# Stargazing Limits of a telescope

1. Apr 4, 2011

### Ryan_m_b

Staff Emeritus
Hi there,

I was reading a novel recently where a character was using telescopes to watch vehicles moving on a planet at many light hours distant. The 'explanation' for his telescopes awesomeness is that it is designed to see distant stars and so seeing people moving on a planet in the same system is easy. However this does not seem right to me.

My knowledge of telescopes and astronomy is limited but I'm interested to know what the limitations are on a telescopes resolution, i.e. is it the length, width etc. I'm also fairly sure I've read somewhere before that whilst the hubble telescope can see distant nebulae it would not be able to see the flag on the moon (which is what flagged up the passage in the aforementioned novel). Ideally I'd like to know how to answer questions such as "what dimensions would a satellite have to be in a 200km orbit to read size 10 font from my hand"

Thanks!

2. Apr 4, 2011

### phyzguy

Try reading this: http://en.wikipedia.org/wiki/Optical_telescope#Angular_resolution . It basically tells you the resolving power of a telescope. For your example, 10 point font is about 2mm, so to read this at a distance of 200 km requires resolving an angle of (2E-3/2E5) = 1E-8 radians. So 1E-8 = lambda/D (ignoring the 1.22 since we're just making a rough estimate). Since the wavelength of visible light is about 5E-7 m, we need a telescope diameter of D = (5E-7/1E-8) = 50 m. Similarly, to see a flag (1 m) on the moon (400,000 km away), requires D = (5E-7 m * 4E8 m / 1m) = 200m, about 100 times bigger than the Hubble telescope. The reason that the Hubble telescope can see distant nebula that are much further away is that they are much, much bigger than a flag.

3. Apr 5, 2011

### Ryan_m_b

Staff Emeritus
Brilliant, thank you :)

4. Apr 5, 2011

### Ryan_m_b

Staff Emeritus
Oh, a potentially unintelligent question but does the brightness of the object make a difference?

5. Apr 5, 2011

### Staff: Mentor

Not really. It is pretty easy to get around a brightness problem by increasing the length of the exposure.

6. Apr 5, 2011

### Ryan_m_b

Staff Emeritus
That makes sense. If I'd have thought about it for a little while I probably could have figured that out from all the microscopy I've done over the years. Cheers!

7. Apr 15, 2011

### test4

That is assuming that astrophotography is your choice of observing.
If visual observing is your flavor, then apparent brightness is critical.

Test,

8. Apr 15, 2011

### Staff: Mentor

Of course.

9. Apr 16, 2011

### test4

In terms of your OP the observer is not using a "Hubble Like" scope.
Hubble uses photography for all observations. In many wavelengths and varying times.

You don't view in "real time" objects through Hubble.
Unless the object is close (such as the Jupiter comet collision)......
You take pictures of long past events.

Even if you could build a big enough scope to resolve detail on a "busy" planet, you would still be looking into the past of said planet regardless of weather or not you used a camera or your eyeball.

So, in reality, you could never watch in real time the events unfolding on a distant planet.

The farther away the planet, the longer in its past you would be viewing.

All telescopes (and all eyeballs...lol) no matter how sophisticated have to "wait" for the photons etc.......to reach the objective lens/CCD (or retina) camera. The speed of light and the matter/energy in between rules what you see at any particular time.

Its so cool.

We will be forever looking into the past.

Test,

Last edited: Apr 16, 2011