Son's: Seeing Objects from Earth

[davidschmid10]

How big would an object have to be in order to be seen from Earth with the naked eye? How about with an average home user's telescope?
David

 

[mgb_phys]

It depends on how it is illuminated - from the title I assume you are limiting this to objects that reflect light from the sun?

Do you mean see as in 'see as a starlike dot' or see as in resolve?

The eye can resolve around 5arcmins, a small telescope perhaps 5arcseconds (60x as much detail) - the moon is around 30arcmins in diamter. So at the distance of the moon you could resolve something 1/6 the moons diamter with your eye and 1/300 the moon diameter with a telescope.
Saturn is the most distant planet you can see with the naked eye, but it has a size of 20arcsec so to your eye it is just a star like dot, it can be seen as a disc with a small telescope. (You can also see the rings)

Then there is the question of how reflective that something would have to be to be sending enough light back to detect with your eye or a telescope.

If you just mean see as a point of light, the galaxy M31 (andromeda) is about 2.5 million light years away!

 

[russ_watters]

... so with the moon being about 2100 miles across, the smallest object you could resolve with the naked eye would be around 6 miles across.

 

[tony873004]

6 miles seems a little small to be resolving with the naked eye. mgb says 5 arcminutes, and 1/6the the Moon's diameter. 2100/6 = 350 miles. But this seems a bit large. I've always thought the figure was more like 1 arcsecond, making Venus almost resolvable as a crescent when it is near inferior conjunction. I would guess that I can resolve things smaller than 1/6 the Moon's angular diameter.

 

[russ_watters]

Oops, that was 5 arcmin for naked eye, 5 arcsec with the telescope...

 

[tony873004]

I just tried an experiment. From across the room, I walked towards a printed sheet of paper until I could read it. Lowercase letters are about 2 millimeters tall, and I needed to be closer than a little over 2 meters away before I could read them. Inverse Tan (2/2000) = 5.73e-02 degrees * 60 = 3.43 arcminutes.

So I can read letters as small as 3.43 arcminutes. But from as far as 3 meters I could tell some sort of shapes to the letters. I couldn't tell "o" from "e" or "w" from "m". But "v" was easy to pick out, as was "r" and "i". I probably couldn't tell you what letters they were (I verified by getting closer), but it was obvious that not all letters had the same shape. I'm ignoring any letter that is taller than 2 mm, such as j,h,t,y. And I could tell there were gaps inbetween the letters.

From 4 meters I could tell that there were gaps between the words, but not the letters. And the letters no longer had obvious differences in shape. So I'm guessing that my resolving power disappears somewhere inbetween 3 and 4 meters, which would translate to between 2.3 to 1.7 arcminutes.

*** added:
I need to pay attention to significant figures here. I didn't measure the letters with calipers, just a ruler, and I paced off the meters. So I probably shouldn't be reporting answers like 3.43, 2.3, or 1.7. I'll just say its about 2 arcminutes. And seeing the words in context certainly helped me read them from 2 meters. I'm not sure how well I would have done receiting random letters like on an eye test.

 

[mgb_phys]

The 6arcmin is a slightly poor average and the definition of resolution is a bit arbitrary.
The raleigh limit says it's when the maximum of one dffraction peak hits the minimum of the other. If you know the shape you are looking for, or are simply trying to determine if something is round or not you can do better than this.

I once had an observing proposal turned down by some peer reviewer who had obviously only done high school physics - they explained that the object was smaller than the diffraction limit of the telescope and so couldn't be obererved. I don't think they could spell speckle-interferometry never mind do it.

You should experiment with something like a 1951 USAF test chart to see what your eyes can resolve. At night your eyes should actually do better since the dark adapted pupil opens up and gives you a bigger aperture.

 

[russ_watters]

Quick related question for you mgb, that I get the impression you might know - my telescope's specs lists a "resolution" of .5 arcsec and a "resolving power" of .42 arcsec. What's the difference? http://www.optcorp.com/product.aspx?pid=1-600-602-892-6394&tb=2

Anyway, "speckle-interferometry" sounds vaguely similar to the method amateurs (like me) use to do planetary imaging. And also kinda related to this thread, there are quite a few amateurs with scopes like mine (though it is above average), and I and others use image stacking to increase the resolution of their images beyond what you can see with your eyes - beyond the theoretical maximum resolution of the scope. I take pictures at a resolution of as much as 1/8 arcsec per pixel. I haven't gotten the most of my equipment yet and those images aren't perfectly sharp, but I would say I'm getting a real resolution of perhaps half that - about .25 arcsec, or 600x magnification which is around double what the scope is theoretically capable of.

5 arcsec may be a little low for an "average" scope - 4" reflectors are getting very common these days for a "first" scope and they have a resolution of around 1 arcsec.

 

[mgb_phys]

Don't know what the difference between resolving power and resolution is except maybe one is the theoretical diffraction limit ( 1.22 lambda/d) and the other is taking into account the optical quality and effect of the secondary.
Either way you are likely to do worse than 0.5" in the visible unless you are on a REALLY good site.

Speckle interferometry isn't quite the same as shift+add. Speckle images are in the pupil plane of the telescope then Fourier transformed to get an image. http://en.wikipedia.org/wiki/Speckle_masking.
You can't do (much) better than the theoretical diffraction limited resolution of the scope - but you can do many times better than atmospheric seeing normally allows.

