Geometric Universe

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The celestial sphere is a hypothetical sphere centered at the center of Earth.

On the celestial sphere, stars are fixed, while the Sun and the planets moves slowly.

The celestial sphere rotates, thus most stars rise and fall daily.

The celestial poles and celestial equator are projections of the poles and equator on the Earth on to the celestial sphere.

Slide 11

Useful Relations

Altitude of north celestial pole = latitude L

Local zenith forms an angle 90°-L with the north celestial pole

Local zenith forms an angle L with celestial equator

zenith

Slide 12

Star Maps

Star maps show the sky East-side West, because it is intended for looking up. There are 88 constellations.

Brighter stars are shown with bigger dots. Many star maps also mark the location/type of deep sky objects, multiple stars, and the Milky Way.

Slide 13

The Solar System

Source: NASA

Slide 14

Motion of the Sun on Celestial Sphere

Vernal equinox (春分), autumnal equinox(秋分) are the points at which the Sun passes

the celestial equator, while summer solstice(夏至) and winter solstice(冬至) are the

northern and southern extreme points of the ecliptic (黃道).

Axial tilt of Earth is 23.44° ≈ 23 ½ °.

Different parts of the sky are in the glare of the Sun in different months.

Slide 15

Ecliptic Plane

the ecliptic plane is the plane in which the Earth orbits.

the ecliptic is the circle form by the ecliptic plane intercepting the celestial sphere

Slide 16

Planetary Motion on Celestial Sphere

Planets usually moves on the celestial sphere from east to west (prograde motion)

near the ecliptic; while sometimes moves from west to east (retrograde motion).

Motion of Mars in 2003 and 2005. Time step=10 days.

Pictures from NASA.

Slide 17

Geocentric Model of Planetary Motion (Apollonius, 260-190 BCE)

Explains qualitatively the prograde and retrograde motions, and brightness variation.

Motion planets around epicycle centers and epicycle centers around the Earth are uniform circular motions.

Note: the centers of epicycles for Mercury and Venus always align with the Sun, which explains their maximum elongations (29° and 48°).

Ptolemy (90-168 CE) modified this model to be quantitatively accurate compared to the observations of the time. His model was used for 1400 years until the Renaissance.