Re: HUBBLE AND DID THE AMERICANS GO TO THE MOON!

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Posted by Ed Cheng on January 03, 2000 at 14:29:39:

In Reply to: HUBBLE AND DID THE AMERICANS GO TO THE MOON! posted by MALCOLM O'DELL on December 31, 1999 at 13:23:45:

> IF THE HUBBLE SPACE TELESCOPE CAN RESOLVE A CAR HEADLIGHT FROM MILLIONS UPON MILLIONS OF MILES AWAY, WHY CAN'T NASA POINT IT AT THE NASA APOLLO LANDING SITES AND PROVE THE LUNAR MODULE AND THE CRASHED ASCENT STAGE ARE REALLY UP THERE ONCE AND FOR ALL!!

It is true that the Hubble Space Telescope can see things very clearly -
one can argue that it provides the clearest view of the sky in visible light
"colors" that humans have ever had. However, its capabilities are still
limited by the laws of physics.

For a telescope with a circular collecting area of diameter D (2.4 m for
Hubble), the smallest feature that one can resolve at wavelength L
(550 x 10^-9 m for visible light) is given roughly by:

resolution = 1.4 L/D = 3.2 x 10^-7 radians

This estimate gives the "diffraction limited" resolution, or the resolution
based on light's wave-like characteristics. It is difficult to improve
upon this limit.

The distance to the Moon is roughly 240,000 miles. Hubble's resolution
corresponds to a physical dimension of

size = x = 0.08 miles = 405 feet = 124 meters

at the Moon's surface ... roughly the size of a football field.

This is quite a bit larger than any of the artifacts you would want to see
on the lunar surface, so even Hubble's tremendous clarity is not enough for
what you would like to do! If we had an aircraft carrier at the lunar
surface, then Hubble could probably get a pretty good look at it.

How far can Hubble resolve a pair of headlights? We can reverse the above
calculation to find out. Let's say that headlights are separated about
1.5 meters. Then we want:

distance = / = 4700 km = 2910 miles

Thus, Hubble can tell that there are two headlights on a car if the car
were at a distance comparable to the separation of the East and West coasts
of the US. If the car were any farther away than this, the two headlights
would appear as a single blob of light - we could still see it, but it
is harder to tell that there are two sources of light instead of one.

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> > IF THE HUBBLE SPACE TELESCOPE CAN RESOLVE A CAR HEADLIGHT FROM MILLIONS UPON MILLIONS OF MILES AWAY, WHY CAN'T NASA POINT IT AT THE NASA APOLLO LANDING SITES AND PROVE THE LUNAR MODULE AND THE CRASHED ASCENT STAGE ARE REALLY UP THERE ONCE AND FOR ALL!! > It is true that the Hubble Space Telescope can see things very clearly - > one can argue that it provides the clearest view of the sky in visible light > "colors" that humans have ever had. However, its capabilities are still > limited by the laws of physics. > For a telescope with a circular collecting area of diameter D (2.4 m for > Hubble), the smallest feature that one can resolve at wavelength L > (550 x 10^-9 m for visible light) is given roughly by: > resolution = 1.4 L/D = 3.2 x 10^-7 radians > This estimate gives the "diffraction limited" resolution, or the resolution > based on light's wave-like characteristics. It is difficult to improve > upon this limit. > The distance to the Moon is roughly 240,000 miles. Hubble's resolution > corresponds to a physical dimension of > size = <resolution in radians> x <distance> = 0.08 miles = 405 feet = 124 meters > at the Moon's surface ... roughly the size of a football field. > This is quite a bit larger than any of the artifacts you would want to see > on the lunar surface, so even Hubble's tremendous clarity is not enough for > what you would like to do! If we had an aircraft carrier at the lunar > surface, then Hubble could probably get a pretty good look at it. > How far can Hubble resolve a pair of headlights? We can reverse the above > calculation to find out. Let's say that headlights are separated about > 1.5 meters. Then we want: > distance = <separation> / <resolution in radians> = 4700 km = 2910 miles > Thus, Hubble can tell that there are two headlights on a car if the car > were at a distance comparable to the separation of the East and West coasts > of the US. If the car were any farther away than this, the two headlights > would appear as a single blob of light - we could still see it, but it > is harder to tell that there are two sources of light instead of one.

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