Egyptian Calendar

Day of the year:

Zodiac to Ecliptic Longitude

Chords and Arcs

• A line running through a circle is refered to as a chord. The part of the cirmcumfrence cut by this line is called the arc
• The chords of a few arcs can be found from Euclid's geometry.
• Other arcs can be found by combining half-angle, and sum and difference formulas. The procedure which Ptolemy uses to find these formulas is called Ptolemy's theorem

Obliquity of Ecliptic and Terrestrial Latitude

• A ring is aligned to the line of the meridian, where the sun reaches its highest point in the sky (noon)
• Degree markings on this instrument allow us to measure the elevation angle of the sun at noon.
• Measure the highest elevation (summer solstice) and lowest elevation (winter solstice) of the sun, throughout the year, for your location

Declination from Ecliptic longitude

Right ascension

Rising Amplitude of the sun

Determine the angle that the sun rises in relation to true east

We can measure the length of the day using a clock.

Terrestrial Latitude from the Longest Day

Length of Shadows at Noon

A vertical rod placed in the ground is refered to a gnomon.

Longest and Shortest Shadows

Oblique Ascension

Length of daytime and night hours

Conversion between different hour lengths

Time of Day and Horoscope

Ecliptic Angles and Zenith Distance

Ecliptic Angles

Length of A Year

Input two observations of the sun at equinox/solstice. Both observations must be the same type of equinox/solstice. Use observations as far apart as possible for maximum accuracy.

Sun's Mean or Uniform Motion

Sun's Apogee and Eccentricity from the Length of Seasons

Determine From:

Parameters

Sun's Equation of Anomaly

Sun's Mean Longitude and Anomaly at Epoch

Determine from the time of a given observation of the sun:

Sun Position Calculator

Determine the position of the sun at any given date and time.

Equation of Time

For a given interval of two observations in true solar time, calculate the corresponding interval in mean solar time. The difference is the equation of time.

Lunar Eclipse Periods

Length of the Synodic Month from Eclipse Periods

Mean Motions

Ratio of Months

Month Lengths

Moon's Mean Motions

Mean and Uniform motions of the moon

Month Lengths

Mean and Uniform Motions

Moon's Apogee and Epicycle Radius From Three Observations

Date and Time of observations

Ecliptic Longitude of the Moon and Sun at each eclipse observation

First observation:

Correcting the Moon's Mean Motion in Longitude and Anomaly

From two observations

Initial Month Lengths

Corrected Month Lengths

Moon's Mean Longitude and Anomaly at Epoch

Month Lengths

Observation

Epoch

Moon Position at Epoch

Correcting the Moon's Mean Motion in Latitude

Find two eclipses with the same magnitude, that occured near the same node, on the same side, and with the moon approximately the same distance from the Earth.

Moon's Argument of Latitude at Epoch

Find two eclipses with the same magnitude, that occured near opposite nodes, on the same side, and with the moon approximately the same distance from the Earth.

Position at Epoch

Moon's First Equation of Anomaly

Moon Position Calculator

Lunar Second Anomaly From Observations

Observations should be made when the moon's mean anomaly and mean elongation are both at 90 or 270 (where the effect is greatest), and the ecliptic angle is 90 degrees (i.e. ecliptic is perpendicular to the altitude circle) so that the effect of parallax on the observed longitude is negligible.

Observations made with Instrument

Moon Eccentricity for Second Anomaly

Direction of Mean Apogee of the Moon

Observations should be made when the moon's mean elongation is at about 45, or 135 (where the effect is greatest), and the ecliptic angle is 90 degrees (i.e. ecliptic is perpendicular to the altitude circle) so that the effect of parallax on the observed longitude is negligible.

Observations made with Instrument

Settings