That’s a bit roomier than the lunar landers were. Those wisps of gas appear to be finely resolved, but they’re billions of kilometers across. Hubble’s resolution is 0.1 arcseconds no matter how far away an object is. But those objects are far, far larger than the Moon. They’re used to seeing magnificent detail in Hubble images, stars in galaxies and wisps of gas in beautiful nebulae. That’s a pretty big surprise to most people. In fact, if you do the math (set Hubble’s resolution to 0.1 arcseconds and the distance to 400,000 kilometers) you see that Hubble’s resolution on the Moon is about 200 meters! In other words, even a football stadium on the Moon would look like a dot to Hubble. It would have to be a lot bigger to be seen at all. Hey, wait a sec! Hubble’s resolution is only 0.1 arcseconds, so the lander is way too small to be seen as anything more than a dot, even by Hubble. It’s 4 meters across, but 400,000,000 meters away. So let’s look at our lunar descent stage. In other words, take the physical size (d) of an object, divide it by the distance (D), multiply that by the constant 206265, and that gives you the angular size (α) in arcseconds (make sure D and d are in the same units!). There is another simple formula you can use to determine the angular size of an object based on its physical size and its distance: (d / D) x 206265 = α. So what does this mean if you want to look at the lunar artifacts? Well, now we have to figure out what the angular size of a given piece of Apollo machinery is, and then compare it to Hubble’s resolution. There are tricks you can do to get slightly higher resolution, but that's getting too picky. So really, Hubble's working resolution limit is about 0.1 arcseconds. Second, there's a statistical rule that says that you actually need an object to be twice that theoretical size to be properly resolved (I won't go into boring details, but you can look up the Nyquist Sampling Theorem if you're looking for an excuse to slack off at work). But this is pretty minor compared to mirror size, and we can ignore it here (plus it's already compensated for in the constant 11.6 that we used above). The first is that there's a wavelength dependence too for a given telescope size, the shorter the wavelength the more resolution you get (a telescope will resolve blue objects better than red ones, since blue has a shorter wavelength). To be totally accurate, there's a twist to this. That's an incredibly small size a human would have to be nearly 8000 kilometers (4900 miles) away to be 0.05 arcseconds in size! Plugging that into the formula, we see that Hubble's resolution is 11.6 / 240 = 0.05 arcseconds. Hubble's mirror is 2.4 meters = 240 centimeters across. There are 3600 arcseconds to a degree, and to give you an idea of how small a measure this is, the Moon is about 0.5 degrees = 1800 arcseconds across.ĭ is the diameter of the mirror in centimeters. An arcsecond is a measure of angular size (how big an object appears to be - if two objects are the same physical size, the one farther away will appear smaller, and have a smaller angular size). What does this mean?įirst, R = the angular size of the object in arcseconds. There is a simple relationship between mirror size and resolving power: R = 11.6 / D. The ability for a telescope to resolve an object is, as you'd expect, directly related to the size of the mirror or lens. But from a mile away that human is far more difficult to see, and from ten miles away is just a dot (if that). The question here is one of resolution: how big does an object have to be before a telescope can resolve it, that is, see it as more than just a dot? As an example, a person standing next to you is easy to see and easily identifiable. Those numbers sound like you should be able to spot them with, say, Hubble. The rovers were about 3 meters long and 2 wide. The descent stages were a little over 4 meters wide (the landing legs spread out were 9 meters across, but are narrow, so the bulk of the stage would be easier to see). The basic idea is that when the astronauts left the Moon, they left behind several artifacts, including the base of the lunar module (called the descent stage) and the rovers (for Apollo 15, 16, and 17). The answer is pretty surprising to most people, but the science doesn't lie. This question is obvious enough, and I've gotten it so many times I decided to write this description of just why this won't work.
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