name: celestial navigation

Introduction: The ability to truly sail the open seas and accurately reach a destination came about because of the invention of accurate timepieces that worked aboard moving ships. Once sailors were able to keep track of the time at a known location (Greenwich, England for example) they were able to find their location on the ocean by using the stars.

Pretend you are lost at sea. You lab partners are your shipmates. You will find your location using the following navigational tools.

• Clock set to Universal Time (Greenwich Mean Time)• Sextant• Star Chart (Our Star Wheel)• Nautical Almanac• Chart of the World

Exercise A. Using a SextantYour instructor will show you how to use a sextant so you can find the altitude stars. Before the lights are out, make sure everyone on your ship has a chance to learn the use of the sextant.Your instructor will tell you the name of three different stars. Enter the names of these stars below and in the appropriate row of the Celestial Navigation Data Sheet.Measure the altitude of each of these stars. Write your values below along with the values from each shipmate. Average these values for each star and enter those averages into the Celestial Navigation Data Sheet.

Star A Star B Star CStar NameAltitudes degrees degrees degrees

your measurementshipmate's measurementshipmate's measurementshipmate's measurement

average measurementCelestial Navigation 7:1 Astronomy 20 – Family of the SunRev: 0.1

EXERCISES

7Name:

Lab Day and Time:

Celestial Navigation“Lost at Sea”

Shipmate 1: Shipmate 2: Shipmate 3:

Exercise B. Finding Co-altitudes and Sub-stellar PointsCo-altitude: Look at the figure below. In the figure you are seen with your sextant measuring the altitude of a star.

Now step back and view that measurement on the whole Earth.

Since the star is so very far away, every person on Earth looks the exact same direction to see the star. Another way to say this is all the lines of sight to the star are parallel. There is one point on Earth at each moment in time that sees the star directly on the zenith. This point is know as the substellar point. If we draw a line from the center of the Earth to the sub-stellar point and another line from the center of Earth to our current position, those two lines form an angle that is called the co-altitude. From the figure above we can see that the co-altitude=(90º-altitude). Enter the co-altitudes of the three stars into the Celestial Navigation Data Sheet.Celestial Navigation 7:2 Astronomy 20 – Family of the SunRev: 0.1

Everyone on the circle of your latitude sees the North Star at the same altitude that you see it. Similarly, for each star, there is a different circle on the Earth that sees that star at the same altitude (and therefore same co-altitude) as you see it. That circle is centered on the sub-stellar point and has an angular measure from the sub-stellar point equal to the co-latitude. See the figure below.

Latitude of sub-stellar point: The latitude of the sub-stellar point is the same as the star's declination.

Look up the declination of each star in the Nautical Almanac and enter those values into the latitude line of the Celestial Navigation Data Sheet.

Longitude of sub-stellar point: The longitude of the substellar point is more difficult because the Earth is rotating and the substellar point is at a different longitude every moment of the day.

The first piece of information we need comes from our clock. Without this we are truly and certainly lost. Your instructor will tell you the date and what time of day your clock reads. This is not local time. This is the time of day at the prime meridian. Record the date and time of day on the Celestial Navigation Data Sheet.Celestial Navigation 7:3 Astronomy 20 – Family of the SunRev: 0.1

The Nautical Almanac gives an angular relationship between the Prime Meridian on Earth (through Greenwich, England) and the 0h right ascension line on the Celestial Sphere (through the Vernal Equinox). This angle is called the Greenwich Hour Angle (GHA) and is depicted in the diagram. This angle depends on the specific day of the year and on the time of day. Look this angle up in the Nautical Almanac and write it on the appropriate space below as well as on the Celestial Navigation Data Sheet.

Next we need to determine where this star is relative to the 0h line on the Celestial Sphere. Normally we would use right ascension for this information. But right ascension is in hours and is measured in the other direction from what we want. Instead we use something called the Sidereal Hour Angle (SHA). The SHA is measured from the 0h line (Vernal Equinox) to the right ascension line of the star. But it is measured in degrees. Look up the SHA for each star and put this information in the appropriate space below.

Star A Star B Star CGHA (degrees)SHA (degrees)

GHA + SHALongitude of substellar

pointIf we add the GHA to the SHA, we will have the number of degrees of longitude that the sub-stellar point is west of the Prime Meridian. Add these two numbers together and place the result in the appropriate space above.

Our value for GHA+SHA may be anywhere from 0º to 720º west of the Prime Meridian. However, longitude is measured from 0º to 180º West of the prime meridian and from 0º to 180º East of the prime meridian. You need to turn however many degrees West of the Prime Meridian into a proper longitude. Write the longitude in the appropriate space above as well as on the Celestial Navigation Data Sheet.Celestial Navigation 7:4 Astronomy 20 – Family of the SunRev: 0.1

Celestial Navigation TableDate:

Time of Day:

Greenwich Hour Angle:

Star A Star B Star CName of Star

Altitude (degrees)

Co-altitude (degrees)

Latitude of sub-stellar point

Longitude of sub-stellar point

Our Latitude:

Our Longitude:

Celestial Navigation 7:5 Astronomy 20 – Family of the SunRev: 0.1

Exercise C. The SeasonsNow it it time to plot our location on our World Chart. Plot the sub-stellar location of one of the stars onto the World Chart. Using the lines of latitude on the chart, span your compass a number of latitude degrees equal to the co-altitude of the star. Use that compass span to draw a circle centered on the star's sub-stellar point. If all is done correctly, you lie somewhere on the circle you have just drawn. Now is a good time to have your instructor check your work.

Instructor’s signature

How do we now determine where on the circle we are?

Draw a circle for the next star. It should intersect the previous circle in two locations. If all is done correctly, we should be on one of those two intersection points.How do we determine which of those two points we are on?

Draw the last circle. Ideally it will cross the other circle at one of the previous two intersection points. However, due to measurement error, it probably won't. You will have narrowed down your location to a small triangular area. Shade in the triangular area and read the longitude and latitude of the center of this triangle. This is your location on Earth. Record your location below and on the Celestial Navigation Data Sheet.

Our Latitude:

Our Longitude:

Now we are no longer lost at sea.


name: celestial navigation

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