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Solar System
Kepler’s First Law of Planetary Motion
- Kepler propounded three laws regarding planetary motion
- Kepler’s first law states that the orbit of each planet is an ellipse with the Sun at one of the foci
- Kepler’s second law states that the line joining the planet to the Sun sweeps equal areas in equal time
- Kepler’s third law states that the square of the sidereal period of a planet is proportional to the cube of its mean distance from the Sun
Orbit of Planets around the Sun
- All planets revolve around the sun in an elliptical orbit
- Ellipse has two foci and two radius vectors
- Radius vector is the line joining the foci to the circumference
- In an ellipse, the sum of both radius vectors remains constant
- Reduction in length of one of the vectors increases the other vector
Perihelion
- Kepler’s first law states, earth revolves around the sun in an elliptical orbit
- Elliptical orbit implies earth will come close to sun and move away periodically
- Perihelion is the point on ellipse where earth is closest to sun
- Perihelion falls on 4 January each year
- Earth is 91.5 million statute miles from the sun at its perihelion
Aphelion
- Elliptical orbit implies earth will come close to sun and move away periodically
- Aphelion is the point on ellipse where earth is farthest from sun
- Aphelion falls on 3 July each year
- Earth is 94.6 million statute miles from the sun at its aphelion
Speed of Revolution of Earth
- Speed of movement of earth is fastest near perihelion and slowest near the aphelion
- Kepler’s second law implies the radius vector sweeps equal areas in equal time
- Therefore, the speed of movement of earth has to reduce when earth is farther away from the sun
Plane of Ecliptic and Equinoctial
- Plane of the ecliptic is the orbital plane of all major planets including earth around the sun
- Plane of equinoctial can be also be called as the equatorial plane or the plane of equator
- Spin axis of earth is tilted by 23 ½ degrees to perpendicular
- Therefore, the planes of Ecliptic and Equinoctial make an angle of 23 ½ degrees
- This is called Obliquity of the ecliptic and is the main reason for changing seasons
Declination of the Sun
- Declination of the Sun is the angle subtended between plane of equinoctial to plane of sun’s position
- Declination is the celestial equivalent of latitude for any celestial body like sun
- In other words, it is the angle that the sun is above or below the equator
- Sun’s declination varies from 23.5 degrees north to 23.5 degrees south over a one year period
Summer and Winter Solstice
- Sun is at its maximum northerly or southerly declination at its solstices
- Solstice literally translated means sun standing still
- Maximum difference in duration of day and night is seen during solstices
- Minimum day to day variation of sun’s position happens at solstices
- Winter solstice is seen on 21 Jan every year when the Sun’s declination is at 23 ½ south
- Summer solstice is seen on 22 Jun each year when the Sun’s declination is 23 ½ north
Vernal and Autumnal Equinox
- Equinox means equal night that occurs when the sun is overhead the equator
- Duration of days and night are equal during equinoxes
- Declination of the sun is zero meaning sun at equinoctial plane
- Maximum day to day variation of sun’s position happens at equinoxes
- Vernal equinox happens on 21 March each year during transit of the sun from southern to northern hemisphere
- Autumnal equinox is seen on 23 December every year during transit of the sun from northern to southern hemisphere
Hours of Day Light
- Daylight time as well as seasons are dependent on the Declination of the sun and Latitude of observer
- Hours of day light are caused due to annual change of declination due to the tilt of earth’s spin axis
- Whole days of continuous daylight and darkness are found at high latitudes
- Sun may not rise or set above 66 ½ deg North and South latitudes
- Minimum daily variation in daylight is seen near solstices
- Maximum daily variation of daylight is seen equinoxes
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