The answer is basically "not a chance". No Earthbound telescope can see the flag on the Moon. Why not? For openers, the Earth's atmosphere is never steady enough to allow resolution below about one arc second for most locations. Beyond that, the telescope required to "see" the flag would need to be absolutely huge! Here is some basic analysis to show what would be needed:
Method 1 will use simple proportions to show what would be needed. The Moon's diameter is approximately 2160 miles. The Moon is nominally about 245,000 miles from Earth, and at this distance it subtends a diameter of about 30 arc minutes in the sky as seen from Earth. There are 60 arc seconds per arc minute, so the Moon is about 1800 arc seconds across. Let's figure out how many arc seconds represent one mile. The calculation is straightforward: if 1800 seconds = 2160 miles, then 1 mile = .83 arc seconds (basically just divide 1800 by 2160).
So, now we know that 1 mile is about .83 arc seconds. How big is the flag? I do not know for sure but let's assume it is 3 feet long on the long side. How many arc seconds is this? We know that 1 mile = .83 arc seconds; the flag is 3/5280 miles wide (or about 5.682e-4 miles). To find out the arc seconds, we simply multiply this value by .83 to get 4.716e-4 arc seconds. A long time ago someone named Dawes determined that the resolution of an optical telescope is basically 4.5 divided by the telescope's diameter (in inches). So, from that we can rearrange the equation to say that the diameter of the telescope needed (in inches) is 4.5 divided by the resolution required (arc seconds). Dividing 4.5 by4.716e-4 comes out to be 9542 inches. Converting this to feet yields about 795 FEET! And this would be the required telescope diameter to JUST BARELY see the flag at all! And, it would only be just visible as a small dot, it would not "look" like a flag at all. Let's say we really want to see the flag and have it look like a flag. We'll have to make some assumptions again. Let's assume that the stripes on the flag are 2 inches wide and we want to just be able to see them. Using the same method as above we can come up with an answer. In this case we need to be able to see something that is 2/12/5280 miles wide, or 3.157e-5 miles. We multiply this by .83 to get the resolution (2.62e-5). Dividing 4.5 by this number yields 171759 inches, or about 14300 FEET! This value is also about 2.7 miles. Clearly it is not possible to build an optical telescope of this size. So, basically the Flag on the Moon remains "invisible" to us here on Earth.
Method 2 will use trigonometry to show the same basic result as above (to be added).
As powerful as Hubble is (above the limits of the Earth's atmosphere), it has no chance of seeing the Flag on the Moon. What could it see? Well, Hubble has a mirror that is 98 inches in diameter. That gives it a resolution of 4.5/98 or about 0.046 arc seconds. If one does the math, this translates to a resolution of about 292 feet. So, Hubble could just detect an object that was 292 feet across on the Moon. To see any detail on an object, it would have to be somewhat larger. To put this in perspective, if a typical pro football stadium was located on the Moon Hubble could make out some basic details (the field could just barely be made out in the center of a very small oval).
Use your browser's "back" button, or use links below if you arrived here via some other path:
This page is part of the site Amateur Astronomer's Notebook.
E-mail to Joe
Roberts
Images and HTML text © Copyright 2007 by Joe Roberts. Please request permission to use
photos for purposes other than "personal use".