New approach for Polar Alignment ( no dependency on siting Polaris)

[antariksha]

Abstract :

The topic of Polar Alignment is not at all new. Lot of approaches, automation tools are available. Yet, some aspects in all the current approaches drove me towards doing some more work. The key aspects of this approach are as follows.

• Ability to do the Polar alignment without polaris sited
• Relatively less complexity than drift alignment
• Ability to address to a good extent the atmospheric refraction to finally locate correct NCP / SCP position
• A good starting point for amateurs who wish to graduate towards sophisticated tools and techniques
• Ability to quickly verify if the polar alignment is intact after one object photographed or viewed, and the equipment is being pointed to another object. This point is mentioned in light of the fact that sometimes the polar alignment gets disturbed and the next object photographed shows star trails. This is especially true if payload is tweaked for next photo imaging.

What is required?

• One should have a good understanding of the sky and ability to identify stars upto Mag 4.5 using star maps and basic concepts of RA and Dec.
• One should have Equatorial mount with ability to fine tune Azimuth and Alt adjustments.
• Availability of cross hair eye piece for the ability to locate the star exactly at the cross hair point.
• It is good to have finder scope attached and the finder cross hair is aligned with the main telescope eye piece cross hair.

Please note this technique is not for the GoTo mounts which many times have Alt-Az mounts fitted with tracking motors. The GoTo alignment is done using 3 Star method.

However, there are a few mounts which are equatorial design and also have GoTo tracking capabilities with RA and Dec motors. For these mounts, it is preferred to carry out polar alignment. The only point about these mounts, is that GoTo should have ability to start the RA motor ( tracking) without doing the 3 Star alignment, in other words, bypassing the steps for 3 Star alignment.

The technique is based on the mathematics around the stellar current positions precisely computed. The technique suggests NCP or SCP alignment using specific pointing stars.

Method

The technique relies upon pairs of stars identified such that pair has same RA or same Dec. The details about finding such pairs, are given in the next section ( Mathematics).

Step 1

• Try to do a very coarse polar alignment using your latitude and pointing the equatorial axis approximately towards a possible Polaris direction. This is only to reduce the iterations in the method below. There is no dependency to visually site Polaris.

Step 2

• Select the pair of stars of the same RA from the table 1 below. Now, while choosing the pair, please select that pair which is closest to the zenith. This will reduce the error due to atmospheric refraction of siting those stars. Choosing such pair, will get better alignment.
• Note that the NCP and SCP lie on the same RA contour of the pair, you have just chosen.
• Locate the first star of the pair in the cross hair eye piece. Loosen the DEC knob of your Eq mount. Let the RA axis not to be loosened. Further, please start the RA motor and hence the tracking. In case of GoTo capability, please ensure the tracking is On, while the 3 Star alignment being bypassed.
• Rotate the telescope around DEC axis such that the second star of the pair is in the Cross hair eye piece. In the first attempt, the second star almost certainly will not be at the center of cross hair eye piece. And you need corrections.
• At this point, take the help of the finder with its wider field of view. Identify the position of the second star whether it is below or above the finder cross hair. Adjust the Azimuth of the mount through the coarse or fine depending on how off the second star has been.
• o   Tip : In case, someone is facing difficulty in finding which direction to move Azimuth of the mount for correction, the following tips may be of use. A simple way to determine is to locate where the second star lies with respect to cross hair. Assume it is on the lower side of cross hair. Then the correction in the Azimuth of the mount should be such that the star is moved upward. It may be noted that your finder can be either inverting or non-inverting. Now, to determine the movement, please hold the finger on the lower side in front of the primary of the finder. And slowly lift the finger towards the center of the primary to obstruct it and continue moving upward. While doing so, please observe from the eyepiece. The blackish ghost image of finger will be seen moving. If movement is lower to upward, the optics is non-inverting. If ghost image moves from up to down, it is inverting. With this small trick, you would know how to apply correction.
• Once the correction is done, please point the finder to the first and then second star alternately simply by rotating around Dec axis of the mount. Both stars will be seen at the cross hair. At this point, coarse polar alignment is done.
• Now, please use the main telescope cross hair to locate the first and then second star using Dec axis movement. If required, please carry out the necessary Azimuth correction. Again, please use the above small trick to find out more on how to apply correction.
• At this point, please note that at the telescope’s high power ( with cross hair eyepiece), the Dec axis is correctly tracing two stars in your pair. Note that NCP/SCP lie on the same Dec axis. The Azimuth alignment of NCP/SCP is achieved. No more touching of azimuth knob of your Equatorial mount now.

