The ideal size for a telescope...

At the end of class Friday, Professor Johnson made a comment about there being telescopes on earth with much, much larger apertures than the 10-25 meters discussed on the problem set (I still think these are pretty big…) I didn’t really think that he was serious, partially because it’s so hard to imagine a telescope mirror being so large, but in fact I was thinking about it wrong: the creatively named Very Large Array, which consists of 27 radio antennas in New Mexico, is capable of making very high resolution measurements. On a side note - If you think its name is unoriginal, then just consider for comparison the Very Large Telescope (VLT) and Overwhelmingly Large Telescope (OLT).

The VLA looks small compared to the Very Large Baseline Array (VLBA), however. VLBA is a system of similar radio antennas, also 25 meters in diameter, which are spread across the whole United States. To the left, the locations of the dishes are shown - image from the NRAO website (you can also go there for more information): http://www.vlba.nrao.edu/

Why is this useful? The relationship between aperture (D), wavelength (l), and angular resolution (q, measured in radians) is as follows for single telescopes:

sin(q)=(1.220)(l/D)

From this, we can see that aperture of a telescope affects what wavelengths of light it can observe at an optimal resolution. Resolution is important because if a source is larger than the resolution of the telescope observing it, then the observation will not contain the entire source. This is called an extended source, as opposed to a point source, which is smaller than the resolution of the telescope observing it. Also, sources that are too close together (that is, the distance between them is smaller than the angular resolution) cannot be accurately studied, as astronomers would not be able to see where one point source ended and the other began! It would just look like one larger, blurrier point source…

HOWEVER – this equation does not hold for the VLBA, because the VLBA is an array, not a single telescope. Instead, for arrays, the relationship depends upon the separation between radio dishes (B) and wavelength of the source (l). Again, the angular resolution is measured in radians (q):

q=(1.220)(l/B)

Regardless, a larger telescope can observe SOME frequencies of light with higher resolution. Longer wavelengths require a larger aperture, which is why the largest receivers on earth study radio waves, which have a higher wavelength than visible light.

Type of light studied	(Approximate) Wavelength	Approximate aperture width to study this light from Earth	Example of a telescope operating at this wavelength
Radio waves	1 cm – 100 m	Antennas are spaced 8000 km across north America	VLBA
Infrared	1000 nm – 0.1 cm	*	Spitzer
Visible	400 nm – 800 nm	10 meters	Keck
UV	10 nm – 200 nm	*	Extreme Ultraviolet Imaging Telescope (EIT)
X-rays	0.01 nm – 10 nm	*	Chandra

*not ground-based telescopes

So – larger telescopes do exist, but not in the capacity that I was imagining. According to a quick Google search, the largest single telescope in the world is the Gran Telescipo Canarias (don’t think you need to be fluent to translate that one…) in the Canary Islands (http://www.universetoday.com/17652/largest-telescope/). It has a 10.4 meter aperture. No single telescope would actually be 1 km or more across, but what Professor Johnson was referring to was the necessity for much larger values of B to study higher wavelength waves (such as radio waves!) which is why the VLBA was built across such a large distance!

Most important thing I took away from this was that depending on what wavelength of light you are studying, different sized telescopes will have different levels of effectiveness. There is no ideal size for a telescope because what you need depends on what you are studying. Bigger isn’t always better!