The video stuff is becoming popular now that zero noise CCD cameras are available.
This is done by my old group http://www.ast.cam.ac.uk/~optics/Lucky_Web_Site/

 

[russ_watters]

Don't know what the difference between resolving power and resolution is except maybe one is the theoretical diffraction limit ( 1.22 lambda/d) and the other is taking into account the optical quality and effect of the secondary.
Either way you are likely to do worse than 0.5" in the visible unless you are on a REALLY good site.

I guess I don't have any scientific reason to believe stacking can do better than the theoretical max, but some of the results look pretty amazing. Here's the best Mars image I've seen so far this season. The image's resolution is .07 arcsec/pixel. The theoretical max is .3 arcsec.


http://www.cloudynights.com/ubbthre...page/0/view/collapsed/sb/5/o/all/fpart/1/vc/1

 

[mgb_phys]

There is information at below the diffraction limit of the scope - the diffraction limit is a bit arbitrary. The MTF falls off fairly quickly though, especially with the effect of a secondary or if the scope isn't perfectly collimated. You can get some useful info to about 1.7x the diffraction limit ( it's a complicated question of signal to noise).

The reason it works is that the atmoshere has bubbles (cells) of different temperature / density - like frosted glass in a bathroom. These vary from a few cm to a couple of metres in diameter ( better at longer wavelengths). As one moves over the scope there is a moment when you are looking through a single cell and so there is very little distortion.

Adaptive optics has a deformable mirror with each segment the size of one of these cells, the system tries to move each sgement to put the perfect image through each cell all on top of each other on the focal plane. Shift+add just does the same thing in software.

ps. Those pictues of Mars are amazing.

 

[tony873004]

I agree. Those Mars pictures are awesome. Someday I want to learn to stack images.

 

[ocpaul20]

It would be nice if we saw some artifacts left on the moon rather than just a few places where the ground has been scorched from the rockets on takeoff & landing. I feel that a moon buggy really should be large enough to show up on some satellite photos somewhere - and in extremely good detail.

Satellite imaging has got to the stage now where they can resolve down to the size of a baseball, so why are the pictures of the moon and Mars so terrible and low-res? Maybe we are not supposed to know that imaging technology has advanced this far. Anyway...

 

[mgb_phys]

None of the moon orbiters had high enough resoluton cameras.
The moon is still pretty large and it would take time to photograph the whole surface in such detail - there isn't a lot there to justify that kind of expense. Spy satelite that can take images that detailed are big and expensive and the data links to get that much data back from so far away would be impressive. There are lunar photos showing dark patches where one of the lunar modules left - it's not burnt ( there is no oxygen) but the dust is blown away to reveal darker rock underneath.

With Hubble or perfect ground based Adaptive Optics the resolution at the moon is still something like 50m so you wouldn't see a moon buggy - even then you ar elooking for a grey dusty object on a grey dusty background.

There is (was?) a plan for a mission to the moon next year rather like the Mars orbiter which will map it to 0.5m resolution.

 

[tony873004]

We've got images of the rovers on the surface of Mars. It's just a little splotch on the image (with tire tracks leading up to it ). So I wouldn't call the Mars images "terrible and low-res".

 

[russ_watters]

It would be nice if we saw some artifacts left on the moon rather than just a few places where the ground has been scorched from the rockets on takeoff & landing.

I have seen artifacts left on the moon - haven't you?

I feel that a moon buggy really should be large enough to show up on some satellite photos somewhere - and in extremely good detail.

Feelings aren't reality.

Satellite imaging has got to the stage now where they can resolve down to the size of a baseball, so why are the pictures of the moon and Mars so terrible and low-res? Maybe we are not supposed to know that imaging technology has advanced this far. Anyway...

Satellites orbit at about 150 miles. The moon is 476,000 miles away. You tell me what the resolution should be...

 

[ocpaul20]

Satellites orbit at about 150 miles. The moon is 476,000 miles away. You tell me what the resolution should be...

I don't know about resolutions etc because I am not an astronomer, so maybe you tell me, but I really don't see what these two facts have to do with anything.

How big is a moon buggy that can carry two people - 15feet long perhaps? Clementine provided some pretty good photos and it was supposed to be mapping the moon. So, where are the pictures of the artifacts then?

 

[russ_watters]

What those two facts have to do with each other is that you can use them to calculate the resolution of a space-based telescope when imaging the moon. If a spy satellite has a resolution of .1 meter when imaging objects on earth, it (or the Hubble, which is basically a spy satellite facing the other direction) would have a resolution of .3 km when imaging an object on the moon.

As for Clementine, here's the map it created: http://www.nrl.navy.mil/clm/
Scale information is provided in the lower-left corner of the map. As you can see, the moon buggy would need to be about 10x bigger to show up on it.

In any case, none of that is really relevant. We have plenty of pictures of the lunar rovers and landers.

Seriously, these questions can be answered easily if you put a little bit of effort into them. "I feel..." isn't effort. I found the Clementine images in 5 seconds via Google. Please, please put some thought into these questions instead of just believing conspiracy theory based on your feelings.

[edit] Oh, wait - you're the one who posted the other thread about Clementine. So you already know the answer to the question you asked - it says right on the link you posted that the resolution is 1km/pixel! Please stop this nonsense.