging rocks and dreaming of taming fire. But it is more than 100 times as distant as OGLE-2005-BLG-390Lb.
It gets worse. Nobody from Earth has seen OGLE-2005-BLG-390Lb. We only know it's there because of gravitational microlensing. The most distant planet we've actually seen is 2M1207b, if it actually is a planet and not some kind of dwarf star, and it's only 173 light years away.
In other news, the "hot Jupiter" that orbits HD 189733 has methane and water in its atmosphere. Here's how we know that. The planet above is not extrasolar; it's wholly terrestrial in origin.
So to sum up, all of the extrasolar planets we've found are in our own galaxy, and pretty close even on a galactic scale, and we've only directly imaged one of them, and the one we've imaged may be more of a failed star than a planet.
Part 2: Which is smaller, the Eagle or a smudge in the HUDF?
The Apollo Lunar Modules are about 14 feet in diameter, with a maximum landing gear spread of about 30 feet. At its closest approach, the moon is 225,000 miles away, or about 1.19 billion feet. So the ratio of size to distance is 1:40 million even if we use the landing gear spread, and 1:80 million if we use the vehicle itself.
The Apollo 17 lander was actually photographed from lunar orbit, but that's a distance of about 69 miles, not 225,000 miles. And it shows up as a single pixel, plus a pixel of shadow. You can see that photo, along with tons of cool zoomable moon landing site photos, here.
Although there are galaxies somewhat larger and much smaller than the Milky Way, let's say for the sake of argument that most galaxies are about 100,000 light years across. The most distant galaxies ever imaged, in the Hubble Ultra Deep Field (shown above), are about 13 billion light years away. Which yields a ratio of size to distance of only 1:130,000, or about 300 times bigger than the moon landers to observers on Earth or in Earth orbit.
Which is why we can see galaxies on the other side of the universe from Earth, but not our own moon landers. The galaxies are indeed shitloads further away, but they are also many, many shitloads larger.
Feel free to poke holes in my math or logic.