• Dates from Stone Age (2800 B.C.)
• Construction spanned 17 centuries

• Sliver of light passes through carved stone at noon on the summer solstice

• Observed the heavens, records of comets
• Historical data still used today

• Geocentric
(Earth Centered) or Ptolemaic,
A.D. 140

• http://www.csit.fsu.edu/%7Edduke/nmoon6.html

• http://antwrp.gsfc.nasa.gov/apod/ap011220.html

• Aristarchus (290 B. C.), forgotten for 1800 years

• Key link from ancient
Greeks during
Dark Ages
• Examples of Muslim terms: Zenith and star names such as
Vega, Betelgeuse

• Rediscovered Aristarchus’s heliocentric model

(On the Revolutions of the Celestial Spheres)
• Published just before his death in 1543
• Starting point of modern astronomy
• Placed on the Catholic
Church’s Index of
Prohibited Books in
1616

• Built a telescope in 1609
• His work supported
Copernicus
• Found 4 moons orbiting
Jupiter

• Published
Sidereus Nuncius
(The Starry Messenger) in 1610
• Banned in 1616

• Contemporary of
Galileo

• The orbital paths of the planets are elliptical, not circular, with the Sun at one focus

st

• An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time

• http://www.youtube.com/watch?v=_3OOK8a
4l8Y&feature=related
• http://www.astro.virginia.edu/class/oconnell/ astr121/im/kepler-2ndanim-NS.gif

• The square of a planet’s orbital period is proportional to the cube of its semimajor axis
P 2 = a 3 where P is in Earth years and a is in astronomical units
• 1 astronomical unit (AU) = avg. distance from the Earth to the Sun

•
•
•
•
•
• Pluto’s semimajor axis (average distance from the Sun) is approximately 40. AU. Calculate the period of Pluto a = 40. AU And a 3 = 64,000
P 2 = a 3
P 2 = 64,000
P =
64,000
P = 250 years

• Published Philosophiae Naturalis
Principia Mathematica in 1687
• Possibly most influential physics book ever written
• Newtonian mechanics  WHY the planets move according to Kepler’s Laws

• The acceleration due to gravity is inversely proportional to the square of the distance

2.8 Newtonian Mechanics
Escape speed : the speed necessary for a projectile to completely escape a planet’s gravitational field.
With a lesser speed, the projectile either returns to the planet or stays in orbit.

• http://galileoandeinstein.physics.virginia.edu/ more_stuff/Applets/newt/newtmtn.html

2.7 Newton’s Laws
Newton’s first law :
An object at rest will remain at rest, and an object moving in a straight line at constant speed will not change its motion, unless an external force acts on it.

2.7 Newton’s Laws
Newton’s second law:
When a force is exerted on an object, its acceleration is inversely proportional to its mass: a = F / m
Newton’s third law:
When object A exerts a force on object B, object
B exerts an equal and opposite force on object A.

2.7 Newton’s Laws
Gravity
On the Earth’s surface, acceleration of gravity is approximately constant, and directed toward the center of Earth

2.7 Newton’s Laws
Gravity
For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them

2.8 Newtonian Mechanics
Kepler’s laws are a consequence of
Newton’s laws ; first law needs to be modified: The orbit of a planet around the Sun is an ellipse, with the center of mass of the planet –Sun system at one focus.

• Discovered Uranus (1781),
• Key figure of The Age of Enlightenment

• Discovered several comets

• Annus mirabilis (1905)
• Published 4 articles in the Annalen der Physik
 Changed views on space, time, and matter matter

• Gravitational singularities
• Black holes

• Antikythera mechanism
 mechanical computer
• ~ 100 BC, Greek

Germany, 1926

New York

Summary of a few important concepts from chapter 2
• First models of solar system were geocentric but couldn't easily explain retrograde motion
• Heliocentric model does; also explains brightness variations
• Galileo's observations supported heliocentric model
• Kepler found three empirical laws of planetary motion from observations

Mars, Jupiter, and
Saturn show retrograde motion because
Question 1 a) planets move on epicycles. b) planets orbit the Sun in the same direction.
c) Earth moves faster in its orbit. d) they are closer than Uranus.
e) they rotate quickly on their axes.

