1. Newbie
Join Date
May 2007
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1

## Hubble resolution

Hi all,

(this is my first post so be gentle with me)

What is the resolution of the Hubble telescope?

I watched a program last night (Horizon BBC on the pending switch on of the LHC at Cerne). In the course of the program a statement was made that Hubble could pick out the glow of a firefly (or similar) on the moon. Can this be taken as gospel? Where can one get an idea of the possible resolution of Hubble?

C

2. You can go here:
http://hubblesite.org

or here:
http://hubble.nasa.gov

3. I'm not sure that means what you think it means...

Light gathering and resolution are not the same thing. Resolution means being able to see an object as a single item, or to see two objects as two distinct things. For example, the Hubble does not have the resolution needed to see the leftover hardware from the Apollo missions Its angular size is just too small.

Spy satellites use optics similar to those in the Hubble. You will often hear their abilities described as "1 meter resolution" or some such. This means that if you were to place a 1 meter square on a background of a different color, it would be visible and take up about 1 pixel in the image. This depends on the distance from the object to the camera though. For telescopes, resolution is measured in degree, arc minutes, and arc seconds. 1 degree = 60 arcmin = 3600 arcsec. A resolution of 1 arc second means that at 10 light years away, an object with a diameter of about 30,000 km would right on the edge of resolution. (May want to wait for a correction on that, though.)

Seeing an object the size of a firefly is well beyond the limits of the Hubble. Seeing a object with light intensity of firefly is not.

The Hubble Deep Field image was created by aiming at one point in space for 100 hours. It recorded images as faint as magnitude 30. The light intensity of a mag 30 object was described in the article I read at the time as being the equivalent of the glow from the tip of a cigar at the distance of the moon.

See below (and maybe above) for corrections.

4. I seem to remember seeing on the hubble site a description of the of the deep field image as:

If you held a pin in each hand at arms length, then crossed the pins, the small square that is formed where they overlap represented the field of view.

5. Field of view is yet another thing than resolution and light sensitivity. Field of view is how much of its surroundings a telescope can see without moving.

6. Order of Kilopi
Join Date
Dec 2004
Posts
11,258
Knowing the field of view and the number of pixels across an image
pretty much tells you the resolution, though. For an image with a
given number of pixels, the smaller the field, the higher the resolution.
For a given field, the greater the number of pixels, the greater the
resolution. Of course, the optics have to be able to provide an image
of sufficient resolution, otherwise you just have lots of fuzzy pixels.

HST might be able to detect and distinguish two fireflies a mile apart
from each other on a totally dark Moon, given a sufficently long
exposure. If they were only half a mile apart they might appear as
a single blob of (very dim) light. The Moon couldn't be totally dark,
though, because Earthshine would light it up far more than the
fireflies would!

-- Jeff, in Minneapolis

7. Well, assuming that the sensor is sized properly...

If the sensor has a massive number of pixels, the resolution could be worse than the calculated value because of diffraction...

8. Hubble's diffraction limit should be under 1/20 arcsecond if everything is figured properly. That would be enough to split two point sources about 250 feet apart on the Moon.

9. IIRC, hubble's diffraction limit is around 1/20 arcsecond, and it has imaged down to about 0.07-0.08 arcsec. So it can get fairly close to the diffraction limit...

10. Member
Join Date
May 2007
Posts
11
I don't recall ever seeing Hubble pictures of the moon close up. One poster in this thread mentioned that the equipment left on the moon would not be visible using the Hubble. Has the Hubble ever been pointed at the region said to have been visited by the Apollo astronauts to see if they could resolve the equipment? I can understand that the remains might be quite small but then again the shadows cast by the sun hitting them at the correct angle would highlight these pieces of equipment much more would they not? Have any researchers actually tried to view the moonlanding sites with the Hubble?
Last edited by Millenium; 2007-May-04 at 02:53 AM. Reason: spelling

11. The moon has been imaged by Hubble. However, as has been pointed out in the past, Hubble is simply not big enough to resolve anything as small as the Apollo debris. (Edit to add: The limit seems to be as small as 300 feet across, give or take a bit.)

Search this site, particularly the Conspiracy Theories section, for "Hubble"

Fred

12. Originally Posted by Millenium
I don't recall ever seeing Hubble pictures of the moon close up. One poster in this thread mentioned that the equipment left on the moon would not be visible using the Hubble. Has the Hubble ever been pointed at the region said to have been visited by the Apollo astronauts to see if they could resolve the equipment? I can understand that the remains might be quite small but then again the shadows cast by the sun hitting them at the correct angle would highlight these pieces of equipment much more would they not? Have any researchers actually tried to view the moonlanding sites with the Hubble?

- http://hubblesite.org/newscenter/arc.../a/format/web/

13. Established Member
Join Date
Dec 2002
Posts
1,471
Originally Posted by cliffconway
...What is the resolution of the Hubble telescope?...
Resolution is from Dawes' Limit: http://en.wikipedia.org/wiki/Dawes_limit

Angular resolution formula:

a = 250000 x W / d, where:
a = angular resolution in arc seconds
W = wavelength in meters (500 nanometers for green light)
d = telescope diameter in meters

E.g.
a = 250000 x 500E-9 / 2.4 (HST mirror size)
a = .05208 arc seconds

Linear resolution formula:

s = tan (a) x d, where:
s = linear resolution in units determined by d
a = angular resolution in degrees
d = distance to object

E.g.
s = tan (1/(3600/.05)) x 240000 miles x 5280 feet per mile
s = 307 ft resolution at 240000 mile lunar distance

Hubble's resolution is far insufficient to image residual Apollo lunar hardware.

14. Established Member
Join Date
Dec 2002
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1,471
Re the original question about HST detecting a firefly on the moon:

Detecting a dim light is different from resolution. Hubble's limiting magnitude is about 30.

The human eye's limiting magnitude under average conditions is 6, so HST can detect 26 magnitudes dimmer light. http://en.wikipedia.org/wiki/Apparent_magnitude

This brightness variation equates to:

Vb = 2.512^26
Vb = 25,148,408,816

So HST can detect light 25 billion times dimmer than the human eye. Is this sufficient to detect a firefly at lunar distance?

You might visually detect a firefly under good conditions at 200 meters. Assuming omni-directional radiation, brightness drops off with the square of the distance. So at 400 meters it's 1/4th as bright, at 800 meters 1/16th as bright, etc. http://en.wikipedia.org/wiki/Inverse_square_law

At lunar distance (386 million meters) a firefly would be 1/(386E6 / 200)^2 as bright or 1/3.7 trillionth as bright.

However HST has only about 25 billion times the human eye's limiting magnitude. This implies HST could not detect a firefly on at lunar distance. This also disregards the effects of lunar glare and contrast, which would make the problem even harder.

15. Banned
Join Date
Dec 2005
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14,315
Originally Posted by Jeff Root
The Moon couldn't be totally dark,
though, because Earthshine would light it up far more than the
fireflies would!

-- Jeff, in Minneapolis

If fireflies were to light up even a tiny bit of the Moon, it'd be the very last thing they did (vacuum...)

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