Geometric Universe

Page
6

Slide 32

Q: What is a day anyway?

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).

As a result, the Sun passes the meridian (highest) at the approximately same time each day. For Greenwich, it is 12:00pm; for HK, it is 12:24pm.

A: A (solar) day is the duration for the Sun to pass the meridian twice.

More:

Slide 33

Q: Can you give some example of planetary events?

A: Some events are:

Conjunctions (合):

Two objects closest from Earth’s point of view

Stationary (留):

When the ecliptic longitude (sometimes RA) do not change

Greatest elongation (大距):

Approximately the best time for observing inferior planets

Transit (凌日) of inferior planets across the Sun:

Mercury: …, 11/1999, 5/2003, 8/11/2006 (during sunrise in HK), 5/2016, …

Venus: …, 12/1882, 6/2004, 6/6/2012 (visible in HK), 12/2117, …

Eclipse (蝕) of Sun or Moon.

Similar events in the Jupiter system.

Slide 34

Continue…

Opposition (衝):

Best time for observing superior planets

For Mars, opposition occurs approximately every 2.14 year. Due to higher orbital eccentricity (0.093) and smaller semi-major axis (1.52 AU), the Earth-Mars distance varies between 0.66 and 0.38 AU (1.52×(1 ± 0.093)–1), giving large size and brightness variation at opposition.

Great opposition of Mars (near perihelion) (火星大衝) occurs every 15-16 years. The one in 2003 was the closest in 60,000 years, which the media made a big deal of. However, as shown on the graph, the other great oppositions such as the 1988 one are not much further away.

Note: since great opposition occurs near perihelion, when Mars is the hottest, planet-wide dust storms could occur, so observe early.

Picture: C.F. Chapin, http://www.astromax.com/planets/images/mars2003.gif

Slide 35

Q: What is Aristotle’s model of the universe?

Aristotle’s (384-322 BCE) model placed the superior planets in right order using their speed on the celestial sphere.

It explains simple phenomena such as daily rise and set of celestial objects, but not the details in longer time scales.

In this model, the Earth is at the center the universe, surround by water, air, fire, etc.

As more were known about the planetary motion through observation, ancient astronomy would transform slowly to a qualitative science, then a quantitative science.