Synopsis:
Introduction
The celestial sphere
The ecliptic
Equinoxes
Right ascension and declination
Horizon diagrams
Directions, rising and setting
Cause of the seasons
Path of the sun in the sky
Introduction
The Hindu way of timekeeping is a very deep science, for it relates the individual to the universe, the microcosm to the macrocosm.
Indian timekeeping is based on distant celestial bodies and is inseparable from astronomy. The positions of these celestial bodies, as observed from the earth, follow periodic patterns. Patterns means mathematics. So timekeeping is essentially astronomical mathematics, where the exact positions and trajectories of celestial bodies are mathematically calculated and used to reckon time on earth.
Be it modern or ancient Indian astronomy, there are some fundamental concepts to be understood. In Part 1 we shall look at these concepts.
The celestial sphere
The celestial sphere is an imaginary sphere of infinite radius against which celestial bodies appear to be projected. The earth is considered to be located at the center of the celestial sphere.
The earth rotates on its axis from west to east while the celestial sphere is fixed.
Fig. 1 — The celestial sphere
The ecliptic
The ecliptic is the great circle formed by the intersection of the plane of the earth’s orbit with the celestial sphere. It represents the apparent path of the sun during the year.
The ecliptic plane is tilted 23.5° with respect to the plane of the celestial equator. (Since the Earth’s axis is tilted by the same angle with respect to the normal to the orbital plane).
Fig. 2 — The ecliptic
Equinoxes
Equinoxes — Vernal or spring and autumnal — are the two points on the celestial sphere where the celestial equator intersects the ecliptic. Vernal equinox is shown in Fig. 3. Autumnal equinox is located opposite the vernal equinox and is not labeled in this figure.
Right ascension and declination
The north and south poles of the earth are aligned with the north and south poles of the celestial sphere. The earth’s equator is aligned with the celestial equator.
Just as points on the earth are located with two coordinates — latitude and longitude, objects on the celestial sphere are located with respect to similar two coordinates — celestial latitude and celestial longitude, also known as declination and right ascension.
The vernal equinox is the point through which the reference celestial longitude, called 0 hour Right Ascension passes. (This is similar to the Greenwich meridian as reference longitude on earth). The celestial equator is the reference celestial latitude, called 0 degree declination. (This is similar to the earth’s equator being the reference latitude, 0 degrees.)
Right ascension is measured eastward up to 24 h along the celestial equator from the vernal equinox. Declination is measured from 0 — 90° N or S of the celestial equator.
Fig. 3 — Equinoxes, Right Ascension and Declination
Horizon diagrams
Your horizon is the line, 360 degrees all around you, where the land and the sky appear to meet.
Fig. 4 — The horizon
The horizon marks the boundary of the one half of the celestial sphere that is visible to an observer at any given time. (The other half of the celestial sphere is not visible since the surface of the earth blocks the view).
Celestial sphere view and horizon view We can switch from the the celestial sphere view (in which we are viewing from space) to the horizon diagram view (in which we are viewing from a location on the earth’s surface). This is done by drawing the plane of the horizon tangent to the surface of the earth on which the observer is standing.
Fig. 5 — Celestial Sphere view and Horizon Diagram view — an observer (white dot) on the northern hemisphere
Cardinal directions, Rising and Setting
Fig. 6 — Apparent rising and setting of stars.
The cardinal directions north, south, west and east defined with respect to the horizon.
North is located on the horizon just below the North star or Polaris. South is located on the horizon exactly opposite north.
Objects appear to rise in the east and set in the west, even though they are fixed on the celestial sphere. This is because of the earth’s rotation on its axis from west to east.
Rising means that the celestial object comes above the horizon and becomes visible. Setting means that the celestial object goes below the horizon and is not visible. When the sun rises, it is day, and when the sun sets, it is night, for the sun is the source of light. Its absence causes darkness. The path of the sun in the sky will be explained below.
