Why Would Any Country Want a Balloon Now?

Today, the US apparently shot down another ... something ... over the north Alaska/Western Canada region.  What's going on?  Is this something new?  More to the point, in this era of spy satellites that can read the license plates on cars from orbit, or listen to small radios like your cell phones, why would anyone go to balloons and other low-tech things like that?  

From my perspective, the answer is a simple truism I've quoted many times: physics is a bitch.  There is nothing that a spy satellite can do that a drone or balloon or something in the atmosphere can't do better for a tiny fraction of the price.  Put another way, any instrument that could be used on a satellite can be made smaller, lighter and cheaper, while returning better quality observations if it can fly at airplane altitudes.  

It's difficult for me to put actual numbers here for a few reasons, but the trends that are important are easy to spot and describe.  Let's start with optical resolution, the ability for that telescope looking down to resolve two objects.  The distance they're apart as an angle can be calculated by the separation you want to resolve and the distance to the magnifying optic (mirror, almost without exception).  The resolution angle you want is given (in radians) by the separation you want resolve divided by the distance from the optic, 

Let's say you want to read letters 2" square from 400 miles - about the altitude of the Hubble Space Telescope's orbit. That's an angle of 2" divided the number of inches in 400 miles, or 2/25,344,000 (inches cancel) or 78.9 nanoradians (78.9*10^-9 radians).  Which works out to be 0.0163 arcseconds.  

The required telescope diameter to achieve that sort of resolution is big.  Probably too big for a spy satellite.  You can calculate how big by using information like this:

Lambda is the wavelength of light, and a commonly used value here is 550 nanometers, the color of a nice blue green light.  It turns out that using the equation on the left, the size mirror to resolve two inches is 8.544 meters diameter.  That's a big telescope; 336 inches diameter.  Until fairly recently, that would have been the largest telescope in the world. 

If we reduce the height from 400 miles to balloon height, let's say 11 miles (close to that 60,000 foot level we read about last week).  That shrinks the telescope to a 9.2" aperture, taking it from among the largest in the world to something like this that hundreds or thousands of amateur astronomers own.  

Another way of saying all this is that any telescope will out perform the same size in an orbiting satellite by the ratio of their heights.  400/11 miles is 36.3636.  Divide that 336" scope derived for 400 miles by that 36.3636 and get 9.24".  

The argument for smaller telescopes is pretty strong.  Or even a fleet of smaller telescopes that can be deployed and recovered after their missions.   

A similar kind of argument can be made for radio monitoring and any system that you put up being made more sensitive by being at a lower altitude.  A commonly used relationship for calculating free space path loss uses the expression:

dB = 37 dB + 20log(f) + 20log(d)

Here, f is the frequency in MHz and d is the distance in miles.  Since we don't know a frequency, let's just pick the same for both, I'll use 1000 MHz, and calculate for 400 and 11 miles.

For 400 miles, loss is 149 dB. 
For 11 miles, loss is 118 dB.

Antenna gain is easy compared to optical, but that difference of about 30 dB more sensitive means about 1000 times more sensitive.  Again, it seems like an obvious conclusion that the lower radio can outperform anything in orbit.  The satellite might be able to compensate for that 31 dB greater losses to orbit with a bigger/better antenna, but gain like that definitely can cost.