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I have a six inch telescope on an equatorial mount and I've been struggling to use the mount properly. For a couple months now, the only strategy I've used is just 'point and look.' I've watched some youtube videos on polar aligning a telescope, but none of the videos ever tell me how I can use polar alignment to find other objects after I've aligned. Is polar alignment even the right method of finding objects? If so, how can I use the degrees and minutes on my RA and DEC knobs to point directly at an object?

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If a mount is polar aligned, it becomes very easy to find objects that have the same Right Ascension or Declination as a bright star. It works like this

1) you align the mount to the pole

2) using a star map, or an app, you try to find an object that has the same R.A. or declination as a bright star. As an example, use Messier 4, which has almost the same declination as Antares.

3) you point the telescope at Antares. Lock the declination axis.

4) Look through the finder, or through the scope using the eyepiece that gives you the biggest field of view. This most often this is the eyepiece that gives you the lowest magnification.

5) move the scope to the west, it rotates around the RA. axis. Messier 4 should now enter the field. Move slowly, and move back to Antares when you get lost.

6) When you see Messier 4, lock the RA. axis too, and center Messier 4 in the field using the fine adjustment controls.

7) There are a couple of other bright objects you can try. I'm not familiar with the Southern sky, but for the Northern sky, Messier 13 can be found starting at eta Her(cules), and moving in declination.

8) a bit harder is Messier 57 in Lyra, you need to start a bit to the north of gamma Lyr, or a bit to the south of beta. Another easy target is IC 4665, which is very close to Beta Ophiuchi (Cebalrai), almost but not quite to the north.

9) Other objects to try are Messier 5 starting with Beta Librae (Zubeneschamali), and Messier 10 starting at epsilon Ophiuch (Yed Posterior).

10) The next step is to try and find objects by using multiple steps, alternating between moving in RA and in declination. You would move to a star or better, to a recognizable star pattern, and continue from there.

11) This way of star hopping works best if the angles moved are not huge. Think 10, 15 degrees. As you get more experienced you will start using the stars in between as waypoints so you can move bigger distances.

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