# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Pointer star question**

**From:**Brad Morris

**Date:**2013 Feb 2, 17:10 -0500

Hi Mark

"Exact" angular separation between Polaris and Merak will depend upon the initial set of coordinates. To what resolution do you need the angular separation to be? An arcminute? An arcsecond?

So rather than just give you an answer, I will give you the tools so that you can compute the distance on your own. Naturally, I will provide an example with the equation.

First, find the Right Ascension and Declination of both objects. I will use

Polaris

RA 2h 31m 52.051s

Dec N 89d 15m 50.64s

Merak

RA 11h 1m 50.52s

Dec N 56d 22m 57.00s

Since the h.m.s format is difficult to deal with, convert it to decimal.

Decimal RA=h+(m/60)+(s/3600k

Polaris

RA=2+31/60+52.051/3600

RA=2.5311252778

Merak

RA=11+1/60+50.52/3600

RA=11.0307

Also, convert the d.m.s format to decimal degrees

Decimal Declination=d+(m/60)+(s/3600)

Polaris

Dec=89+15/60+50.64/3600

Dec=89.2640666667

Merak

Dec=56+22/60+57.00/3600

Dec=56.3825

You will need to convert RA to Sidereal Hour Angle. SHA=360d-(RA*15d/h).

Polaris

SHA=360-( 2.5311252778*15)

SHA=322.0331208333

Merak

SHA=360-( 11.0307*15)

SHA=194.5359

The angular separation between the two bodies is then given by

arccos(sin(dec1)*sin(dec2)+cos(dec1)*cos(dec2)*cos(SHA1-SHA2))

arccos(sin( 89.2640666667)*sin( 56.3825)+cos(89.2640666667)*cos( 56.3825)*cos( 322.0331208333-194.5359))

arccos(.8283548032)

34.069894429 Degrees

or

34 Deg 4 min 11.62 sec

THIS DOES NOT ACCOUNT FOR REFRACTION.

Now you have the keys to compute the distance between any two stars.

Regards

Brad

Hello all! I've been a lurker for several years now but I've been unable to find an exact answer the angular separation between polaris and merak, does anyone know what it is? Thanks, Mark.

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