Step 3

• Site the pair of stars of the same Dec from the table 2 below. Now, while choosing the pair, please identify roughly the midpoint of them. Now, select that pair whose midpoint is relatively closest to the Zenith. With this, one star is relatively East ward and other one almost at a same distance but Westward. This will reduce the error due to atmospheric refraction of siting those stars. Choosing such pair, will get better alignment
• In case you are unable to select a pair, please read Step 4.
• Note that the NCP and SCP lie on the centre of the Dec circle which the above pair inscribes.
• Locate the first star in the cross hair of finder. To locate the second star, please lock Dec axis. But loosen the Eq axis and rotate the telescope around Eq axis. Please carry out Alt adjustments of the mount. Please use similar procedure and tricks as in the step 2.
• Once the two stars are in the cross hair positions of the telescope, the polar alignment is completed.

Step 4 ( only if you could not carry out Step 3)

• Site the pair of stars of the same RA from the table 1 below. Now, while choosing the pair, please select another pair which is off zenith. Please try to select such pair which has both stars approx same elevation from horizon, so that their atmospheric refraction is almost same. Effectively, we cancel the atmospheric refraction influence.
• Please note that in step 2, NCP/SCP is located to be on one of the RA lines. Now, we use another RA line with this newly selected pair. Again, for these stars to be centred, please keep Eq axis fixed and only move Dec axis ( similar to step 2). However this time, the mount corrections to be done are using Alt adjustments.
• Once the two stars are in the cross hair positions of the telescope, the polar alignment is completed.

Mathematics

 

The starting point was the star catalog where the Epoch 2000 is taken as baseline. Then I selected the stars brighter than mag 4.5. I applied the corrections due to Earth Precession and also the individual star’s proper motion. With the base data was ready for today's’ star positions. Then I programmatically picked up all pairs for same RA (within 0.001 difference) and later all pairs with same Dec (within 0.001 difference).

I found mag 4.5 to be heuristically optimal. This magnitude is sufficient for visual locating these stars. Also, the number stars shortlisted from the main catalog is good enough to give sufficient number of required pairs.

The pairs located today may not be valid after say couple of years due to Earth Precession and stellar proper motion. The below two tables will need fresh computation then.

Disclaimer: I have tried few of the above mathematically found pairs from my location 19 Lat 73 Log. I use Bresser ExOS 2 mount. After the polar alignment, the tracking was tested for 10 min which was adequate for my current level of astrophotography.

At different altitudes, different latitudes, this is not tested. I believe, the method will definitely work for small exposures. It is to be validated if this method works for very long exposures.

Star Pairs

Table 1 : Star pairs with same RA ( useful for Step 2 and 4)

 

