02 Observing the local sky

1. Patterns in the sky

Keywords: Periodic events, Day - Night cycle ↔ The sky, Patterns in the sky » Constellations, Celestial Sphere

» the sky: stars, planets, moon, ...

» 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)

» ... 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.

» ... 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.

» ... 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.

2. Circling the sky

Keywords: Perception: motion of objects on the sky, Coordinate System-1: Local sky, Measurements: angles, Angular units, Coordinate System-2: Location on Earth, Coordinate System-3: Path of Stars on sky, Annual changes.

The Local Sky

» In reality, we are the ones who are moving.

» ... because Earth rotates in the opposite direction: west → east

» ... the daily motion of the stars would appear as circles

The Local Sky: The sky as seen from wherever you happen to be standing. The zenith is where your head is pointing upwards when you stand. The meridian is an imaginary half circle: North → Zenith → South.

Angle Measurements

» ... Instead we measure angles in the sky:

Angles: Measuring angular size of an object.

Angles: Measuring angular distances between a pair of objects.

Geographical Coordinate System

» ... creating a new coordinate system: geographical 

» Similarly, a location on Earth has to be represented with two angle measurements:

Geographical Coordinate System.

Celestial Coordinate System

» ... motion of objects in the sky can be observed.

» ... creating paths on the celestial sphere.

» Altitude of the Celestial Pole = Your Geographic Latitude 

See Celestial Coordinate System for more details. 

Celestial Sphere: Local sky is overlayed (and streched) to the celestial sphere.

Annual Changes

3. The reason for seasons

Keywords: Earth centered view vs Sun centered view, Definition: Ecliptic, Definition: Solstices and Equinoxes, Definition: Seasons, Calculating periodic changes => Tropical Year.

Celestial Sphere: Earth centered view

Solar System: Sun centered view


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

» ... we feel the seasons

Solstices and Equinoxes

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

4. The precession of Earth's axis

Keywords: Definition: Precession, Earth's Precession, Axis tilt.

Precession: One cannot easily feel an annual change in Earth axis. However, it also wobbles on a much longer scale (26 000 years). The region around the celestial pole is given on the right panel. The path of precession of Earth's axis (yellow) is given starting from 1 AD.

5. The Moon: Our constant companion

Keywords: The Moon, Change in its appearance: phases, Periodic changes: Synodic/Sidereal Month, Seeing the same face of the Moon, Eclipses, Eclipse: Lunar, Eclipse: Solar.

» ... these changes lead to → Lunar Phases

Lunar Phases. Experiment: Circle around yourself a spherical object while it is lit by an homogeneous light source. Observe how dark regions (not lit) appear, change and disappear.

Periods and motion of the Moon

Sidereal Month: The time required to complete one revolution around Earth with respect to background stars → 27.3 days (360 degree rotation around the Earth).

Synodic Month: The period of completing phase cycle (eg. New Moon to New Moon) → 29.5 days (takes longer than Sidereal Month).

The Moon's phase. We always see (nearly) the same face of the Moon. This is due to the synchronous rotation of the Moon with Earth. Therefore, the Moon's 1 rotation around itself (rotational period) is equal to 1 rotation around Earth (orbital period).


Definition of an eclipse: Any time one astronomical object casts a shadow on another.

Due to the geometry of lunar phases one would expect the followings: 

» ... Moon's orbit is inclined to the ecliptic plane by ~ 5 degrees.

Eclipse. Casting a shadow on an object.

Definition of Nodes: The two points in each orbit (Moon's around the Earth and Earth's around the Sun) at which the Moon crosses the ecliptic plane.

Predictions: The times when the lines of nodes are directed towards the sun are favorable.

» ... eclipse seasons ~ 18 years, 11 1/5 days → Saros Cycle

Nodes. Eclipse occur only when three objects are aligned at nodes.

Lunar Eclipse. Because of the shadow size Lunar eclipses takes hours.

Solar Eclipses. Since the shadow of the Moon is narrow, its cast on Earth moves fast (Shadow speed: >1700 km/hr ~ 470 m/s) and lasts shorter. Thus, creating three different types of solar eclipses: Total (Moon covers the sun totally), Partial (Moon passes over Sun with an offset), Annual (Moon is closer to Earth, creating a ring on the sun).

6. Celestial timekeeping

Keywords: Sidereal day vs Solar day, Synodic month vs Sidereal month, Tropical year vs Sidereal year, Planetary Periods.

A sidereal day is the time it takes any star to make a circuit of the local sky. A solar day is measured similarly but by timing the sun rather than a star.

Solar vs Sidereal Day

Synodic vs Sidereal Month

Tropical vs Sidereal Year

Each year the location of the equinoxes and solstices among the stars shifts about 1/26 000 of the way around the orbit.

This amounts to 1/26 000 ~ 20 minutes

Planetary Periods