Earth and Solar System

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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