Sr No	First star  (name)	First star HD Id	Second star ( name)	Second star HD Id
1	Gam Cas	5394	37 And	5448
2	Nu Per	23230	19 Tau	23338
3	Ups Tau	28024	71 Tau	28052
4	90 Tau	29388	53 Eri	29503
5	Kap Lep	33949	Rho Ori	33856
6	The Aur	40312	Del Aur	40035
7	Gam Mon	43232	Eta Gem	42995
8	Eps Gem	48329	30 Gem	48433
9	13 CMa	50013	V0415 Car	50337
10	Omi CMa	50877	The CMa	50778
11	P Pup	63922	Xi Pup	63700
12	Chi Car	65575	11 Pup	65228
13	Del Hyd	73262	E Vel	73634
14	B Vel	74180	V343 Car	74375
15	Iot Cnc	74739	Eps Hyd	74874
16	31 Leo	87837	Alp Sex	87887
17	Pi Cen	98718	Sig Leo	98664
18	Lam Mus	102249	Nu Vir	102212
19	Alp Crv	105452	Del Cen	105435
20	Gam Cen	110304	Gam Vir	110380
21	5 Boo	120477	2 Cen	120323
22	SHT 56	129116	Alp Lup	129056
23	Del Her	156164	Pi Her	156283
24	102 Her	166182	Pi Pav	165040
25	110 Her	173667	Phi Sgr	173300
26	Zet Cap	204075	Gam Pav	203608
27	Del Gru	213009	Del Cep	213306
28	Iot Cep	216228	Mu Peg	216131
29	Bet Peg	217906	Bet Psc	217891

 

Table 2 : Star pairs with same Dec ( useful for Step 3)

 

Sr No	First star  (name)	First star HD	Second star ( name)	Second star HD
1	7 Cam	31278	Gam UMaj	103287
2	Iot Cyg	184006	The Boo	126660
3	H Persi	26630	Dmi?? Cass	4180
4	Pi Aur	40239	Iot Her	160762
5	39 Cyg	194317	Omi Persi	23180
6	Eta Peg	215182	Zet Cyg	202109
7	Iot Cnc	74739	Bet Tau	35497
8	Bet Peg	217906	Vet Cyg	183912
9	54 Leo	94601	Alp Vul	183439
10	Alp Tau	29139	Gam Gem	47105
11	Mu Ceti	17094	Lam Ori	36861
12	Omi Psc	10761	Bet Cnc	69267
13	Pi Ori	30836	Del Hyd	73262
14	3 Agr	198026	Lam Agr	177756
15	Iot Ori	37043	Iot Vir	124850
16	Lam Eri	33328	Eta Eri	18322
17	The Lib	142198	Del Crv	108767
18	Bet Cet	4128	Bet CMaj	44743
19	88 Aqr	218594	Pi Sgr	178524
20	88 Aqr	218594	Xi Oph	156897
21	4 Xi CMaj	46328	3 Eri???	18978
22	Rho Pup	67523	Omi CMaj	50877
23	Omc Cau???	56139		61555
24	Bet Hyd	103192	43 Eri	28028
25	2 Cen	120323	Eps Sgr	169022
26	Alp CrA	178253	Mu Seo	151890
27	Bet CrA	178345	Lam Gru	209688
28	Phi Cen	121743	Eta Cen	127972
29	Eta Col	40808		73634
30	Vel	78647	Gam Phe	9053

 

Good luck

Ashirwad Tillu ( ashirwadtillu@gmail.com), user name ( antariksha)

Edited August 24, 2019 by antariksha
Last line ( user name) : edited the forum

[michael8554]

Very interesting Ashirwad. 

What is a typical PA error you get with this method, in arcmins? 

Michael 

[antariksha]

Hello Michael, I have not computed PA error yet. It would be a good exercise to take up. I am from India, and the monsoon  ( seasonal rains) are still active, the sky is cloudy.   I can probably revert in another few weeks. None the less, as I have mentioned, I have seen the tracking with no drift, to be working well for 10 min with my Bresser ExOS2 mount.

Ashirwad

[michael8554]

1 hour ago, antariksha said:

monsoon  ( seasonal rains)

Been to India several times, climate change has brought brief monsoon type rains to the UK too.......

Michael 

[antariksha]

Oh...

But the best part of the monsoon is, the dust gets settled. Once the clouds are gone, the sky is clear, we get excellent terrestrial visibility too. These are the best days for observations.