1. Celestial Navigation Getting Started Amy Hopkins

2. Materials Sextant Sextant Watch Watch Nautical Almanac Nautical Almanac HO 249 or HO 229 HO 249 or HO 229 Planispheric Astrolabe Planispheric Astrolabe

3. What We Want to Know Our location on Earth Our location on Earth

4. What We Observe Predetermined location of one of the 57 bodies in Space using the Nautical Almanac Predetermined location of one of the 57 bodies in Space using the Nautical Almanac The exact time using a watch The exact time using a watch The altitude of the astronomical body using the sextant The altitude of the astronomical body using the sextant

5. What a Sextant Tells Us Sextant Measures an Angle Sextant Measures an Angle Breaks those angle measurements into degrees, minutes, and seconds (1/10) Breaks those angle measurements into degrees, minutes, and seconds (1/10) Each Degree represents 60 minutes Each Degree represents 60 minutes If we take each minute and break it down further into seconds (60mins x 60seconds) the sextant can give us up to 3600 different readings within any degree. If we take each minute and break it down further into seconds (60mins x 60seconds) the sextant can give us up to 3600 different readings within any degree. The reading of a Sextant will look like the following The reading of a Sextant will look like the following 45˚ 20.2 minutes 45˚ 20.2 minutes We call this sexagesimal notation. We call this sexagesimal notation. Take a minute and turn your sextant to this measurement. Take a minute and turn your sextant to this measurement.

6. The Light House Example Zenith as a reference point Zenith as a reference point Distance Distance 90˚ 0.0 90˚ 0.0

7. Tangent A line which touches a circle or ellipse at just one point. A line which touches a circle or ellipse at just one point. The blue line is a tangent to the circle. The blue line is a tangent to the circle. Note the radius to the point of tangency is always perpendicular to the tangent line (a 90 degree angle). Note the radius to the point of tangency is always perpendicular to the tangent line (a 90 degree angle).

8. How it Works Must calculate tangent h. Must calculate tangent h. The lighthouse is H tall. The lighthouse is H tall. I am standing a particular D (distance) away. I am standing a particular D (distance) away. So tangent h or So tangent h or tanh = H/D

9. The Challenge

10. Why Two Shots This is why we need two measurements. This is why we need two measurements. From two different celestial bodies From two different celestial bodies We create our lines of position. We create our lines of position.

11. The Solution

12. Altitude Intercept 1 st Coordinate System We only have our measurement of altitude and time. We only have our measurement of altitude and time. Now we make one nautical mile the length of time it takes to see the astral body change one MINUTE of altitude (as measured on the sextant) Now we make one nautical mile the length of time it takes to see the astral body change one MINUTE of altitude (as measured on the sextant) This gives us our intercept!!!! This gives us our intercept!!!!

13. Practical Approach If you are at 38degrees and 32.6 minutes I am at 38 degrees and 42.8 minutes We just need to find the difference. We are 10.2 nautical miles away or 10.2 minutes difference on our sextant.

14. Intercept Method Reading 1 - Calculate and plot your assumed location or deduced reckoning. Reading 1 - Calculate and plot your assumed location or deduced reckoning. Reading 2 – Calculate your location using your celestial navigation tools. Reading 2 – Calculate your location using your celestial navigation tools. When you compare these two plot lines they will give you only one of 3 possible results. When you compare these two plot lines they will give you only one of 3 possible results.

15. More Complications Let’s redesign the lighthouse to be the sun, moon, or stars. Let’s redesign the lighthouse to be the sun, moon, or stars. Sun, Moon, and Stars have a complex pattern of movement. Sun, Moon, and Stars have a complex pattern of movement. We don’t know how "tall" these astronomical bodies are. We don’t know how "tall" these astronomical bodies are. We need the height to find our tangent h. We need the height to find our tangent h. Earth is round, not flat Earth is round, not flat The sky is dome shaped The sky is dome shaped

16. Map Distortion Serious issue for navigation Serious issue for navigation Where is the map most distorted? Where is the map most distorted? How do each of these maps counteract the distortion? How do each of these maps counteract the distortion?

17. Practical Approach If you are at 38degrees and 32.6 minutes I am at 38 degrees and 42.8 minutes We just need to find the difference. We are 10.2 nautical miles away or 10.2 minutes difference on our sextant.

18. Result A If the observed altitude is exactly the same as your computed altitude then you are standing on exactly the same “circle of altitude” as our deduced reckoning. If the observed altitude is exactly the same as your computed altitude then you are standing on exactly the same “circle of altitude” as our deduced reckoning.

19. Result B Our observed altitude is less than our computed altitude. We must be farther away from the circle of altitude. Our observed altitude is less than our computed altitude. We must be farther away from the circle of altitude.

