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17. Polaris – Azimuth and Latitude. Presented By: Kelly Curtin, Asst. Professor. Course Outline. Navigational Astronomy Lecture 1 & 2 Mean Time / Apparent Time Lecture 3 Time Zones, Zone Description, Chronometer Time Lecture 4
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17. Polaris – Azimuth and Latitude Presented By: Kelly Curtin, Asst. Professor
Course Outline • Navigational Astronomy Lecture 1 & 2 • Mean Time / Apparent Time Lecture 3 • Time Zones, Zone Description, Chronometer Time Lecture 4 • The Earth, Celestial, And Horizon Coordinate System Lecture 5 & 6 • The Spherical Triangle Lecture 7 • Circle of Equal Altitude Intercept Lecture 8 • Time Diagram, Right Ascension Lecture 9 • The Nautical Almanac, Finding GHA, LHA, and Dec. Lecture 10 & 11 • Instruments For Celestial Navigation Lecture 12 • Sight Reduction of the Sun, Stars, Planets, Moon Lecture 13 - 15 • Plotting and Advancing / Retarding the Assumed Position Lecture 16 • Calculating Time of Meridian Passage (LAN) Lecture 17 • Calculating Latitude at Meridian Passage Lecture 18 • Calculating Time of Sunrise/ Sunset/ Twilight Lecture 19 • Star Shooting Schedule / Pub. 249 Lecture 20 • Azimuth and Amplitudes Lecture 21 – 24 • Polaris – Azimuth and Latitude By Lecture 25 • Star – Finder – Stars, Planets, Selecting the 3 best Stars Lecture 26 • The Complete Day’s Work Lecture 27 & 28
XVII: Polaris Latitude by Polaris Polaris • Because A Star Is Considered An Infinite Distance Away From The Earth, It’s Light Rays Are Considered Parallel To One Another. From Wherever You Observe The Star On Earth There Is No Angular Difference At The Star. • Someone Observing Polaris At 1° North Would Be Seeing A Parallel Ray Of Light As Someone Observing Polaris At The North Pole NP E
XVII: Polaris Latitude by Polaris Polaris • Someone At 1° North Would See Polaris About 1° Above The Horizon. • Someone At The North Pole Would See Polaris At About 90 ° Of Altitude. (At Their Zenith) • Someone At 45° North Would See Polaris At About 45° Of Altitude NP E
XVII: Polaris Latitude by Polaris CNP Polaris • The Only Problem Is That Polaris Is Not Exactly Coincident With The Celestial North Pole. It Has A Small Diurnal Circle Near The Celestial North Pole • To Correct For These Differences The Polaris Star Tables Have Been Set Up To Calculate Latitude From An Observed Altitude (Ho) And Entering Arguments Of LHA Of Aries, Latitude, And Month Of Year NP E
XVII: Polaris Latitude by Polaris Polaris Entering Arguments for LHA of Aries: Entered in appropriate column and row which corresponds to units NP Entering Arguments for Latitude: Entered with Latitude closest to DR latitude E Entering Arguments for Month: Entered with Month
XVII: Polaris Latitude by Polaris Entering Arguments for LHA of Aries: a0 correction Entered in appropriate column and row Entering Arguments for Latitude:a1 Correction Entered with Latitude closest to DR latitude Entering Arguments for Month: a2 Correction Entered with Month The Formula for Latitude By Polaris is found at the bottom of the Table in the Nautical Almanac and Reads: Latitude = Apparent Altitude (corrected for Refraction) -1° + a0 + a1 +a2 Because Apparent Altitude Corrected for Refraction = Observed Altitude (Ho) This formula is more easily stated as: Latitude = Ho -1° + a0 , + a1, +a2
XVII: Polaris Latitude by Polaris Example: On July 29th at 1930 ZT your DR λ is 164° 26.0’E. You observe Polaris with a Hs 23° 46.8’. Your index error is 2.7’ off the arc, and the height of eye is 56.0 feet. What is your latitude by Polaris?
XVII: Polaris Latitude by Polaris Example: On July 29th at 1930 ZT your DR λ is 164° 26.0’E. You observe Polaris with a Hs 23° 46.8’. Your index error is 2.7’ off the arc, and the height of eye is 56.0 feet. What is your latitude by Polaris? Step #1 Calculate Ho Hs 23° 46.8’ i.c. + 2.7’ Dip (56.0) -7.3’ Ha 23° 42.2’ alt. corr. -2.2’ Ho 23° 40.0’
XVII: Polaris Latitude by Polaris Example: On July 29th at 1930 ZT your DR λ is 164° 26.0’E. You observe Polaris with a Hs 23° 46.8’. Your index error is 2.7’ off the arc, and the height of eye is 56.0 feet. What is your latitude by Polaris? Step #1 Calculate Ho Step #2 Calculate LHA Hs 23° 46.8’ ZT 1930 - 00 i.c. +2.7’ ZD -11 Dip (56.0) -7.3’GMT 0830 - 00 Ha 23° 42.2’ GHA 065° 54.0’ alt. corr. -2.2’inc. 7° 29.2’ Ho 23° 40.0’ GHA 073° 23.2’ +E λ 164° 26.0’ LHA 237° 49.2’
XVII: Polaris Latitude by Polaris Example: On July 29th at 1930 ZT your DR λ is 164° 26.0’E. You observe Polaris with a Hs 23° 46.8’. Your index error is 2.7’ off the arc, and the height of eye is 56.0 feet. What is your latitude by Polaris? Step #1 Calculate Ho Step #2 Calculate LHA Ho 23° 40.0’ LHA 237° 49.2’ Step #3 Calculate Latitude from Table Ho 23° 40.0’ - 1° +a0 + 1° 43.9’ +a1 + .6’ +a2 +1.0’ Latitude 24° 25.5’ N
XVII: Azimuths & Amplitudes The Azimuth of Polaris A Special Table Was Created In The Nautical Almanac To Determine An Azimuth Of Polaris. Two Entering Arguments Are Required: The LHA of Aries The Observers Latitude *This Table Was Created Because Polaris Is Not Exactly on the North Celestial Pole. Depending Upon the Time of Day and Your Location Polaris’ True Bearing May Differ From Due North “000°”
XVII: Azimuths & Amplitudes The Azimuth of Polaris Example: On March 17, 2001 at DR Position: L 33° 15.0’ N at 0200 – 00 GMT, Polaris Bears 358.6° PGC. Calculate the Gyro Compass Error Tabulated Azimuth 359.2° T Observed Bearing 358.6° PGC Gyro Compass Error 0.6° E
XVII: Azimuths & Amplitudes The Azimuth of Polaris CNP Polaris True Ø 359.2° NP OBS Ø 358.6° PGC Earth Gyro Error = 0.6° E
