1. Free Falling

2. History of Astronomy

3. Eratosthenes ( 276 –194 B.C.) measured circumference of the Earth
Eratosthenes read of a well in Syene, Egypt which at noon on June 21 would reflect the sun overhead.
A year later, Eratosthenes in Alexandria observed the shadow of a stick and measured the angle to be 7.2 deg,
The distance between Alexandria and Syene is about 740 kilometers
X/740 = 360/7.2
X=38,057 km or 22,940 mi

4. a A B B A Simple Trig: Sin (a)= A/B or A = (B) Sin(a)
The distance to Mercury & Venus A B
90 deg A a a B
When the planet Venus or Mercury are at greatest elongation, measure the angle between the Sun and the planet at Sunset. The distance of Earth to Sun is 1 A.U.
Simple Trig: Sin (a)= A/B or A = (B) Sin(a)
Using this method Mercury and Venus were .4 and .7 A.U. from the Sun respectively.

5. Claudius Ptolemy ~ 200 A.D. Born in Alexandria, Egypt.
His model of the Solar system strived to explain the motion of the planets.
He presumed that the Earth was at the center of the Universe (geocentric) a theory that had been proposed by Aristotle.

6. Geocentric Theory
The planets & Sun revolve around the Earth. The circles are epicycles, where the planets appear to go into a loop and then continue onward.

7. He explained the motion of the planets this way!

8. Copernicus: –1543
Copernicus proposed the heliocentric model, with circular orbits, and uniform motion.
The model was less accurate for predicting positions, but more “physically realistic”

9. He also had a simple explanation for retrograde motion, the planet moved backwards for a short period of time.

10. Galileo Galilei
Galileo was among the first to turn a telescope to the sky.
He developed the Scientific Method,
and the Law of Inertia.

11. Telescopes: Galileo’s earlier work:
1590 Masses fall at same rate, heavier do not fall faster (unless affected by air resistance). First to experiment
1604 He observed a supernova
Telescopes:
1609 He hears of the invention of a telescope, which uses eyeglass lenses.
Works out details of better lenses and , builds improved ones himself.

12. Telescope Discoveries The Moons of Jupiter
Clear example of four objects that do not orbit the Earth.

13. Telescope Discoveries
On the Moon he saw mountains, valleys and (Earthlike) features .
Sunspots
He showed they were really on the Sun.
But the Sun was made in the image of God!

14. Galileo’s Venus Observations
Detects the phases of Venus
Phases show that Venus must orbit the Sun.
From our text: Horizons, by Seeds

15. Tycho Brahe ( )
He was of Danish nobility. Lost his nose in duel (so he had a metal one made).
He built very accurate instruments for measuring sky positions.
He hired Kepler to try to understand the motion of Mars and shortly thereafter he died.

16. Tycho and his great quadrant at Uraniborg
Tycho and his great quadrant at Uraniborg. Tinted engraving from Tycho's Astronomiae instaurata mechanica, published in Wansbeck in Completed in 1582, something like the mural quadrant was evidently planned upon Tycho's arrival on Hveen in 1576, since the accurately aligned wall on which the quadrant was later mounted was built into Uraniborg at the onset. The accuracy of this instrument, based on comparison with eight reference stars, has been estimated to 34.6 seconds of arc.

17. Johannes Kepler ( )
He was born sickly and poor and, went to work with Tycho to escape 30 Years War.
Kepler proposed a geometrical heliocentric model with imbedded polygons ,but had to gave up (clever, but not better).

18. He finally determined, that the planets moved along elliptical paths, with the sun at one of the foci of the ellipse.
Since the planets’ orbits are close to circular, nothing is located at the other focus.

19. Properties of Ellipses
An ellipse is defined by two constants :
(1) eccentricity e 0=circle, 1 = line
e=0
e=0.98
Same focus, at the sun

20. Properties of Ellipses
(2) semi-major axis = a
1/2 length of major axis b a
a = Semi-major axis
b = Semi-minor axis ( we will not use)

21. Law I Kepler’s Three Laws
Sun
Planet
Law I
Planets orbit the Sun in ellipses with the Sun at one focus of the ellipse.
Note: There is nothing at the other focus or in the center.

