raindrop wrote:
Please explain why the lower loop of the analemma is longer than the upper one. Since earth is at perihelion in January and moves faster then, the loop closer to the winter solstice should be shorter than the upper near the summer solsticeone. Earth is moving slower when at apehelion in August. This is going to bother me until someone explains it.
![Image](http://www.uwgb.edu/dutchs/Graphics-Geol/Astronomy/Ecliptic1.gif)
However, the apparent longitudinal angular velocity of the sun around the earth is not a constant (54.23' long/day) for TWO different reasons.
Assuming the earth went around the sun in a circle then the sun would appear to go around the earth at a constant speed of 109.72km/day (40,075km/365.2422). However, at the equinoxes the ecliptic crosses the longitude lines at an angle of 23.5º so that the apparent longitudinal angular velocity of the sun is slowed down to ~54.23' long/day. At the solstices the ecliptic not only crosses the longitude lines directly (at zero angle) but the physical distant between longitude lines on the ecliptic is very short such that the apparent longitudinal angular velocity of the sun is speeded up to ~64.49' long/day. This explains the figure 8 pattern.
However, since the earth goes around the sun in a ellipse with perihelion around the northern winter solstice the apparent longitudinal angular velocity of the sun is especially fast [(54.23 + 12.43)' long/day] at this time whereas at aphelion around the northern summer solstice the apparent longitudinal angular velocity of the sun is only moderately fast [(54.23 + 8.16)' long/day]. The earth's slight elliptical orbit hence makes for an unsymmetrical figure 8. Mars's extreme elliptical orbit makes for a teardrop analemma. Pluto's extreme elliptical orbit is trumped by its extreme axial tilt and therefore has a figure 8 analemma.