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PHYS 155 – Introductory Astronomy
- observing sessions:
Sunday – Thursday, 9pm, weather permitting
http://www.phys.uconn.edu/observatory
- Exam - Tuesday March 20,
- Review – Monday 6:30-9pm, PB 38
Marek Krasnansky
Thursday
03/15/2007
• 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

Motion of the Sun, Moon, planets
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
●
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
• Venus:
• Moon:
• Crescent phase – Venus between the Sun and Earth
– Galileo Galilei – the first to observe gibbous phase of 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.
Stellar Parallax - 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.
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
Geocentric Models
-Tycho Brahe
- 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)
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.
(1546 - 1601)
Kepler's Laws of Planetary Motion
Kepler's first law:
The orbit of each planet is an ellipse with the Sun at one focus.
Kepler's second law:
As a planet moves around its orbit, it sweeps out equal areas in equal
times.
Kepler's third law:
2
P =a
3
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
c
e=
0≤e1
a
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.
animation
Kepler's Laws
- planets move faster near perihelion and slower near aphelion
Kepler's Third Law
Kepler's third law
2
P =a
3
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
M1,M2- masses of the orbiting objects