Geometric Universe

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(1) A planet is a celestial body that

(a) is in orbit around the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid body forces so

that it assumes a hydrostatic equilibrium (nearly round) shape, and

(c) has cleared the neighborhood around its orbit.

A “dwarf planet” is a celestial body that satisfies, (a) and (b) but not (c), and is not a satellite.

All other object orbiting the Sun, except satellites, are called “Small Solar System Bodies”.

More:

Since some recently found “minor planets” are similar in size or even bigger (Eris) than Pluto, there was a need for redefinition. The new definition is based on planetary formation theory that, given enough time, a large enough object would be able to collide with or scatter away objects and dominate its orbit. The redefinition has been criticized and remains controversial. Note also that the line between (2) and (3) is left for later meetings. For many small object, the hydrostatic equilibrium condition (b) is not easy to test.

Slide 44

Q: After the invention of telescope, how was position/angle measured?

A: First by using wired micrometer eyepiece, then by measuring photographic plate.

More: The wired can be moved to match the star’s position. In some other eyepieces, a patterned glass is placed at the focus for reading out data. Angles can be measured from a photographic plate using the focal length and the lengths measured on the plate.

Slide 45

Q: We’ve been focusing on the development of the West, what about the work of Chinese?

A: Ancient Chinese astronomers developed sophisticated tools to observe the positions of celestial objects. Unfortunate their work did not affect the western astronomy development much.

More: As an example, the drawing on the right shows an invention in the Song Dynasty. The main instruments (red, blue, and yellow) are driven by water-powered gear systems to simulate Earth’s rotation and tell time automatically.

Source: HK Science Museum,

星‧移‧物‧換

Slide 46

Q1: Was Copernicus the first to think the Earth moves around the Sun? Q2: Did Copernicus model have epicycles?

Ancient Greek and Indian astronomers had proposed heliocentric views. However, Copernicus model was the first to have the good length, time, and angle parameters. It was the reasonably close to modern model of the Solar System.

In Copernicus model, the epicycles are used to account for elliptical orbits; where as Ptolemy’s epicycles are used to account for Earth’s motion.

Since the full Copernicus model is rather complex, the simplified heliocentric model is usually presented to students. This toy model does not have epicycles, but in practice, it has almost no predictive value.