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Distances EM = MO.

This is the geocentric model that agrees quantitatively with observations of the time. From the time of Apollonius to Ptolemy, planetary theories changed gradually from qualitative to quantitative science.

A:

Slide 36

The reasons are:

the elliptical orbits of the planet are close to a circle

the eccentric takes the role of a focus, approximating Kepler’s first law

Ptolemy’s equant has the effect of approximating Kepler’s second law

Using Tycho’s data, Kepler refitted Ptolemy’s model, which gave a maximum error of only 8’ for Mars.

Since uncertainty for Tycho’s data is only 1’, Kepler was forced to give up the circles.

Eccentric/Sun

Equant

Comparing the elliptical orbit of Mars (red) to a circle (blue).

A: Ptolemy was approximating Kepler’s law, without knowing it.

More:

Slide 37

The two models are equivalent if constructed as shown. The vectors pointing from the Earth to the planet are always the same between the two models.

Copernicus used his own observation as well as Ptolemy’s data to obtain parameters to his model.

The precisions of the two models are the roughly same.

Earth

Sun

Slide 38

A: Great care for accuracy, a whole lifetime of pursuit, and a lot of support.

More:

He was the first one to notice the problem relating observation accuracy and have the ability to improve on them. He improved the sight with a slit design, and also added gradual scale to improve reading. Very large instruments help measuring smaller angles, but they requires stronger materials and mechanical parts. To support Tycho’s work, the King of Denmark granted him the estate of the island Hven, on which he built world’s best observatory called Uraniborg.

Left: The sight’s aligned horizontally if the star can be seen just on the CBGF edge and ADHE edge at the same time. The vertical alignment can be found similarly. For solar alignment, sunlight is allowing to pass thru the hole in the front and fall on a circle drawn on the ABCD plate.

D=3 m

Slide 39

More: A typical Galilean refractor had a plano-convex objective lens with 30-40 inches focal length; plano-concave eyepiece of focal length about 2 inches focal length. It was good enough to discover Lunar features, Jupiter’s four moons, phase of Venus, as well as sunspots.

- 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

- Newton’s law of universal gravitation
- Newton’s Law of Gravity
- Motion
- Newton’s third law of motion
- Radiation
- Friction
- Magnetic field uses sound waves to ignite sun's ring of fire

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