20. Result C If the observed altitude is more than the computed altitude than we must be closer to the center of our circle of altitude or our assumed or dead reckoned position. If the observed altitude is more than the computed altitude than we must be closer to the center of our circle of altitude or our assumed or dead reckoned position.

21. Keeping it Real! http://aa.usno.navy.mil/data/docs/celn avtable.php offers an online Intercept Method calculator http://aa.usno.navy.mil/data/docs/celn avtable.php offers an online Intercept Method calculator http://aa.usno.navy.mil/data/docs/celn avtable.php http://aa.usno.navy.mil/data/docs/celn avtable.php

22. Putting it Together If we are in the middle… If we are in the middle… We use our dead reckoning to get an assumed lat and long. We use our dead reckoning to get an assumed lat and long.

23. Quick Chart Review Scale Scale Legend Legend Depth Depth Declination Declination

24. Scale

25. Legend

26. Depth The numbers of depth are for low tide. The numbers of depth are for low tide. White colors indicate deeper water. White colors indicate deeper water.

27. Compass Rose A compass rose is used to measure directions using true or magnetic bearing. A compass rose is used to measure directions using true or magnetic bearing. True direction is printed around the outside True direction is printed around the outside magnetic is printed around the inside. magnetic is printed around the inside. Variation is the difference between true and magnetic north for the covered area. Variation is the difference between true and magnetic north for the covered area. It is printed with annual change in the center of the compass rose. It is printed with annual change in the center of the compass rose.

28. Celestial Mechanics 2 nd Coordinate System Celestial Mechanics is the study of the movements of the celestial bodies. Celestial Mechanics is the study of the movements of the celestial bodies. Or rather our view of the celestial bodies as the earth rotates. Or rather our view of the celestial bodies as the earth rotates.

29. Sketching the Heavens North and South Let’s create a vast celestial sphere. Above the north pole we will name Polaris as the north celestial sphere and 180 degrees away would be the South Celestial Sphere Let’s create a vast celestial sphere. Above the north pole we will name Polaris as the north celestial sphere and 180 degrees away would be the South Celestial Sphere Now let’s create a celestial equator Now let’s create a celestial equator This measurement of degrees is called Declination This measurement of degrees is called Declination The declination information is contained in the Nautical Almanac The declination information is contained in the Nautical Almanac

30. Sketching the Heavens First we must pick a zero or beginning point First we must pick a zero or beginning point We call that the First Point of Aries We call that the First Point of Aries

31. Point of Aries At a right angle to the celestial equator at the point of Aries becomes zero At a right angle to the celestial equator at the point of Aries becomes zero This is not a meridian line but rather an hour circle or as zero is called This is not a meridian line but rather an hour circle or as zero is called HOUR CIRCLE OF ARIES HOUR CIRCLE OF ARIES This is the celestial equivilent of the Prime Meridian and it becomes zero This is the celestial equivilent of the Prime Meridian and it becomes zero

32. Sidereal Hour Angle SHA This is the measurement of the meridian lines that span the celestial heavens This is the measurement of the meridian lines that span the celestial heavens Then only span westward 0-360˚ Then only span westward 0-360˚ We only measure in one direction so east and west are no longer necessary We only measure in one direction so east and west are no longer necessary

33. Declination N S Sidereal Hour Angle W This is the coordinate system used for celestial navigation This is the coordinate system used for celestial navigation The nautical almanac tabulates the positions of stars in SHA The nautical almanac tabulates the positions of stars in SHA Based on GHA or Greenwich Hour Angle or LHA Local Hour Angle Based on GHA or Greenwich Hour Angle or LHA Local Hour Angle The Almanac is in GHA The Almanac is in GHA

34. Altitude Azimuth 3 rd Coordinate System Your zenith Your zenith 180 degrees from you zenith is Nadir directly on the other side of earth 180 degrees from you zenith is Nadir directly on the other side of earth We can only see the things above our horizon line We can only see the things above our horizon line Anything below our horizon line is denoted as negative altitudes Anything below our horizon line is denoted as negative altitudes We need more than altitude to place a pinpoint a celestial body in our sky We need more than altitude to place a pinpoint a celestial body in our sky We need an Asimuth We need an Asimuth

35. Azimuth Zn We measure in reference to the horizon such as 0 degrees at true north We measure in reference to the horizon such as 0 degrees at true north Runs clockwise up to 360 degrees Runs clockwise up to 360 degrees

36. Altitude Azimuth Uses the altitude in horizontal circles Uses the altitude in horizontal circles –Principal verticle circle (due north and south) Azimuth in vertical circles Azimuth in vertical circles –Each has an upper branch and a lower branch –Prime Vertical Passes through 90 (which would be due east) 270 (which would be due west) Passes through 90 (which would be due east) 270 (which would be due west)