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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 28

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.

More:

Slide 29

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 30

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.

Slide 31

The celestial sphere rotates about 360.9856° daily, i.e. it takes about 23 hr 56 min for stars to go around in a circle. In other words, stars rises 4 minutes earlier each day. (360/365.25 ≈ .9856, 24x60/365.25 ≈ 3.94).

- Astronomy and Space Science
- Length: Power of Ten
- Units of Length
- Time Scales
- Angles
- Celestial Sphere
- Useful Relations
- Motion of the Sun on Celestial Sphere
- Ecliptic Plane
- Planetary Motion on Celestial Sphere
- Advantages of the Heliocentric Model
- Further Developments
- What is a constellation?
- How does the coordinate systems on the Celestial sphere look like?
- Where exactly is the center of the celestial sphere?
- I heard that the definition of the ecliptic plane has been changed, is it?
- What’s the relation between solar motion and the calendar?
- How was the Sun/Earth orbit modeled by Greek astronomers?
- What is the cause for precession of the equinoxes?
- What is a day anyway?
- Can you give some example of planetary events?
- What is Aristotle’s model of the universe?
- What does Ptolemy’s geocentric model look like?
- Ptolemy model looks quite different from Kepler’s, why did it work so well?
- How to transform between geocentric and heliocentric models?
- One arcmin is about the size of a HK$1 coin in 88 m away, how did Tycho Brahe achieve this accuracy without telescopes?
- Did Galileo really invented the telescope?
- Was Galileo jailed?
- Does the discovery of phase of Venus disproves the geocentric theory?
- What is a planet?
- After the invention of telescope, how was position/angle measured?
- We’ve been focusing on the development of the West, what about the work of Chinese?
- Was Copernicus the first to think the Earth moves around the Sun? Did Copernicus model have epicycles?
- What are the true advantages of the heliocentric model?
- What is the role of human/Earth in cosmology?
- Can you suggest some equipments for schools?
- Can you give us some references?
- Are there any useful classroom teaching kits available?
- Sources of Pictures in this Talk

- Space Radiation
- Waves & Sound
- Understanding Heat Transfer, Conduction, Convection and Radiation
- Static and Kinetic Friction
- Newton's laws of motion
- Newton’s law of universal gravitation
- Newton’s laws of motion

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