Polar Alignment with Polaris

How to Achieve Quick Polar Alignment Based on Local Sidereal Hour

Various methods of achieving telescope polar alignment exist. They vary from the quick and imprecise to the tedious and highly accurate. The method here will be in-between these extremes of setup time and accuracy. It is basically the method used by auxiliary polar alignment telescopes and can be used to check the accuracy of such.

The Local Hour Angle Method
The method works by calculating the Local Hour Angle (LHA) of Polaris at the time polar alignment is desired. The LHA here is the position angle of Polaris with respect to the celestial pole. The zero point is at meridian passage when Polaris is directly above the pole. Meridian passage happens when an objects right ascension (RA) coordinate coincides with Local Sidereal Time (LST). Six sidereal hours after meridian passage an object will be directly west of the pole (LHA of 90-degrees), twelve sidereal hours after passage it will be directly below the pole (LHA of 180-degrees) and eighteen hours after it will be east of the pole (LHA of 90-degrees). For a given RA position a particular LHA will occur at the same LST.

The circle that Polaris traces in a 24-hour sidereal hour period will cover every possible LHA. In this worksheet the LHA of Polaris is visualized on charts that simulate the view through a finder or telescopic wide-field. Telescope alignment is obtained by aiming the telescope in altitude and azimuth to mimic the view on the charts.

Accuracy of this alignment will depend on: 1) how true the optical axis is with the polar axis and 2) the degree that you can accurately place Polaris in the field-of-view. The later is best done with a reticle eyepiece having an index point or circle whose distance from the field center equals the apparent separation of Polaris from the pole. Lacking that you can make a position guestimate based on the fact that Polaris is about -degree from the pole. This would be of the way from the center of a 6-degree finder field. Wide-angle 2" eyepieces or a low-power eyepiece coupled with a focal reducer can achieve a sufficient field (at least 1.5-degrees) through the main scope of many systems.

Align your finder or eyepiece cross marks with the declination and right ascension telescope axes. Do this by moving slightly in RA or DEC while sighting an object through the eyepiece. Rotate eyepiece so cross mark lines up with object movement. This will make it easier to judge the location of Polaris in the field-of-view.

Charts Displayed
The first chart on this sheet displays the position of Polaris for any instant and the second chart for 45-degree intervals from meridian passage for the next 24-hours. It is easier to do alignment when Polaris reaches an angle that is a multiple of 90-degrees because it only needs to be centered on the cross hair and then offset in only one dimension of either azimuth or altitude along that cross hair. In particular once your mount has been aligned on Polaris at an east or west cardinal point it will be setup correctly for the latitude of your observing location. If you can leave the mount's altitude locked in position between observing sessions, do so. For the next observing session from that location you'll only need to concern yourself with azimuth orientation.

For the charts to be of use you will need to input accurate data. All required data is input through blue data fields in the vicinity of the chart.

CHART #1 Calculations

CHART #1 Data Input Instructions

Adjust Chart View
Across the top of the chart are inputs that control how the chart is displayed. From left to right they are:

  • Field Width -- enter the degree value that corresponds to the optical view thought the instrument you will be using. This value must be at least 1.5 degrees in order to include Polaris.
  • Mirror Image -- set this to 1 if the optical view is reversed left-to-right (mirrored) compared to the naked-eye view. Set this to 0 if there is no reversal.
  • Upside Down -- set this to 1 if the optical view is upside down compared to the naked-eye view. Set this to 0 if there is no change.

Note that a typical finder and a Schmidt-Cassegrain without star diagonal will yield a mirrored and upside down view so both the last two values would be 1. A star diagonal used on a refractor or Schmidt-Cassegrain will yield mirror views so mirror should be 1 and upside-down 0. You can tweak the view using the built-in graph formatting to change the number of grid lines so that the outer concentric circle represents the finder view and the inner circle the eyepiece view.

Adjust Date/Time
Down the right-side of the chart is data representing position in time. From top to bottom they are:

  • Calendar Date -- Date during polar alignment.
  • UT -- Universal Time at instant of alignment.

Remember that converting your watch time to UT can cause the date to rollover. This is true in North America at summer start where in UT the sun doesn't set until the next day: 8:30 PM EDT is 4-hours behind UT; so: 20:30 + 4 = 00:30 UT the next day. In this example the date entered would be that next day.

Chart #1: Position Angle of Polaris to North Celestial Pole

Chart #1 Output Data

Observer Location
Longitude of observing site from User Constants sheet.

Polaris Coordinates and Epoch
Located below the location input, this displays Polaris RA and DEC location for the epoch year listed:

  • RA of Polaris -- Polaris coordinate for epoch.
  • DEC of Polaris -- Polaris coordinate for epoch.
  • Epoch Year -- equinox and date of coordinates.

Polaris location is taken from the STARMAT table and processed to the date of observation. The observation date is then converted into year format and displayed as the epoch year.

Polaris Statistics
This is directly below the chart and lists various statistics about Polaris at the instant of observation. The first column contains values in decimal degrees followed by the same value in deg:min:sec notation. Included here are: arc separation from pole, smallest field width centered on pole that includes Polaris and position angle of Polaris from meridian passage.

Chart #2 Explained

This chart is meant to give a quick indication of when Polaris will be at one of eight special points around the celestial pole. These points are at 45-degree increments -- or every 3 sidereal hours and are the easiest to align on for users of simple cross hair eyepieces. Immediately following the chart is the Polaris Position Table that numerates the date and time that these points are reached. The first of the eight points is selected as the next one in the future of the time and date entered for Chart #1.

Since it is based on data from Chart #1, no new data need be entered for this chart and the accompanying table. Orientation of the chart is taken from Chart #1 and is displayed at the top of the chart. Field of view is fixed. No correction is made for precession or nutation so the times listed in the table may be off by a second or two.

CHART #2 Calculations

Chart #2: Polaris in 45-Degree Increments Around the Pole

Note: Because of rounding the "Sec" column may display 60. Treat this as zero and increment the minute.

Astro Utilities Electronic Book Copyright 1999 Pietro Carboni. All rights reserved.


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