Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 10: Equation of Time

Key Ideas

Length of a Solar Day is set by:: Ellipticity of the Earth's Orbit; Obliquity of the Ecliptic
Equation of Time: Difference between solar and clock time
The Analemma
Sunrise, Sunset, and Sundials

The Ellipticity Effect

The Earth orbits the Sun in an ellipse. It moves faster when closer to the Sun and slower when farther away
Near Perihelion:: Slightly longer than average solar days (noon to noon); The Sun will appear to move Eastwards each "clock" noon
Near Aphelion:: Slightly shorter than average solar days; The Sun will appear to move Westwards each clock noon

The Tilt Effect

The Sun moves 1 degree per day, but the 23.5 degree tilt of the ecliptic means this motion is not always directly East-West
Only the Eastward motion of the Sun determines the length of a Solar Day
Near Winter/Summer Solstic:: Sun moves faster Eastward because there is almost no North-South motion (shorter day)
Near Equinoxes:: Sun moves slower Eastward because it has substantial North-South motion (longer day)

The Equation of Time

The time of solar noon relative to clock noon is set by these two effects:
The Ellipticity Effect:: Sun and clock time agree twice per year (perihelion and aphelion)
The Tilt Effect:: Sun and clock time agree four times per year (equinoxes and solstices)

Hypothetical Analemmas

How would the analemma appear if:: The Earth's axis of rotation was not tilted?; The Earth's orbit were circular?; The solstices occurred at perihelion and aphelion?

Sunrise, Sunset

The Winter Solstice has the shortest amount of daylight of the year, however the Sun is several minutes ahead (west of clock time then.
Implications:: The earliest sunset is a couple weeks before the Winter Solstice (Sun is West of clock time); The latest sunrise is a couple weeks after the Winter Solstice (Sun is East of clock time)

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.