Telescope Orthogonality Revisited 2019 revised 20191116-2041 This text and pdf file is located at http://jimmyjujames.com/orthogonality/Orthogonality-Explained.txt http://jimmyjujames.com/orthogonality/Orthogonality-Explained.pdf The following logic is free to all. Copy, cut, paste, correct and share. Telescope Orthogonality on my Astro-Physics 900GTO mount I have a (conical 10'' F/4.5) Newtonian on an Astro-Physics 900GTO mount on their 8'' portable pier :) I have put a lot a thought into orthogonality to the point of obsession and now in my dreams, formulas in an OpenOffice spreadsheet, graphics, what, why (2X) and have accumulated 8 shims in the process and I still may not understand. 1.) Where is an Orthogonality error noticeable 2.) Dec = 0 3.) Dec = 90 4.) Orthogonality Error Explained 5.) Why (2X) 6.) Calculate RA seconds of a (2X) error with Keypad on an Astro-Physics mount 7.) Calculate RA seconds of a (2X) error with a stopwatch on an Astro-Physics mount 8.) Calculate needed shim thickness from the RA seconds of a (2X) error 9.) Related Links 1.) ******************************************* An orthogonality error is most noticeable at 2 locations. 1.) After a meridian flip back to the same star, the star will be displaced by 2 times (2X) your orthogonality error. No big problem. Re-center, re-calibrate and your good to go until you flip back to the other side and have to re-center and recal. Most of the time not a problem. 2.) Close to NCP your viewing point goes above, below, left or right of NCP but never exactly on NCP No big problem either. If your (1X) orthogonality error is greater than 45 arc-min, you will not be able to center Polaris 2.) ******************************************* For a star at Dec = 0 or close to equator A shim will increase or decrease your viewing point's RA. No affect on Dec at Dec = 0 3.) ****************************** For Dec = 90 or close to NCP Same (2X) error at NCP, (2X) error from east to west but in Dec. Will explain further below. A shim will increase or decrease viewing point's Dec. No affect on RA at Dec = 90 If you have an orthogonality error, your viewing point will not converge at NCP. Your viewing point at closest approach to NCP will be tangent to a circle around NCP. The radius of this circle is your (1X) orthogonality error. The diameter of this circle is your (2X) orthogonality error. You can not get closer to NCP than your (1X) orthogonality error. At closest approach to NCP Moving RA will draw a viewing point circle around NCP This circle is all RA's displaced (1X) from NCP Moving Dec will draw a line tangent to this circle moving parallel to your present line of RA and moving further away from NCP. No combination of RA and Dec can get closer to NCP with your present orthogonality error. Due to an orthogonality error, your closest viewing points to NCP will draw a circle around NCP Centering an object inside this circle is impossible with your present orthogonality error Centering an object between NCP and this circle is impossible with your present orthogonality error If your orthogonality error is greater than 45 arc-min's, Polaris will be inside this circle and you will not be able to center Polaris in telescope with your present orthogonality error. 4.) ****************************** Orthogonality error explained? ----------------------------------- ----------------------------------- 20191120 What is an orthogonality error? An orthogonality error is always in line with the counter-weight shaft. With the counter-weights down and scope pointing at NCP. An orthogonality error will cause the scope's viewing point to be above or below NCP. To the left or right of NCP is not an error. You can move Dec to remove any left or right offset. Rotating RA from east side to west side will move the scope's viewing point around NCP tracing out half of a circle around NCP. Scope will hit the pier before the other half of circle completes. Radius of this circle is your (1x) orthogonality error. Diameter of the circle is 2 times (2x) your orthogonality error. If you move the counter-weight shaft to west side and horizontal/level with ground, the scope's viewing point will be either east or west of NCP by (1x) your orthogonality error. If you move the counter-weight shaft to east side and horizontal/level with ground, you will miss NCP by 1x on the other side of NCP. 1x on one side of NCP, meridian flip and 1x off on other side = 2x orthogonality error when flipping from east to west side. If you move scope from NCP to zenith to Dec=0 to SCP, your scope's viewing point will be east or west of meridian by your 1x orthogonality error everywhere along that path. You will have to shim the front or rear ring to bring your viewing point back to NCP. After minimizing your orthogonality error, future meridian flips should result in star in FOV on both sides. If not then you may have flexure and/or worm needs re-meshing and/or something is loose and needs tightening. ----------------------------------- ----------------------------------- Here is a thought experiment on an orthogonality error. Starting with counter-weights down and scope pointing at NCP (Position 3) Mount stays powered off at all times. Lock RA axis. Release Dec axis You can move the scope's viewing point left to the west and back right passing NCP and moving to the east. Move back to NCP and lock the Dec axis. Dec is now exactly on NCP and not off to the left or right. If you have an orthogonality error, the scope will be viewing just above or below NCP not to left or right. Earlier you rotated Dec to exactly on NCP eliminating any left or right error, Your orthogonality viewing error will only be above or below NCP by (1X). Left or right can be corrected by moving Dec to NCP and is not an error. If viewing is below NCP by (1X), you need to add a shim under front ring. If viewing is above NCP by (1X), you need to add a shim under rear ring. 5.) ******************************** Why (2X)? In the following example our orthogonality error causes our viewing point