Cause of the seasons
The cause of seasons is the tilt of the earth’s axis by 23.5°. The tilt changes — the number of hours of day and night at different times of the year — the directness of the angle of sun’s rays (which changes the amount of solar radiation received in an area)
The northern and southern hemisphere experience opposite seasons at the same time.
Fig. 7 — Cause of seasons — tilt of the earth’s axis
Spring Equinox (March 21 or 22)
The overhead sun (most direct light, 90°) is over the equator. The equator receives the largest amount of solar radiation.
The northern hemisphere is in the spring equinox, while the southern hemisphere is in the autumn equinox.
The two hemispheres receive a similar amount of solar radiation, and the length of day and night is the same at all places on the earth.
Fig. 8 — Spring Equinox (March 21 or 22)
After this day, it is spring in the northern hemisphere, where the day is longer than the night. In the southern hemisphere, it becomes autumn, when the day is shorter than the night.
Summer solstice (21 or 22 June)
The overhead sun is over the Tropic of Cancer. It receives the largest amount of solar radiation.
The northern hemisphere is in the summer solstice, while the southern hemisphere is in the winter solstice.
The length of daytime in the northern hemisphere, is the longest in the year, while that of the southern hemisphere, is the shortest in the year. There are 24 hours of daylight at the Arctic circle and 24 hours of darkness at the Antarctic circle.
Fig. 9 — Summer Solstice (21 or 22 June)
Autumn equinox (22 or 23 September)
The overhead sun is over the equator again. The equator receives the largest amount of solar radiation.
The northern hemisphere is in the autumn equinox, while the southern hemisphere is in the spring equinox.
The two hemispheres receive a similar amount of solar radiation and the length of day and night is the same at all places on the earth.
Fig. 10 — Autumn equinox (22 or 23 September)
After this day, it is autumn in the northern hemisphere where the day is shorter than the night. In the southern hemisphere, it becomes spring, when the day is longer than the night.
Winter solstice (21 or 22 December)
The overhead sun is over the Tropic of Capricorn. It receives the largest amount of solar radiation.
The northern hemisphere is in the winter solstice, while the southern hemisphere is in the summer solstice.
The length of day time in the northern hemisphere is the shortest in the year, while that of the southern hemisphere is the longest in the year.There are 24 hours of darkness at the Arctic circle, and 24 hours of daylight at the Antarctic circle.
Fig. 11 — Winter solstice (21 or 22 December)
Path of the sun in the sky
The sun does not rise exactly in the east and set exactly in the west on all days during the year. The point where the sun rises and sets on the horizon changes depending on the day of the year, that is, where the earth is in its orbit around the sun (or equivalently, where the sun is in its ecliptic).
Fig. 12 — Paths of the sun on different days of the year
There are two motions of the sun from the point of view of the observer on the earth. 1)The motion of the sun along the ecliptic (traversing the ecliptic in a year) due to the revolution of the earth around the sun. (indicated in red) 2)The apparent rising and setting motion of the sun in the sky (traversing the sky in a day) due to the rotation of the earth on its axis. (indicated in yellow and orange)
For a person on the northern hemisphere, Summer solstice (June 21) — On the summer solstice, the sun reaches its most northerly declination of +23.5 °. The longest day of the year is indicated by the greater section of the yellow line remaining above the horizon
Autumn equinox (March 21) — On the autumn equinox, the sun has a declination of 0°, since the ecliptic intersects the celestial equator. The day and night being equal is indicated by equal sections of the orange line remaining above and below the horizon.
Winter solstice (December 21) — On the winter solstice, the sun reaches its most southerly declination of ‑23.5 °. The shortest day of the year is indicated by the smaller section of the yellow line remaining above the horizon.
Spring Equinox (September 22) — During the spring equinox, the sun has a declination of 0°, since the ecliptic intersects the celestial equator. The day and night being equal is indicated by equal sections of the orange line remaining above and below the horizon.