Reading about the Star KIC 8462852, it has been said that the SETI project turned its radio telescopes towards the star to search for extra terrestrial radio signals as the star had strange fluctuations in light. How can we point from earth a radio telescope towards a star which is 1480 light years away whilst the earth is spinning at 1675 km/h and keep it focused or, in the case of a radio telescope, aligned in order to try and receive radio waves??
Part of the answer that I suspect the original questioner needs is that although the Earth is indeed spinning very fast, the amount the surface of the Earth moves relative to an astronomical object is tiny.
So you put motors in the base of the telescope so that it slowly turns to look at the same patch of sky. You don't need to refocus because telescopes are looking at objects so far away that focus doesn't matter. You don't need to do anything else because the Earth's movement is smooth and continuous, and it's not about how fast you're moving, it's about how quickly you're turning. In our case, one complete circle every 24 hours which is pretty slow.
Focus at infinity just means that you set the focus of the telescope so that an object which is infinitely far away would be in perfect focus. It depends on the quality of the telescope, but the practical difference between focus at infinity and focus at the actual distance disappears after a few miles or so. At the distance of stars, there is essentially no difference at all.
First you are talking about pointing the telescope at the source not focusing it on the source. Telescopes are generally focused at infinity, and there is no need to compensate for the Earth's rotation in the focusing.
The speed of motion of the telescopes location on the Earth is also not directly relevant, what is relevant is the apparent rotation of the sky around the projection of the Earth's axis onto the sky. That is (in the Northern hemisphere) the rotation of the sky about the pole star.
There are a number of ways of dealing with the earth rotation.
Actually use it to scan over the sources
Drive the telescope to keep it pointing in the direction of interest
Track the source (use multiple channels to measure the source error from boresight and drive the telescope to to null the error).
This really has nothing to do with radio telescopes per se, but is common to all telescopes including optical.
Because the speed of light is so much faster than the speed of the telescope, the star looks like it is standing still in the sky so the telescope only needs to track it as it moves across the sky at 15-degrees per hour.
However, the speed of light isn't infinite, and there is a measurable effect there. When you're riding in a car while it is raining and the rain preferentially hits your windshield, to you it looks like the rain is coming from some location in front of you even though it is falling straight down, and because of this when you try to look directly at the source of the rain, you look tilt your head forward rather than look straight up. The same thing happens with light from stars. Because the Earth is going around in its orbit and spinning on its axis, light falling "straight down" on us looks like it is coming from a position a little ahead. This is called stellar aberration. It isn't a large effect, but it is large enough that if you're trying to figure out very precisely where the stars are, then you need to correct for it.
There are two processes to manage this:
First, the telescopes (really, big antennas) are aimed mechanically and move so they can maintain their reception of a specific star/source/sky location over time.
However, except for stars immediately in the vicinity of the pole stars, the star will eventually go below the horizon. Once this happens the telescope/antenna cannot receive anything further until the source appears above the horizon again.
What happens at this point is we have many telescopes/antennas around the world that are collectively controlled. Long before a star/source/etc falls below the horizon for one telescope, another telescope further west has already pointed at it, and is receiving the same signal. Once this switchover has occurred, the previous telescope is free to select another target - something else on the other side of the planet that will be falling below the horizon for telescope further east.
In this way:
- The telescopes are under constant use pointing at interesting things
- Things which need continuous monitoring can be monitored without interruption despite the world turning
- We can observe anything at any time, as long as there's available time on the radio telescope network
- Sharing resources allows scientists to conduct science more completely and inexpensively
- By having 2 or more telescopes pointing at the same object at once, we can effectively increase the signal to noise ratio and get better data - it's technically very similar to having one earth sized single antenna rather than two tiny (relatively) antennas.
- With central control of a whole participating worldwide network, scientists can react very quickly to sudden phenomena, like bursts, at any time, regardless of the position of the earth
The way telescopes work is pretty much the same in the optical and radio wavelengths- the telescopes collect electromagnetic radiation, rather than focusing at a point. There are multiple reasons for this, the main one being the amount of photons reaching the telescope from the region of interest is pretty low.
In order to collect more photons, the telescope (or telescope array) has to 'look' into the area of interest for a long time- this is achieved in case of earth based telescopes by mechanically steering the antennae, so that they are pointed in the same direction for a long amount of time. The principle is pretty much the same in space.
For looking at KIC 8462852, SETI used the Allen Telescope Arry, which is basically a set of 42 antennae scanning the skies in radio wavelengths. The problem of earth's rotation is basically solved in two steps by (radio) telescopes.
By steering the antenna(e) as decided by the software so that the antenna points at the same position of the sky. For a star at ~1500 light years, the angular speed required is pretty small and can be easily supplied by the modern telescopes.
Even if the star (or any other object of interest) passes below the horizon, the telescope can simply continue its work on the next day, gathering more photons. Of course, other telescopes can take over from this one, but the end result is the same- collecting more photons.
Let's say you go out on a warm summer day, lie down and look up at the stars. For some reason you manage to not fall asleep, while you only look at one star the whole night. You will have no problems pointing your eyes at this star (except for falling eyelids), like it is no problem to point a telescope at one star.
Edit: curiousdannii is right, I didn't explain how. I will do this now: There is a machine called motor, or motor drive, or engine, which converts electrical energy into motion energy. With a little engineering, you can use this motion energy to turn the telescope.
The smart antennas are already in work and software controlled beam forming is also pretty much in use now.
Therefore, at even this very high spinning speed of the earth, the tracking of the stars at large distances is not that difficult.
Also high speed data acquisition and compression algorithms are there to help. So it's been with help of control engineering been possible to point at a specific celestial object.