Download Celestial Sphere • Constellations are patterns of stars on the sky

Celestial Sphere
• Constellations are patterns of stars on the sky: these are are not actually close to each
other
• Celestial Sphere: a large imaginary sphere centered on the Earth
• Celestial poles: points directly above the earth’s poles
• Celestial equator: great circle directly above the earth’s equator
• The angle between the horizon and the NCP is the same as your latitude
• What part of the celestial sphere you can see depends upon you latitude (from the
NCP you can only see half the sky)
• Celestial Sphere appears to rotate around the celestial poles (1 day cycle)
• This is because of Earth’s rotation
• Sun’s path on the Celestial Sphere: Ecliptic
• The Sun’s position relative to the stars appears to change (1 yr. cycle)
• Reason: Earth’s revolution around the Sun
• The Moon’s position relative to stars also appears to change (1 month cycle: sidereal
month: 27.3 days)
• Reason: Moon’s revolution around the Earth
Seasons and Calenders
• The cause of seasons: NOT the varying earth–Sun distance
• It’s the tilt of the Earth’s axis relative to the orbit around the Sun
• Therefore the ecliptic is tilted relative to the celestial equator
• Equinoxes: the Sun crosses the celestial equator
• Solstices: the Sun furthest away from the celestial equator
• 1 Year: time between one Vernal equinox to the next
• 1 synodic month: from new moon to new moon: 29.5 days
Aristotle, Ptolemy & Copernicus
• Aristotle showed that the earth is spherical
• Earth’s circumference was measured by noting different positions of the Sun at noon
at two different places
• Problem with the Geocentric view of the Universe: retrograde motions of planets
• Ptolemy’s explanation: epicycles
• Copernicus : Heliocentric model — can naturally explain retrograde motions if outer
planets are slower
Kepler & Galileo
• Kepler: laws of planetary motions
– 1: orbits of planets are ellipses with the Sun at one focus
– 2: A line from a planet to the Sun sweeps equal areas in equal times
– 3. The square of the orbital period is equal to the cube of the semi-major axis
• Galileo observed with a telescope: found rotating Sunspots, mountains on the moon,
discovered Jupiter’s moons and phases of Venus
• Strongly supported heliocentric model
Newton’s Laws
• 1. An object remains at rest, or moves in a straight line at constant speed unless acted
upon by an outside force
• An object moving in a circle is being accelerated
• 2. Acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass
• 3. For every action, there is equal and opposite reaction
• Gravity is an attractive force between two masses
• Gravitational force varies directly with mass and as inverse square of the distance
Application of Newton’s laws
• Orbits of any pair of objects are conic sections with the center of mass at one focus
• Elliptical orbits possible if orbital speed is smaller than the circular velocity or larger
than the circular velocity but smaller than the escape velocity
• Angular momentum is conserved
• Kepler’s third law also comes naturally from laws of gravity