Aligning an equatorial mount

The earth rotates about its axis once every day. When observing an object with a telescope, we have to compensate the rotation of the earth. An equatorial mount compensates this motion if the following 2 conditions are met:

  1. its polar axis is parallel with the polar axis of the earth;
  2. the mount rotates about its polar axis at exactly the same rate as the earth rotates about its axis

The first condition is met if the mount is correctly set up. The procedure of setting up an equatorial mount is called polar alignment.

The second condition requires some basic math, as the way humans measure days differs from the way astronomers measure days.

Solar day

The earth revolves around its axis once every day. In the meantime, the Earth also orbits the Sun once per year. If you combine both movements, you'll notice that we humans count a day between two noons (when the sun crosses the meridian), meaning there are about 365.25 days in a year (remember there is a leap year nearly every 4 years). We subdivide each day in 24 hours.

Sidereal movement

When looking at the background stars as a reference, you will probably have noticed that depending on the time of the year, you see different constellations. Why is this? This has to do with the fact that the earth revolves around the sun. Imagine the sky would be transparent in bright daylight, then you would see the sun in front of the background sky. Every day as we count our 24 hours time interval between two noons, you'll see that the Earth actually rotates a bit too much according to the distant background stars: about 1° per day (actually 1/365.25°). This means that in one 24-hour day the earth actually rotated 360° plus 360°/365.25. In how much time does the earth then rotate the full 360 degrees according to the stars?

  • 360° + 360°/365.25 → 24h
  • 1° → 24h / (360 + 360/365.25)
  • 360° → 24h * 360 / (360 + 360/365.25) = 24h * 0.9972696469 = 23.93447152651h = 23h56m04s = 86,164 seconds

In other words, the Earth makes a full revolution of 360° with respect to the distant stars in 23h56m04s. This is 3m56s less than our normal 24 hour day (24h = 86,400 seconds). An equatorial mount will have to rotate around its polar axis in 23h56m04s in order to compensate the rotation of the Earth. The Earth rotates from West to East (the sun rises in the East and sets in the West), hence the equatorial mount will have to rotate from East to West.

Polar alignment of an equatorial mount

There are a number of good resources available on the Internet that explain the procedure. It is slightly different if you live in the northern or southern hemisphere.

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