Geometry of the Sky & Time

Part A (Worlds & Light)
➤ Week-1: Observing the Sky & The Nature of Light
➤ Topic-1: Geometry of the Sky & Time

1. Celestial Sphere

2. Geometry of the Sky

3. Celestial Timekeeping

4. Seasons

1. Celestial Sphere

Day ↔ Night

» the sky: stars, planets, moon, ...

2000 - 3000 stars are visible to the naked eye during the night.
People of nearly every culture gave names to patterns in the sky:
- the patterns of stars seen in the sky → constellations

» Early Astronomers used constellations for navigational purposes -or- for calendars to predict planting/harvesting

» Today's Astronomers however use the constellations to refer to a large area of the sky (like continents)

During the night the constellations seem to move smoothly across the sky from east to west.

» ... but relative locations of stars remain unchanged as the sky move

» ... the stars must be firmly attached to a Celestial Sphere surrounding the Earth (see the picture on the right).

Celestial Sphere: Earth is at the center. The Sun is having a path on the sphere (yellow). Constellation patterns are drawn on the sphere. Even Milky Way is distributed on the surface of the sphere.

If the celestial sphere is imaginary, why is it still useful in astronomy?
What does it represent correctly — and what does it distort?

2. Geometry of the Sky

Modern Standpoint: apparent motion of stars is the result of the spin (rotation - not of the celestial sphere but of the earth)

» ... Even though Celestial Sphere is an incorrect description we still use the idea as a convenient fiction to visualize the position of the stars in the sky.

Illusion: The stars in a particular constellation may appear to lie close to one another

» ... but they may be quite far apart in reality because they may lie at very different distances from Earth.

» ... due to lack of perception when we look into space

» ... we should be concluding that the stars are so far away

Celestial Sphere: A clear view of the sphere with only the Sun's motion (ecliptic: red line). Poles and equator of the sphere are emphasized as well as rotation axis of the Earth.

If Earth stopped rotating but continued orbiting the Sun, what would happen to:
(1) the day–night cycle?
(2) the apparent motion of stars?
(3) the meaning of a “day”?

3. Celestial Timekeeping

Solar vs Sidereal Day

Solar Day = 24h 00m 00s (noon/midnight to noon/midnight)
Sidereal Day = 23h 56m 4.098s

What is the physical difference between a solar day and a sidereal day?
Why must they differ?

Why do stars rise about 4 minutes earlier each night?
What must Earth do beyond one full rotation for the Sun to return to the same position in the sky?

4. Seasons

Celestial Sphere: Earth centered view

Solar System: Sun centered view

Why does the Sun move along the ecliptic rather than along the celestial equator?

Definitions

The apparent motion of the sun on the sky over the course of a year relative to the stars, defines a path on the celestial sphere known as ecliptic
Earth's axis remains pointed in the same direction in space (to the star called Polaris)
The axis doesn't change the direction in which it is pointing. The change in which the hemisphere is tipped toward the sun occurs only because Earth moves between opposite sides of the sun in its orbit. That's why the two hemispheres experience opposite seasons.
The Northern Hemisphere tilt of the Earth's axis causes warmer summers and cooler winters.

Thus, due to the height of the sun above horizon and length of the day ...

» ... we feel the seasons

Solstices and Equinoxes

Summer Solstice: the point on the ecliptic where the Sun is at its Northernmost point above the celestial equator.
Equinoxes: the two points where the ecliptic intersects the celestial equator (short for equal day and night)
Vernal (spring) Equinox:
- associated with the end of winter
- the start of a new growing season
- time keeping:

Annual Changes: Maximum and minimum elevations of the Sun corresponds to solstices, and in between equinoxes occur.

If Earth had zero axial tilt, how would daylight duration vary throughout the year?

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