to be just below NCP by (1X) Dec axis is still locked from Section-4 above. Release the RA axis and rotate RA to (Position 1) Counter-weight shaft level on East-side and scope still pointing at NCP Due to your orthogonality error the scope is now viewing to the right (East) of NCP by (1X). Recap: Position 3 was viewing below NCP by (1X) Position 1 is viewing to the right (East) of NCP by (1X) Dec axis is still locked. Release RA axis and rotate RA to (Position 5) Counter-weight shaft level on West-side and scope still pointing at NCP Lock RA Due to your orthogonality error the scope is now viewing to the left (West) of NCP by (1X). Recap: Position 3 was viewing below NCP by (1X) Position 1 was viewing to the right (East) of NCP by (1X) Position 5 is viewing to the left (West) of NCP by (1X) (1X) + (1X) = (2X) orthogonality error when moving from west-side to east-side or east to west-side Moving RA draws one-half of the orthogonality error circle around the lower half of NCP The radius of this circle is your orthogonality error (1X) The diameter of this circle is your orthogonality error times 2 (2X) Moving Dec will move viewing point tangent to this circle moving parallel to your present line of RA and moving away from NCP. Same 2X error along meridian from East to West side at any Dec, but you will need to reposition scope in Dec to re-center star if not at Dec = 90. As you move away from Dec=90, the circle generated by moving RA will become an arc. You are at one end of this arc when on the east side and the other end of arc when on the west side. This arc is your (2X) orthogonality error. As you approach Dec=0, the arc becomes a straight line at Dec=0 6.) ************************* How to calculate your (2x) orthogonality error in RA seconds with Keypad. Example 1 of 2 With Keypad press Goto and goto a star close to Meridian and Equator You need to be close to your meridian so you do not hit the pier after a Goto meridian flip back to same star. You need to be close to Equator (Dec = 0) so 15 arc-sec/second is 15 arc-sec/second. At Dec = 0, 15 arc-sec/second is 15 arc-sec/second At Dec = 30, 15 arc-sec/second is 13 arc-sec/second At Dec = 48, 15 arc-sec/second is 10 arc-sec/second At Dec = 60, 15 arc-sec/second is 7.5 arc-sec/second At Dec = 88, 15 arc-sec/second is 0.5 arc-sec/second With NSEW buttons Center star At Main Menu Press RA/DEC/Rev button at bottom right Press 9-Re-Calibrate You should hear a beep telling you that you have Re-calibrated on the last keypad Goto star Back to the Main Menu Press 1-Object Press RA/Dec=> Record the displayed RA Record which side the mount is on (East or West-side) Do a Goto meridian flip back to same star using meridian delay feature on an Astro-Physics mount 1E or 2E will goto to East side 1W or 2W will goto to West side Press NSEW keys and re-center star At Main Menu Press 1-Object Press RA/Dec=> Record the displayed RA Record which side the mount is on East or West-side Subtract smallest RA from larger RA Convert the resultant RA Hours:Minutes:Seconds to RA seconds Example: 12:11:10 - 12:07:56 = 00:03:14 00:03:14 would be 194 RA seconds This is your (2X) orthogonality error in RA seconds Use these RA seconds to calculate needed shim thickness below If East-side RA was largest, place shim under Front ring If West-side RA was largest, place shim under Rear ring 7.) ***************************** Calculate RA seconds using a stopwatch Example 2 of 2 Here is a second way to calculate your (2X) orthogonality error in RA seconds with a stopwatch Goto a star close to Meridian and Equator Center star Re-Cal Do a goto meridian flip and back to same star Turn tracking to off With a stopwatch count the number of seconds it takes for the Earth to rotate scope back onto the star. These seconds are your (2X) orthogonality error in RA seconds and should be the same as calculated in Section-6 Example 1 above Use these RA seconds to calculate needed shim thickness below If mount was on the East-side when you turned tracking off, place shim under Front ring If mount was on the West-side when you turned tracking off, place shim under Rear ring 8.) **************************** How to calculate needed shim thickness using small angle approximation in radians or Trigonometry Example: 10 inches from front ring to rear ring 20 RA seconds is your (2X) orthogonality error calculated in Section-6 or 7 above 4 RA seconds = 1 arc-min 20/4 = 5 arc-min is your (2X) orthogonality error 5/2 = 2.5 arc-min is your (1X) orthogonality error 2.5 arc-min is your (1X) orthogonality error Where does the 3438 come from? 360 * 60 = 21,600 arc-min per 360 degrees 21,600 / (2 * 3.14) = 3438 arc-min per radian Finally we can calculate the needed shim thickness Both of the following answers should be identical Using Small angle Approximation in Radians 10 * 2.5 / 3438 = 0.007 inches Using Trigonometry Tangent uses degrees (2.5 / 60) converts arc-min to degrees 10 * tan(2.5 / 60) = 0.007 inches If East-side RA was largest, place shim under Front ring If West-side RA was largest, place shim under Rear ring If mount was on the East-side when you turned tracking off, place shim under Front ring If mount was on the West-side when you turned tracking off, place shim under Rear ring 9.) ************************************** Links related to an Orthogonality error http://www.astromart.com/common/image_popup.asp?image=/images/forums/810000-810999/810742.jpg&caption https://groups.yahoo.com/neo/groups/ap-gto/conversations/messages/52869 http://www.company7.com/library/techin/orthogonality.html I disagree with Company7's example calculations or is it the wording or me? I think Company7's example calculates a shim thickness twice the actual needed thickness. As always, I may be wrong again but Wisdom comes to those who seek it (Was over the front door of my College Library) Jimmy Andrews 33.6N, 88.6W The above text or pdf file is located at http://jimmyjujames.com/orthogonality/Orthogonality-Explained.txt http://jimmyjujames.com/orthogonality/Orthogonality-Explained.pdf