A gift from the Past...

I will begin by drawing a general Diagram on the Plane of the Meridian. This sketch illustrates a case with the observer (Navigator) in approximate Latitude 15 North:

Z is the zenith N and S are the intersections of the North and South points of the horizon with the meridian. Pn and Ps are the Poles Q' and Q mark the intersections of the Equator with the meridian.

This Diagram continues a thought from the previous Appendix, which you may wish to review if this diagram isn't making sense to you.

That logical thought is:

• Since the Pole is elevated from the horizon by a number of degrees equal to Latitude, and
• Since the Equator is always 90 degrees from the Poles, then

The Celestial Equator is depressed from the Zenith a number of degrees equal to Latitude.

How interesting! If we had a means of knowing where the Equator crossed in our sky, we could always know our Latitude directly. Of course, the sky doesn't have some great line painted on it to mark the Equator, so we need something that exists in the physical universe on our Meridian which has a definite relationship to the Celestial Equator. That of course leads us directly to the million-dollar idea...

Objects in the sky have known declinations. Remember that a "declination" is simply the North-South relationship of a body to the Celestial Equator. So the only thing that remains is to get the body on our Meridian! That will of course happen once each day, as the sky seems to turn in its endless westward movement over our heads. In principle, we could use an observation of any object as it crosses our meridian; however, in practice, the Sun is used since most celestial objects are invisible during the day, and the horizon itself is invisible during the night and we seldom have the luck to catch some object exactly on the meridian at twilight, when we have both stars and a horizon.

When the Sun crosses our meridian, this event is called "noon"; and so an observation of the Sun at this time, formally called local apparent noon, is known as the "Noon Sight".

Determining Latitude by the Noon Sight is simplicity itself. We merely observe the Sun when we believe the time is near noon. We keep observing every minute or so, watching the Sun climb ever higher, until at some point it seems not to climb anymore--noon! We note the time at which this final observation was made, and it need not be accurate down to the second. We consult the Nautical Almanac to determine the Sun's declination at the time of observation, and we are ready to draw our Diagram on the Plane of the Meridian. In this example, we will consider ourselves to be in the Northern Hemisphere during Winter. A typical Diagram may look like this:

Z is the zenith N and S are the intersections of the North and South points of the horizon with the meridian. Pn and Ps are the Poles Q' and Q mark the intersections of the Equator with the meridian. Since it is Winter, the Sun is in South Declination, which is below the Equator in this Diagram.

How easily we can see the relationship between Latitude, Altitude, and Declination! The sketch shows that these 3 angles will exactly fill that 90 degrees between horizon and zenith. No trig involved!!

A similar Diagram for Summer shows that relationship, too:

Z is the zenith N and S are the intersections of the North and South points of the horizon with the meridian. Pn and Ps are the Poles Q' and Q mark the intersections of the Equator with the meridian. Since it is Summer, the Sun is in North Declination, which is above the Equator in this Diagram.

Now we see how to construct these Diagrams on the Plane of the Meridian for everyday use:

• Draw the circle with the zenith to the top and the horizon as the diameter perpendicular to it.
• Draw the Pole elevated from the horizon by your Latitude.
• Draw the Equator perpendicular to the axis of the Earth.
• Draw in the Declination of the Sun, either North or South of the Equator.
• Study the diagram to find which relationship will add to exactly 90 degrees.

And in this way, people were able to determine Latitude at sea without highly accurate clocks, and without reference to computers, tables, or elaborate mathematics beyond the grasp of the uneducated mariners from long ago...

The last Appendix (as of November 1996, anyway) will deal with the basis of the formulas used for a general solution of altitudes and azimuth, regardless of whether the body is on the meridian or not.

Go to the Celestial Navigation Appendix on Spherical Triangles.

Go to the Celestial Navigation Appendices.

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Go to the Entry Point to this tutorial