In astronomy, an equatorial mount is an extremely helpful invention, that becomes essential when photographing the cosmos. If you ever photographed the night sky, you are probably aware of an effect called star trailing (which can be annoying, but can also be used to create fantastic photos).

The Earth spins around its axis, which, fortunately for Humans, creates the day and the night. Though we can’t feel this rotation, it is nonetheless quite fast: at the equator, the rotation speed of the Earth is about 1674 km per hour!
The effect of the rotation is clearly visible on a camera sensor. If your shutter speed is low enough (i.e. the exposure time is long enough), you might experience star trailing on your pictures, which makes your stars appear as small strokes rather than dots. And as you increase the focal length of your lens or telescope, the exposure time at which star trailing starts to appear becomes smaller.
When you observe the sky with a fixed telescope, you run into a similar issue. The stars don’t trail, of course, but the target you’re observing quickly moves out of your field of view. So you need to move your telescope a few inches and recenter your target, which quickly becomes annoying.
How an equatorial mount works
Equatorial mounts can have various designs and names, the most famous one being probably the GEM (German Equatorial Mount), but they all have the same function: compensating the rotation of the Earth.

The principle is simple: the Earth rotates around an axis (counter-clockwise in the Northern hemisphere, and clockwise in the Southern hemisphere). If the mount is aligned along this axis, and if it rotates at the same speed as Earth (about 1 revolution every 24 hours) but in the opposite direction, then the movement of the Earth and that of the equatorial mount cancel each other. In other words, the mount will be able to track the stars, and if you attach a camera to the mount, the stars will appear as fixed to the camera.
TimeLapseSteve made an interesting video that shows how a motorized equatorial mount works. In the first seconds of the video, the mount is off and as expected, the sky is moving. But when the mount is turned on, you can see how the mounts tracks the stars and how the Moon remains fixed.
Worth mentioning: if you place your cursor near one of the stars when the mount is on, you can see that it is not 100% fixed. This happens when the mount is not properly aligned with the axis of the Earth. The better the alignment, and the more static the stars will appear.
A basic equatorial mount is mechanical, and rotates thanks to a set of knobs you need to turn. More sophisticated mounts are usually motorised.
Aligning the equatorial mount with the axis of the Earth
In practice, a mount needs to be aligned with the axis of the Earth to work properly. But how can we do that? Well, luckily for us, aligning a mount is pretty straightforward and can be done in 4 steps (provided you are in the Northern hemisphere).
1. Finding the geographic North
The geographic North gives you an approximate direction of where the axis of the Earth is pointing to. To find it, you can use a standard compass (make sure there’s no metal around you), or alternatively, the compass app on your smartphone.
Your mount needs to point in the direction of the geographic North. It doesn’t need to be 100% precise, you can fine tune this later on.
However, your mount does need to be perfectly levelled horizontally. The use of a precise bubble level is recommended, otherwise your polar alignment will be inaccurate.
2. Finding your precise latitude
The latitude depends on where you are on Earth: on the equator, it is equal to 0°, on the North and South Poles, it is equal to 90°. In Munich, where I live, my latitude is about 48°. To know your precise latitude, you can use the compass app of your smartphone, check a service like Google Maps, or this latitude finder tool by the NASA.
The latitude will give you the angle which you need to orient your mount at (as shown on the diagram above).
3. Finding the Polaris, the North Star
Polaris, also known as the North Star, is a star located 430 ly above the North Pole. With an apparent magnitude of about 2, it’s not the brightest star (ranked 49th), but it’s bright enough to be seen in most skies on Earth.
It is well known since centuries, and was used extensively by navigators and travellers alike for a very convenient reason: it always points North. Even better: it is virtually located on the axis of rotation of the Earth (well, close enough anyway).
Consequently, to align our mount with the axis of our planet, we simply need to point the mount to Polaris. In astrophotography, this process is called the polar alignment.

Finding Polaris can prove difficult for the beginner astronomer. After all, the stars all look the same, and our naked eyes can see no less than a few thousands!
If you are lucky enough to live in an area without light pollution, you will see much more stars in the sky. So, which one is Polaris?
Well, there is an easy way to find it. First you need to locate a constellation called the Big Dipper (or Ursa Major). This constellation is well known for its shape, and is made of bright stars.
If you trace a virtual line starting from the right side of the dipper, about 6 times its height, you will find a bright star. That’s Polaris! And it’s also forming the end of a smaller constellation, the Little Dipper (or Ursa Minor). This one is harder to detect, because it’s made of dimmer stars, unlike the Big Dipper, which usually stands out in the night sky.
4. Centering Polaris in the reticle of the mount
In order to perform a polar alignment, equatorial mounts are equipped with a finder scope. This little scope usually sits directly inside the mount, and has a reticle in which you can center Polaris.
In theory, if your mount is aligned precisely enough to the geographic North, and the latitude is set correctly, Polaris should be directly visible in the polar scope.

In reality, Polaris isn’t exactly aligned with the axis of rotation of the Earth, and there is a slight deviation. It seemed too good to be true, right? Actually, relatively to us, Polaris is also moving like any other star. So we need to take into account this small deviation.
Luckily for us, we now have smartphones connected to the Internet. Some applications can do all the calculations for us, based on the time and location, and tell us where exactly to center Polaris in the reticle.
With my iOptron SkyGuider mount, for instance, I’m using an application called Polar Scope Align. It’s free, accurate and compatible with most equatorial mounts.
To perform an accurate polar alignment, equatorial mounts have small knobs that allow you to make precise adjustments.
I live in the southern hemisphere, there’s no Polaris!
Indeed, if you are in the southern hemisphere, you won’t be able to see Polaris. The stars are completely different from the northern hemisphere.
Good news: polar alignment is still possible, without using Polaris but another star called Sigma Octantis (or Polaris Australis), that is close enough to the axis of rotation of the Earth.
Bad news: unlike its boreal cousin, Polaris Australis is harder to find, because it’s 25 times dimmer, with apparent magnitude of about 5.5.
You can find a pretty good tutorial on how to polar align in the southern hemisphere on Alain Maury’s blog.