22. Kepler’s Law II
2) A line between a planet and the Sun sweeps out equal areas of the ellipse in equal amounts of time.

23. P2 = a3 Kepler’s Laws Law III
The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P2 µ a3
If P is measured in earth years, and a is measured in AU, then the formula becomes
P2 = a3

24. P must be in earth years, and a in AU.
Using the Third Law
P2 = a3
P must be in earth years, and a in AU.
A planet is located 4 au form the sun, what is the period of the planet ?

25. Summary of Kepler’s Three Laws
I. The orbits of the planets are ellipses with the sun at one focus.
II The orbital path sweeps out equal areas in equal time.
III The orbital period squared is proportional to the average distance cubed (usually expressed in earth years and A.U.s).

26. Isaac Newton ( )
One of world’s greatest scientists, co-inventor of calculus.
He discovered the law of Universal Gravitation, Three Laws of Motion and he was able to explain Kepler’s Laws.
Personally rather obnoxious. Had poor relationships with women. Did most of his work before he turned 25!

27. Newton’s Laws The First Law ( Inertia )
A body continues to move as it has been moving unless acted upon by an external force.
A body at rest
upon by some
An astronaut, floating in space, will float in a straight line , unless some force acts upon him/her.
stays at rest ,
unless acted
force .

28. or a = F/m The 2nd Law Newton’s Laws F = (mass) a
Forces acting on a body can produce an acceleration to a body.

29. For every action there is an equal and opposite reaction
The 3rd Law
Newton’s Laws
For every action there is
an equal and opposite reaction

30. Newton’s Law of Universal Gravitation
Every object in the universe attracts every other object with a force that is directly proportional to the product of its masses, and inversely proportional to the square of its distance.

31. More distance less force - less distance, more force

32. M1 M2 d
More mass more force – less mass, less force
2M1 M2 d
2M1
2M2 d

35. Mass, Energy
and Momentum

36. What is mass and weight ?
Weight is the attraction of gravity for an object. Mass is how much matter an object contains.
Mass does not depend on gravity. One kg on Earth is one kg everywhere in the universe.
Weight would be different for each planet, due to gravity.

37. Temperature Scales
Astronomers use the Kelvin scale, because it starts with 0 degrees, where there is no molecular motion .
On the microscopic level , the average kinetic energy of the particles within a substance is called the temperature.

38. Three Basic Types of Energy
Kinetic Energy
Energy due to motion
Potential Energy
Stored energy
Radiative Energy
Energy transported by light
Energy can change from one form to another.

39. Conservation of Energy
Energy can be neither created nor destroyed.
It merely changes it form or is exchanged between objects.
The total energy content of the Universe was determined in the Big Bang and remains the same today.

40. Potential Energy
gravitational potential energy is the energy which an object stores due to its ability to fall.
It depends on:
the object’s mass (m)
the strength of gravity (g)
the distance which it falls (d)
E=mgh m d g

41. Energy is stored in matter itself andthis mass-energy equation is how much energy would be released if an amount of mass, m were converted into energy.
E = mc2
[ c = 3 x 108 m/s is the speed of light; m is in kg, then E is in joules]

42. The Acceleration of Gravity
Ignoring air friction
As objects fall, they accelerate.
The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10 m/s2,or 32 ft/s2.
The higher you drop the ball, the greater its velocity will be at impact.

43. Conservation of Angular Momentum
Angular momentum = rotational momentum
Spinning objects rotate faster when radius shrinks, and rotate slower when their radius expands.
Experimental evidence indicates that angular momentum is rigorously conserved in our Universe: it can be transferred, but it cannot be created or destroyed.

44. When an ice skater goes into a spin, if the skater moves their arms inward, the rate of spin increases, and if the arms are move outward, the rate of spin slows down.
When they bring their arms in, this shortens the distance from the mass in the arms to the rotation axis, so the velocity of that mass must increase accordingly for the product of the two to remain the same.
This is conservation of angular momentum.

45. The End