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
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.
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.
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
Stars rise and set - like the sun, moon and planets ...
» In reality, we are the ones who are moving.
Objects appear to rise in the east and set in the west
» ... because Earth rotates in the opposite direction: west → east
If you could view the celestial sphere from outside,
» ... the daily motion of the stars would appear as circles
Since we live on Earth, we see only half of the celestial sphere.
It is called the local sky.
Two angle measurements are required to locate any object in the local sky.
Each angle has a zero point.
Azimuth (direction) - Starts from North, measured along East, South, West and back to North
Altitude (elevation) - Starts from the horizon rises upto Zenith (direction where your head is pointing).
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.
Due to lack of perception in the sky we cannot tell the true sizes of objects or the true distances between objects just by looking at them.
» ... Instead we measure angles in the sky:
Angles are measured in sexadecimal units:
1 complete circle = 360 degrees (2π radians)
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds
Angles: Measuring angular size of an object.
Angles: Measuring angular distances between a pair of objects.
Geographical Coordinate System
The local sky can be stretched to the whole Earth surface.
» ... creating a new coordinate system: geographical
» Similarly, a location on Earth has to be represented with two angle measurements:
Longitude (along the rotation direction of Earth) - Starts from Greenwich, plus values towards East, minus values towards West.
Latitude (subtended from Equator) - Starts from Equator, plus values towards North, minus values towards South.
Geographical Coordinate System.
Celestial Coordinate System
The local sky can be extended further until it reaches to the celestial sphere which has a radius of infinity.
When the local sky is overlayed to the celestial sphere
» ... motion of objects in the sky can be observed.
» ... creating paths on the celestial sphere.
Circumpolar stars never rise or set but instead make daily counterclockwise circles around NCP
Non-circumpolar stars never rise and remain constantly below the horizon.
The rest of the stars daily rise in the east and set in the west.
The paths of the Sun, Moon and planets follow these rules as well.
From the geometry and by observing the local sky, Geographic Location on Earth can be calculated:
» Altitude of the Celestial Pole = Your Geographic Latitude
Similarly each object on the celestial sphere can be identified from two angles.
See Celestial Coordinate System ⤤ for more details.
Celestial Sphere: Local sky is overlayed (and streched) to the celestial sphere.
As we orbit the Sun over the course of a year it appears to move against the background stars in the constellations.
If we could see both the Sun and the stars we would notice the Sun gradually moving eastward along the ecliptic.
The constellations along the ecliptic are called constellations of the Zodiac.
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
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
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.
We can notice the daily and annual changes.
However a much longer cycle exist: a gradual change in the direction that Earth's axis points in space: precession
Precession can occur with any rotating object.
Each cycle of Earth's precession takes about 26 000 years
In about 13 000 years, the axis will point to the star Vega
Axis tilt remains close to 23.5 degree throughout the cycle.
It is caused by gravity's effect on a tilted rotating object
Object should not be a perfect sphere
Law of conservation of angular momentum
We observe pulls from the Sun and Moon; they try to reduce the tilt.
However since Earth continuously rotates around the same axis this tug of war between gravity and rotation precesses the axis.
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.
Nearest object to Earth and second bright in the sky
We observe two types of change in the Moon's motion in the sky.
Rise and set times
» ... these changes lead to → Lunar Phases
New Moon: not visible (The Moon cannot be distinguished from Sun's light)
First and Third Quarters: The angle between Sun - Earth - Moon is 90 degrees
Full Moon: The disk of the Moon is fully illuminated by the Sun.
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:
A new moon always blocks our view of the Sun.
Earth would always prevent sunlight from reaching a full Moon.
So, why there is not always a solar/lunar eclipse every new/full moon?
» ... 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.
The nodes of the Moon's orbit must be nearly aligned with the Sun and Earth.
The phase of the Moon at this alignment must be either new or full.
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
Solar Day = 24h 00m 00s (noon/midnight to noon/midnight)
Sidereal Day = 23h 56m 4.098s
Synodic vs Sidereal Month
Synodic Month = 29.5 days (due to phases)
Sidereal Month = 27.3 days
Tropical vs Sidereal Year
Tropical Year = 365 days - 20 minutes (due to seasons)
Reason: Precession of Earth's axis.
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
Sidereal Year = 365 days
Sidereal Period: It is the time it takes to orbit the Sun.
Synodic Period: It is the time between being lined up with the Sun in our sky one time, and the next similar alignment.
Conjunction: elongation of 0 degree (inferior: Sun - Planet - Earth; superior: Planet - Sun - Earth)
Opposition: elongation of 180 degrees
Quadrature: elongation of 90 degrees