PHYS 155 – Introductory Astronomy observing sessions: - observing sessions: Sunday – Thursday, 9pm, weather permitting - Exam - Tuesday March 20, - Review – Monday 6:30-9pm, PB 38 Thursday 03/15/2007 Marek Krasnansky

Models of the solar system –Geocentric –Heliocentric Kepler's laws

Models of the Solar System ● Successful model has to explain observations Experimental observations: motion of the Sun, Moon and planets movement on the ecliptic eclipses relative speed, how much they move with respect to each other retrograde motion Venus, Mercury – always close to the Sun phases of the planets stellar parallax

● on the ecliptic everything orbits in one plane ● Venus, Mercury – always close to the Sun ● relative speed ● distances from the Earth – closer objects move faster Motion of the Sun, Moon, planets

Eclipses the Moon orbits around the Earth

Retrograde Motion Motion that is backward compared to the norm; we see a planet in apparent retrograde motion during the periods of time when it moves westward, rather than the more common eastward, relative to the stars. retrograde motion

Phases of Venus Crescent phase – Venus between the Sun and Earth – Galileo Galilei – the first to observe gibbous phase of Venus Moon: Venus:

Stellar Parallax Parallax - the apparent motion of a relatively close object with respect to a more distant background as the location of the observer changes. - The apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in the Earth's orbit of the Sun each year. Stellar Parallax

Geocentric Models - Ptolemy the Earth (Geo, in Greek) – in the center, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn the simplest model can't explain retrograde motion – Epicycle (Ptolemy) Discrepancies between the predicted and true positions of the planets artificial, the planets orbit around empty space

- all planets (except the Earth) orbit around the Sun - the Sun and Moon orbit around the Earth - can not explain stellar parallax (not observed at that time) Geocentric Models - Tycho Brahe

Heliocentric Models - the Sun (helios, in Greek) in the center - Aristarchus, Copernicus - planetary orbits – circles - naturally explains everything we need - not more accurate than Ptolemy's model

Johannes Kepler ( ) Believed Copernicus was correct. Worked very hard to see if Tycho’s data matched with Copernicus’s theory. Realized that the orbits cannot be perfect circles. The orbits were elliptical. Discovered 3 mathematical laws of planetary motion.

Kepler's Laws of Planetary Motion Kepler's first law: Kepler's first law: The orbit of each planet is an ellipse with the Sun at one focus. Kepler's second law: Kepler's second law: As a planet moves around its orbit, it sweeps out equal areas in equal times. Kepler's third law: P - is a planet's orbital period in years a – semimajor axis of a planet's orbit in AU.

Astronomical Unit (AU) ● a unit of length defined by the distance from the Earth to the Sun 1 AU = 150 million kilometers = 93 million miles

Kepler's Laws of Planetary Motion

Ellipse F1, F2 – foci (focus) a – semimajor axis b – semiminor axis e - eccentricity

Ellipse ● Drawing an ellipse with a string of fixed length ● Eccentricity describes how much an ellipse deviates from a perfect circle

Kepler's First Law The orbit of each planet is an ellipse with the Sun at one focus. animation

Kepler's Second Law As a planet moves around its orbit, it sweeps out equal areas in equal times. Kepler's Laws animation - planets move faster near perihelion and slower near aphelion

Kepler's Third Law Kepler's third law

Kepler's Third Law

Generalizing Kepler's Laws - Kepler's laws - apply to the solar system, the Sun is in the focus - can be derived from Newton's law - more general result – applicable to any orbiting objects

Generalizing Kepler's Laws Kepler's first law - the orbits are ellipses, the center of gravity is in the common focus - Orbits can also be unbound parabolas and hyperbolas Kepler's third law G – gravitational constant M 1,M 2 - masses of the orbiting objects