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The Hour Angle (HA) is measured west from the observer's meridian in hours, mins, seconds.

How is the Hour Angle used to help plan observations during the night at a telescope?

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Imagine an hour which goes counter-clockwise. On the left, there are the numbers from 0 to 12, and on the right, there are the same, but the negative numbers.

Empty HA hour

Now imagine yourself standing in the middle of such dial. If you have HA = 0, you know that the star is on the meridian. If HA = 6 or HA = -6, then the projection of star onto the celestial equator is on the horizon. If you have HA = 12, then the star lies on the opposite side of the meridian. The same is valid for decimal values. HA hour with labels Look also at this simulation for demonstration of the hour angle, and at the Wikipedia page about this.

But beware! The altitude isn't the same as hour angle. HA is based on equatorial system, but the altitude is based on the horizontal system. The altitude tels you the height of the star, but the HA tells you the position of the star in the fictional dial.

The right ascension is useful because the star is (less or more) standing still in it. RA is for the distant star constant. But HA with the combination of declination tells you more presentable coordinate system. If you know RA and if you want to know, where the star is, you have to know date and hour, and you can't imagine the position easily. But if you know HA, you know it easily, you just look at the upper dial. (Note that we are looking toward the North in the upper image.) For example, do you know where the RA = 0 is located now? Of course not. And do you know where the HA = 0 is located now? Yes, you can just look at the dial. HA = 0 line is also called the meridian. Also, you can easily convert from HA to RA and conversely using current sidereal or astronomer time. (Look at the Wikipedia article.)

Short answer: You can easily imagine hour angle (HA), meanwhile, you cannot imagine the right ascension (RA) so easily.

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