# What size camera aperture can read a license plate from Earth orbit?

Answer: About 20 meters. Th Hubble Space Telescope’s aperture is 2.4 meters. So, you really can’t do it at the present time.

This is one of a large, seemingly inestimable number of practical need-to-know and esoteric questions addressed in Lawrence Weinstein’s book Guesstimation 2.0: Solving Today’s Problems on the Back of a Napkin, a followup book on the earlier Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

I should say that I personally have an uncanny ability to estimate things. This comes from being an archaeologist with a lot of experience in CRM. For years I had to estimate how much projects would cost and at the same time, how much dirt needed to be moved, how big patches of land were, how thick layer of dirt might be, and how many rusty nails were sitting in a big-ass pile of rusty nails. And so on. I am very rarely surprised at the number something turns out to be. Weinstein’s book is an attempt by an expert estimator to help you to learn to be almost as good as I am at this. Just as important, probably, is that he actually goes ahead and makes these estimates so you can see what the answer to interesting questions might be.

Having said that do remember that estimation is a sociopolitical act as well as a mathematical activity. One can produce estimates that are helpful to a particular cause. You may already be familiar with the question of “should we use cloth or disposable diapers” which became the hotbed of discussion several years ago between environmentalists and economists (who are almost always anti-environmentalist, given who tends to butter their bread, as it were). I would not want to guess at Weinstein’s politics, but he shows the bias we often see with number crunchers. In asking the question, how much of a car’s energy requirement would we obtain if we covered the car with solar panels, we seem to see an unfortunate anti-environmental slant. The answer is calculated with numbers that seem biased against getting a very large number and still end up being between 2 and 8%. This is written off as insignificant, but I’m pretty sure that if I came up with a version of gasoline that gave everyone 8% better mileage, I’d get rich.

Anyway, it is a fun book and if you are planning to give someone a present that will cost about 10.00, this is a good choice because they probably don’t already have it!

Stock up on napkins!

1. #1 A Farkas
Cambridge, MA
November 3, 2012

Wrong. You may be thinking of the focal length. An aperture of 20m would require a camera at least 2,000m long (that’s my guesstimate). Aperture (or f-stop) is the size of the opening in the lens that lets light through. A smaller aperture will allow more in focus, and so would make it easier to see a license plate, but the real measure of resolution is the focal length of the lens.

November 3, 2012

A Farkas, the information provided here is directly from the cited book, so I doubt I’m “wrong” since I made no claim.

You should get a copy of the book, find all the stuff the author got wrong, and post it!

3. #3 Ken
November 3, 2012

Aperture to a photographer has a different (but related) meaning to an astronomer. In telescopes we are concerned with how much light we can possibly gather onto a primary surface before focusing that light through the telescope. Most large telescopes use a mirror of some kind for that surface. The useful diameter of that primary surface is often called an aperture since it relates to the opening required for light traveling in a straight line to make use of that surface.

The ability to optically resolve an object of a certain size at a distance is (in part) dependent upon the size of that primary surface.

If you really want to get confused with the terminology, start talking about the characteristics of cameras which are placed into the telescope at the focal point. To muddle things further, make those cameras digital and add in some filters in front of the focal plane at different distances.

It took me many hours of research just to learn the often conflicting terminology used to buy a good telescope and a camera for it. It’s obvious the technologies were not invented together.

November 3, 2012

Aha!

5. #5 lyle
November 3, 2012

Note that the question is not well determined do you allow multiple images and synthetic aperture software to do the job? Here is a link to a navy research page that talks about resolution to a few centimeters using this technique: http://www.nrl.navy.mil/research/nrl-review/2003/remote-sensing/lucke/

Note the comment about otherwise you go to several meters (likely greater than 5) in size. While not yet implemented in space, it appears that the computer changes optical observing just like it has changed radio observing and also synthetic aperture radar.

November 3, 2012

@A Farkas: There are a number of limitations; one is the so-called “diffraction limit”. To make out the lines on the plate, these have to be at least twice the width of the “Airy disk”, and at a distance of , say, 120km for a very low orbit spy satellite you still need a very large lens or mirror. The other limitation is the rate of arrival of photons. The size of the Airy disk also depends on the wavelength of light. As an example of the effect of mirror size and the wavelength at which an observation is made, the James Webb Space Telescope will have a mirror which dwarfs that of Hubble – and yet the mid and far-infrared observations will have a resolution far lower than that of Hubble’s visible wavelength cameras. If you want some idea of how big the Airy disk is for the wavelengths visible to humans, just look through a telescope pointed at stars (well, except for our sun). The stars cannot be resolved – the speck of light you see is the Airy disk. The Keck Telescope on Mauna Kea uses 2 very large telescopes separated by a large distance to achieve what is effectively a much larger optic, and it is one of the highest resolution telescopes on the planet.

7. #7 solarspace
November 4, 2012

farkas. no.
you seem to be confusing focal length with f-ratio. which is the ratio between a scope’s focal length and it’s aperture. so yes, aperture size is of key importance in determining maximum useful magnification

http://starizona.com/acb/basics/equip_magnification.aspx