Just after sunset Venus and Jupiter are dancing together in the Western sky. Venus is the brighter of the two, in fact she's the brighter than anything but the Sun and Moon. Throughout the month of June, at least as seen from Earth, they've been getting closer and closer and tonight they'll be within about 2 degrees of each other. On June 30th only a third of a degree of arc separates them.
Believe it or not I'm going to attempt to link astronomy and 5G mobile wireless, so hang in there.
Astronomers measure the angular separation in degrees. You can easily break this down - the separation between any point on the horizon and the zenith overhead is 90 degrees, halfway to the zenith is 45 degrees, the moon is about a half degree wide. Beyond that you can use your body - your arms and fingers turn out to be fairly useful for rough measurements. Here's what I have used since I was a teenager:
° Stretch your thumb and little finger as far from each other as you can. The span from tip to tip is about 25 degrees
° Do the same with your index finger and little finger. The span is about 15 degrees
° Clench your fist at arms length, and hold it with the back of your hand facing you. The width is about 10 degrees
° Hold your three middle fingers together; they span about about 5 degrees
° The width of your thumb at arm's length is about 2 degrees
° The width of your little finger at arm’s length is about 1 degree.
Depending on your vision you may want to close an eye doing this. This even works for very tall and very short people as their arms and hands tend to scale with height. You can measure some known objects and calibrate your hand if you want.1 A quick calibration can be done on June 27th or July 2nd when Venus and Jupiter are almost exactly 2 degrees apart - see if your thumb just covers them.
All fine and good, but most of the objects in the sky tend to be much smaller. The moon is about a half degree or thirty arc minutes wide. Most of the objects you can resolve into some shape are measured in arc seconds. Stars appear as points of light from Earth - their disks are below most resolution limits. The angular resolution of your eye or a telescope has a theoretical limit depending on the wavelength light being imaged and diameter of the instrument's mirror or lens. Angular resolution improves (is a smaller number) when the wavelength decreases and the diameter of the lens or the diameter of the mirror or lens increases - at least to a point.2 Our atmosphere is turbulent causing stars to twinkle and, through a telescope, are blurry at higher magnifications. Astronomers rate the quality of the sky in terms of 'seeing' - the best possible angular resolution you can obtain. At Mauna Kea or La Palma spectacular nights can drop as low as 0.4 arc but normal quality at an observatory is more like 1 arcsecond. If you were only looking for resolution, Earth based observatories could get by with mirrors well under a half meter in diameter. But a large mirror is a light bucket - and huge mirrors collect a lot of light allowing astronomers to record extremely faint objects.3
The diagram shows the relative scale of some telescopes. You'll notice a few of them have multiple mirrors in two flavors. It is much cheaper to build several high quality small mirrors than one enormous piece of glass. Often these are combined to tile the parabolic shape of a larger mirror. The second flavor, interferometer telescopes, is more exotic using widely separated mirrors. Through some tricky optics the separate mirrors act like segments of a very large mirror. They lack its light gathering power, but have the its resolution. They're tricky to operate, but are a path to affordable resolution.
The next chart is a bit messy , but is just the angular resolution equation. The horizontal axis is the limiting resolution in arcseconds and the vertical axis is the effective diameter of the aperture. The red dot in the lower right is the pupil of your eye - a bit less than a centimeter in diameter when fully dilated. The diagonal lines represent the wavelength of light. An ideal eye looking at reddish light can resolve about 20 arcseconds. Bluish light has a shorter wavelength and the resolution improves to about 10 arcseconds. If we could see into the ultraviolet and beyond we could resolve smaller angles. The blue star is the Hubble Space Telescope - it gets down to something under 0.1 arcseconds beating any Earth-based telescope without adaptive optics.
We were looking West at Venus and Jupiter. Now shift your gave South towards the spout of Sagittarius' teapot - the direction of the center of our galaxy. Near the center is an enormous black hole. At 4.3 million times the mass of the Sun Sagittarius A* is approximately supermassive. It is difficult to calculate its size, but the current limit is something smaller than about 15 times the Sun's diameter. That may sound large, but we're about two thirds of the way out from the center of the Milky Way- 26,000 light years away. That makes it a very small target. So an interesting question comes up - can you take a picture of it, or more properly its accretion disk?4
There is a big problem. The center of the Milky Way is full of dust which prevents us for seeing it in visible light. The region is more transparent to certain radio wavelengths, but that presents a problem, At best a radio wave's wavelength is thousands of times less than visible light. You would need a radio antenna kilometers long just to match the resolution of a one meter optical mirror.
The resolution needed is about what it would take to resolve a baseball on the Moon - something around 50 micro arcseconds. Referring to our handy chart we see this is just possible with apertures of several thousand kilometers with submillimeter wavelengths. It turns out a variation on the trick used in multi-mirror interferometer telescopes saves the day.
If you record information in a passing radio wave including the precise time it was recorded and combine that with similar information from other antennas you can synthesize an effective aperture that is the distance between the antennas. You want as many different length paths as possible, so you need to find submillimeter radio telescopes thousands of kilometers apart and and attach extremely accurate atomic clocks to create a long baseline interferometric array. A telescope potentially the size of the Earth. This is still a work in progress, but it is amazing astrophysics.5
Time to circle back. Submillimeter radio waves are often absorbed by the atmosphere as well water vapor. The telescopes are located on high mountain tops in very dry regions and at the South Pole in Antarctica. Over the years radio astronomers have built a deep understanding of how short wavelength radio waves are absorbed.
Very little communication is done above 10 GHz, but the lure is a lot of available spectrum. One millimeter radio corresponds to 300 GHz. Radio astronomers have done pioneering work studying how these radio waves are absorbed by the atmosphere. Some of the 5G radio schemes are looking for such virgin territory. Some of the problems may turn out to be good points. Attenuation is strong at many of these frequencies, but limited range, assuming you have a high density of access points, translates into potentially huge amounts of bandwidth per radio. We may even be able to minimize backhaul costs and perhaps route around carriers entirely. A long shot, but maybe...
It is remarkable that astronomers work with such diverse wavelengths of light. In doing so they've been early pioneers in understanding how light travels through the atmosphere. Some of that work will allow us to image a black hole as well as to pave the way for the next generation of mobile devices.
1 Radians are more popular in astrophysics, but astronomers often stick with degrees. Self calibration is just the thing for a nerdish experience. Measure your family and see how close your measurements are.
3 There are a couple of ways around the seeing limit. One is to orbit a telescope - the effective angular resolution of the Hubble Space Telescope is only limited by its optics. The other trick is to use adaptive optics. It is possible to measure atmospheric turbulence and correct for it in real time. This is still fairly exotic and is mostly used on big research telescopes, but the improvement is stunning. The VLT improves from about 1 arcsecond to as 30 to 50 arcseconds with the adaptive optics switched on.
4 Matter accelerates as it falls towards a black hole radiating energy along the way. This forms a bright accretion disk and the object that can be imaged.
5 a paper here (pdf)