Mars, Jupiter, and
Saturn show retrograde motion because
Question 1 a) planets move on epicycles. b) planets orbit the Sun in the same direction.
c) Earth moves faster in its orbit. d) they are closer than Uranus.
e) they rotate quickly on their axes.
As Earth overtakes and
“passes” the outer planets, they seem to slow down and reverse direction.

How did the geocentric model account for day and night on
Earth?
Question 2 a) The Earth rotated.
b) The Sun rotated.
c) The geocentric model couldn’t account for day and night.
d) The Earth revolved around the Sun.
e) The Sun orbited Earth.

How did the geocentric model account for day and night on
Earth?
Question 2 a) The Earth rotated.
b) The Sun rotated.
c) The geocentric model couldn’t account for day and night.
d) The Earth revolved around the Sun.
e) The Sun orbited Earth.
The geocentric model held that the Earth was motionless in the center of the universe.

Epicycles were used in Ptolemy’s model to explain
Question 3 a) why planets moved in the sky.
b) why Earth was at the center. c) why retrograde motion occurred.
d) why Earth wobbled on its axis.
e) why inner planets were always seen near the Sun.

Epicycles were used in Ptolemy’s model to explain
Question 3 a) why planets moved in the sky.
b) why Earth was at the center. c) why retrograde motion occurred.
.
d) why Earth wobbled on its axis.
e) why inner planets were always seen near the Sun.
Planets were assumed to move uniformly on an epicycle, as it moved uniformly around Earth.

The geocentric
model was supported by
Aristotle because
Question 4 a) stars don’t seem to show any parallax. b) we don’t feel as though Earth moves.
c) objects fall toward Earth, not the Sun. d) we don’t see an enormous wind.
e) All of the above were valid reasons.

The geocentric
model was supported by
Aristotle because
Question 4 a) stars don’t seem to show any parallax. b) we don’t feel as though Earth moves.
c) objects fall toward Earth, not the Sun. d) we don’t see an enormous wind.
e) All of the above were valid reasons.
If the Earth rotated and orbited, we would feel its motion.
In Aristotle’s time, the size of the solar system and distances to stars were assumed to be much, much smaller. Parallax was expected to be seen.

The heliocentric model assumes
Question 5 a) planets move on epicycles.
b) Earth is the center of the solar system. c) the stars move on the celestial sphere.
d) the Sun is the center of the solar system. e) Earth’s axis wobbles over 26,000 years.

The heliocentric model assumes
Question 5 a) planets move on epicycles.
b) Earth is the center of the solar system. c) the stars move on the celestial sphere.
d) the Sun is the center of the solar system. e) Earth’s axis wobbles over 26,000 years.
Heliocentric models proposed by Aristarchus and others were considered wrong by Aristotle and his followers.

Copernicus’ important contribution to astronomy was
Question 6 a) proving planets move around the Sun in elliptical orbits.
b) the theory of gravity. c) proposing a simpler model for the motions of planets in the solar system.
d) discovering the Sun was not at the center of the Milky Way.
e) discovering the four moons of Jupiter.

Copernicus’ important contribution to astronomy was
Question 6 a) proving planets move around the Sun in elliptical orbits.
b) the theory of gravity.
c) proposing a simpler model for the motions of planets in the solar system.
d) discovering the Sun was not at the center of the Milky Way.
e) discovering the four moons of Jupiter.
His heliocentric model easily explained retrograde motion because planets orbited the Sun at different speeds.

Copernicus’ heliocentric model was flawed because
Question 7 a) he assumed planets moved in ellipses.
b) he didn’t know about Uranus and Neptune.
c) he couldn’t account for gravity.
d) he couldn’t explain retrograde motion.
e) he assumed planets moved in circles.

