Geometric Universe

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A few amendments have been made since then.

In 2006, the IAU adopted a new definition:

the ecliptic pole is explicitly defined by the mean orbital angular momentum vector of the Earth-Moon barycenter in an inertial reference frame.

This change is to better agree with dynamical theories, however, the actual change in value is extremely small.

As a result the Earth’s orbital plane is very slightly different from the ecliptic plane.

A: Yes, but for all purpose in this course, the change has no real effect.

More:

Slide 29

Q: What’s the relation between solar motion and the calendar?

Solar motion on the ecliptic is not uniform (due to the Earth’s elliptical orbit), hence seasonal lengths are different.

The mean tropical year, i.e. the mean duration for the Sun to pass though the same point on the ecliptic twice, is 365.242 190 419 days (epoch 2000).

A good approximation is 365 + 97/400 = 365.2425 days. This leads to 97 leap years in every 400 years (Gregorian calendar). The rule for assigning leap year is: leap years are all years divisible by 4, except for those divisible by 100 but not 400. E.g. 1900, 1999 are not leap years; 1996, 2000, 2004 are leap years.

A less accurate approximation is 365 + ¼ = 365.25 days. This leads to a leap year in every 4 years (Julian calendar). But in the order of hundreds of years, the calendar will become less accurate. This approximation, however, is convenient for many estimations.

A: The Sun’s position relative to Vernal Equinox is important for determining the seasons and the calendar. A major function of the calendar was for agriculture.

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Slide 30

Q: How was the Sun/Earth orbit modeled by Greek astronomers?

A: Seasonal lengths are sensitive to the Sun’s motion, therefore the non-uniform motion of the Sun was discovered early. In Hipparchus model, the Earth is shifted off-center of the deferent. This point is called the eccentric. Effectively, this model approximates the Kepler ellipse and area laws.

More:

Using the length of seasons (i.e., time taken for the Sun to pass between equinoxes and solstices), Hipparchus found parameters to his model, which agreed well with observations until Tycho/Kepler’s time.

Note that the length of seasons changes over time, due to precession of the equinoxes. However, eccentricity does not change.

Slide 31

Q: What is the cause for precession of the equinoxes?

Pictures from Wikipedia.

A: Precession is caused by the torque applied by the Sun, the Moon, and the planets. The torque is the result of the gravitational pull on Earth’s equatorial bulge.

More: The lower left picture explains the effect due to the Sun. The lower right picture shows the 26000 year period precession of the north celestial pole.