Latitude and obliquity

This page is used twice, once in the introductory pages, and again in the solar measurement pages. I did this because the introductory pages require values of latitude and obliquity to explain the process of obtaining Sun and star positions in the sky. I did not have values for latitude and obliquity when I started, so my early data on the Sun and stars was necessarily incomplete. It was only after the solar work had been completed that the star positions could be determined. I felt that a preview of the final solar results would help the reader understand the basic geometry used to build a star catalog. The data that appears on this page is explained only later in the solar section of the website.

In order to convert altitudes into declinations, Tycho needed to know his latitude. There were no accurate maps in his day, much less GPS, so he measured the minimum and maximum altitudes of stars near the North Pole and used the average of these two altitudes to get the altitude of the pole.

The altitude of the pole is one's latitude. For example: near the Earth's equator, Polaris (the North Star) has an altitude near zero and thus one's latitude is near zero. Near the geographic North Pole, the altitude of Polaris is near 90 degrees, thus the latitude near the pole is near 90 degrees.

The tilt of the Earth's axis (called the obliquity angle) causes the seasons, and we notice it as the Sun being high in the sky as it crosses the meridian in summer (in the northern hemisphere), and low in the sky at a winter noon. This change in the meridian altitude is due to the tilt of the Earth's rotation axis relative to the Earth's orbit plane.

Because the celestial equator and the celestial North Pole are at right angles to each other, the average of the maximum and minimum meridian altitudes of the Sun defines the altitude of the celestial equator. The latitude of the observer is then 90 degrees minus the altitude of the equator.

Here is the Sun's altitude over the course of a year, as measured by my telescope, and the quantities that can be deduced from it:

With this data, I was able to determine that my altitude of the equator was 50.98 degrees, thus my latitude is 39.02 degrees north. Modern GPS values give a latitude of 39.01 degrees, but I will use my value in all later calculations.

Add 2458849.5 to the MJD to get the full Julian date.

The total altitude variation was +/- 23.432 degrees, showing that the Earth is tilted this amount relative to its orbit plane.

All this from measuring the meridian altitudes of the Sun.

Now I know that in the earlier diagrams, EQ = 50.98 deg, LAT = 39.02 deg, and EPS = 23.432 deg.

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