Copernicus’ heliocentric model was flawed because
Question 7 a) he assumed planets moved in ellipses.
b) he didn’t know about Uranus and Neptune.
c) he couldn’t account for gravity.
d) he couldn’t explain retrograde motion.
e) he assumed planets moved in circles.
Copernicus’ model still needed small epicycles to account for observed changes in planetary speeds.

Question 8
Who published the first astronomical observations made with a telescope?
a) Hipparchus b) Galileo c) Tycho d) Copernicus e) Kepler

Question 8
Who published the first astronomical observations made with a telescope?
a) Hipparchus b) Galileo c) Tycho d) Copernicus e) Kepler
Galileo published the “Starry
Messenger” in 1610, detailing his observations of the Moon,
Jupiter’s moons, stars, and nebulae.

Question 9
Which of Galileo’s initial observations was most challenging to established
geocentric beliefs?
a) craters on the Moon b) sunspots c) lunar maria d) satellites of Jupiter e) stars of the Milky Way

Question 9
Which of Galileo’s initial observations was most challenging to established
geocentric beliefs?
a) craters on the Moon b) sunspots c) lunar maria d) satellites of Jupiter e) stars of the Milky Way
Seeing four moons clearly move around Jupiter disproved that everything orbited Earth and showed Earth could orbit the
Sun and not lose its moon, too.

Question 10
Which hero of the
Renaissance postulated three “laws” of planetary motion?
a) Kepler b) Newton c) Galileo d) Tycho Brahe e) Copernicus

Question 10
Which hero of the
Renaissance postulated three “laws” of planetary motion?
a) Kepler b) Newton c) Galileo d) Tycho Brahe e) Copernicus
Note that Isaac Newton is also well known for three general laws of motion.
But Kepler’s laws are about objects in orbits, such as planets orbiting a star.

Question 11
Kepler’s 1st law of planetary orbits states that a) planets orbit the Sun.
b) orbits are noncircular.
c) orbits are elliptical in shape.
d) all of the above are correct.

Question 11
Kepler’s 1st law of planetary orbits states that a) planets orbit the Sun.
b) orbits are noncircular.
c) orbits are elliptical in shape.
d) all of the above are correct.
Kepler’s laws apply to all orbiting objects. The Moon orbits Earth in an ellipse, and the Space Shuttle orbits Earth in an ellipse, too.

Question 12
Earth is closer to the
Sun in January. From this fact, Kepler’s 2nd
law tells us a) Earth orbits slower in January.
b) Earth orbits faster in January.
c) Earth’s orbital speed doesn’t d)change.

Question 12
Earth is closer to the Sun in January. From this fact,
Kepler’s 2nd law tells us a) Earth orbits slower in
January.
b) Earth orbits faster in January.
c) Earth’s orbital speed doesn’t change.
Kepler’s 2nd law means that a planet moves faster when closer to the star.
Faster
Slower

Question 13
Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital a.
speed.
b.
period.
c.
shape.
d.
velocity.

Question 13
Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital a.
speed.
b.
period.
c.
shape.
d.
velocity.
Kepler’s 3rd law P 2 = a 3 means more distant planets orbit more slowly.
Venus’ Period = 225 days
Venus’ axis = 0.7 AU
Earth’s Period = 365 days
Earth’s axis = 1.0 AU

Newton’s law of
gravity states that the force between two objects
Question 14 a) increases with distance.
b) depends on the state of matter
(solid, liquid, or gas).
c) can be attractive or repulsive.
d) increases with mass.

Newton’s law of
gravity states that the force between two objects
Question 14 a) increases with distance.
b) depends on the state of matter
(solid, liquid, or gas).
c) can be attractive or repulsive.
d) increases with mass.
The attractive force of gravity increases with greater mass, and
decreases quickly with greater distance.
The force doesn’t depend on the kind of matter.