Earth’s Orbit and the Seasons

Seasons on the Earth

1 KW/m2 1 KW/m2

1 m2 2 m2

In winter a bundle of light is spread over a bigger area than in summerowing to the inclination away from the Sun

Receives only halfthe heat and light

Phases of Moon: Earth-Sun Positions

‘Horns’ of a crescent moon always point away from the Sun

What time ofday doesthe full moonrise and set ?

What timeof day doesthe new moonrise and set ?

Full Moon rises at dusk and sets at dawn

The New Moon rises and sets with the Sun (lies in the same direction as the Sun)

Lunar Eclipse (around Full Moon)Umbra and Penumbra- total or partial obscuration

Umbra – dark part of the shadow; Penumbra – lighter part of the shadowEarth’s maximum umbra at Moon’s distance is 9200 Kms; the penumbra is 16000 Kms across

Total Solar Eclipse: Total obscuration of the Sun by the Moon, possible because the

angular size of Moon equals Sun’s

Solar Eclipse (at New Moon):Visible from a narrow ‘band’ across the Earth

Diameter (Moon) = 3476 Km = ¼ Diameter (Earth)Moon’s umbra reaches only a small area < 270 Km where solar eclipse is visible

Annular Solar Eclipse:(when the tip of moon’s umbra doesn’t quite

reach the earth)

Eclipses occur on Line of Nodes:Earth-Moon-Sun must be in line

Why do eclipses NOT occur each new and full moon?The E-M-S line can may deviate by up to 5 degrees

Solar and Sidereal Day

• How long is one day ?

• From noon (Sun directly overhead) to noon ?

• How long does it take for the Earth to complete one rotation on its axis ?

Orbital and angular motion of the Earth

Rotation period of Earth

must be less than one solar day

NoonT=0h

T=23h 56m 04s

(Sidereal Day)

T=24h

(Solar day)

Noon

Not to Scale

Solar & SiderealDays

• The earth moves each day by 1 degree in its orbit around the Sun. So each day the earth has to rotate a bit more to reach the noon position

• To rotate one extra degree requires

24 x 60

---------- = 4 minutes

360• Solar day (noon-to-noon = 24 hours) is

rotation period with respect to the Sun

4 minutes longer than the true rotation period of the Earth with respect to the stars called the

Sidereal day = 23h 56 m• 366 sidereal days per year

Solar and Lunar Calendar• Rotation of the earth = 1 solar day

• Revolution around the sun = 365.2422 d

• Orbital period of moon = 1 month = 29.5306 d

• Lunar OR solar calendars are possible, but not both since a month is not (i) exact no. of days, and (ii) year is not exact no. of lunar months

12 x 29.5306 = 354.3672 days, not one year

• Solar calendar is the one most widely used

• Roman Julian Calendar year = 365 d + leap yr

Gregorian-Julian Calendar• Problem with Julian Calendar average yr

is 365.25 d, 11 minutes too long !

• By the 1500’s, the time of Pope Gregory, the calendar was ahead of astronomical time keeping by more than two weeks

• Gregorian reform:

Century years not divisible by 400 are ordinary years, not leap years

(Example: 1700 AD was not a leap year, but 2000 AD was)

Motions of the Earth:Rotation on its axis (day), Revolution or orbit around the Sun (year), and Precession of the

Polar N-S axis

Position of the north star changes due to the slow precession of the Earth’s axisdue to the gravity of the Sun – just like the wobbling axis of a spinning top

Precession and the location of Polaris: Period 26,000 Yrs