1. Announcements Website
First Homework Due January 31
First observatory session January 31 at 7pm, weather allowing.

2. Motion
x = v * t
v = a * t
x = ½ * a * t2

3. Question
A spaceship accelerates from rest at 20gees (200m/s/s) steadily for 1.2 days (105 seconds). How far has it travelled?
2x107m
5000m
1012m
104m

4. Newton’s Laws
Law #1: A body at rest or in motion remains that way unless acted upon by an outside force.
Law #2: a=F/m
Law #3: For every action there is an equal and opposite reaction.

5. Law #1
A body in motion remains that way unless acted upon by an outside force.
No Forces
Contact Forces (electrical)
Gravity

6. Law #2 F=ma a=F/m Have a mass Apply a force Acceleration Results
F = Force
m = mass
a = acceleration
F=ma
Have a mass
Apply a force
Acceleration Results
a=F/m
Note: Law #1 is special case of Law #2 (F= a=0)

7. Question
A force of 250 Newtons is applied to a 100kg object. How fast does it accelerate?
2.5m/s/s
25m/s/s
0.4m/s/s
4m/s/s

8. Law #3 For every action there is an equal and opposite reaction.
For every ma there is an equal and opposite ma.
Big one doesn’t move much
Equal Mass Implies Equal Acceleration

9. But What is F? a=F/m not enough because we don’t know what F is.
Need a new law to describe forces
There are Four KNOWN Forces
Gravity
Weak Nuclear Force
Electromagnetism
Strong Nuclear Force
In order of strength
Gravity Weakest

10. Newton’s Law of Universal Gravitation
(Law #3 Satisfied)
G = 6.7x10-11 in mks units
Value of G is measured. Nobody knows why it is the value it is.
Electrical Force Equation Similar

11. Question
What is the weight of a 100kg person standing on the surface of the Earth. (in Newtons) M=6x1024kg. R=6000km
a) 6.7x1021N
b) 1.6x108N
c) 1000N
d) 6.7x10-3N

12. But What is a Force? Newtons Laws Give Value, and Show what to do.
Force is an Exchange of Virtual Particles

13. Orbits
Falls Freely
Hits Surface
Misses Surface
From Sideways Motion

14. Physics of Orbits sideways velocity central acceleration
If you balance things just right, you have an orbit.
Too Little Sideways V = Crash
Too Much = Escape to Infinity
Earth

15. Circular Orbit
circle
implies
Kepler’s Law

16. Example
Calculate the period of a planet that is the same distance from the star Sirius that the Earth is from the Sun.
r=1.5x1013cm
G=6.7x10-8
M=4x1033g
About 9 Months

17. Non-Circular Formula 2r Same Formula for P Fast
Focus
Same Formula for P
Use half orbit length for r
Fast
Slow

18. Escape Velocity Fall from Large Height
Same Energy Needed to Reverse and Fly Away
Escape velocity is the speed
at which object must be thrown
upward to escape and never come
down.

19. Example
Earth
R=6x108cm
M=5x1027g

20. Question What is the escape velocity of the Moon?
M=7.35x1022kg, R=1738km
a)2000km/s
b)200km/s
c)20km/s
d)2km/s
e)0.2km/s

21. Answer: D
Moon
R=1700km
M=7x1022kg

22. Surface Gravity Force of Gravity at Surface of Body is So
The acceleration of a body
near the surface.
Independent of mass. or
Remember Galileo and the Leaning Tower of Pisa

23. Gravity on Earth
1 gee is 9.8m/s per second

24. Spin Up When a body is spinning “Angular Momentum” is conserved
For spherical body:
As R decreases P decreases
Spin up of ice skater.
Same for Collapsing Stars

25. The Sun

26. The Sun Falls into “Disk Stability”
99.9% Ended in Sun (0.1% in Jupiter)
Probably the Same Around All Stars -- Planets are Common
Shoots Planet-Size
Bullets into Space

27. Most of Mass Forms Ball in Center
A Star Is a Hot
Ball of Hydrogen
(plus 11% Helium)
One Million Miles

28. Question Why is the Sun spherical while the planets orbit in a disk?
A) They actually orbit in a sphere
B) The planets hit each other if they don’t all lie in the same plane
C) The Sun has lost spin over time, while planet orbits cannot
D) The Sun will eventually evolve to a disk

29. Answer: C
The surface of the Sun is orbiting at far less than orbital speed. (just like the Earth) Back when it was first forming it spun much faster and was closer to a disk.

30. What Stops the Fall? Gravity Gets Stronger As Material Gets More Dense
R smaller implies F greater
The smaller it gets, the faster it falls in!
Why doesn’t it just become a black hole?
Or worse yet, a point-like singularity of mass?

31. Scaling
Scientists often do “scaling” do avoid all those large numbers.
For example, the Sun is ABOUT a million times the mass of the Earth and a hundred times the size.

32. Question
What is the surface gravity of the Moon in gees? R=.01Re, M=.25Me?
a).04
b)4
c)16
d).16

33. Answer d

34. Temperature Temperature is a Measure of the
Random Kinetic Energy per Particle
The faster the atoms move, the higher the temperature.
But we’re talking about random motion.
If they all move together, then the object moves.

35. Thermal Pressure Thermal Gas Pressure Balances Gravitational Pressure
Balloon
Every Time An Bounces Off
Edge of Balloon It Keeps It From
Collapsing
That’s Pressure
Pressure is Force per Unit Area

36. Pressure is Proportional to Temperature
Low Temperature
Atoms Move Slowly
High Temperature
Atoms Move Fast

37. A Star Is Held Up By Thermal Pressure From Below
Gravity
Outer Mass
Individual Atoms Don’t
Orbit Entire Inside of
Star Like This
They Jostle Each Other
But Effect Is The Same

38. Temperature Scales Fahrenheit – Celsius Kelvin
0=salt water freeze 100=human body
Celsius
0=pure water freeze 100=water boil (sea level)
C=(F-32)x5/9
Kelvin
0=absolute zero degrees between freeze and boil
K=C+273
-273C = 0K = Absolute Zero
At Absolute Zero Atoms Stop Moving

39. Thermal Pressure Pressure Is Proportional to Temperature x Density
P Pressure
V Volume
n # moles
R Constant
T Temperature (K)
Ideal Gas Law
Chemistry Style
P Pressure
V Volume
N # atoms
k Constant
T Temperature (K)
Ideal Gas Law
Physics Style
Pressure Is Proportional to Temperature x Density

40. A Star Always Balances Gravitational Pressure with Thermal Pressure
Pressure Balance
A Star Always Balances Gravitational Pressure with Thermal Pressure
At Each Point Inside
Thermal Pressure (Jostling)
Gravity

41. But We Have a Problem The Sun is Luminous Radiates Energy Into Space
Luminosity is Power Radiated -- ergs/second
The Energy Comes From Motion of the Atoms
Temperature Drops
What Happens When T Drops?

42. Luminosity Effect When T Drops Thermal Pressure Can’t Hold Off Gravity
The Sun Shrinks -- Radius Drops
Energy is Released as Gas Falls Deeper Into Gravity Field
Temperature Rises
Note – Loss of Energy Results in
a) Temperature Rise
b) Radius Decrease

43. But Wait A Minute… Isn’t the Sun Stable?
The Sun has been remarkably stable for 4 billion years as evidenced by geological records.
This collapse is the process by which the Sun coalesced.
But then it stopped. Why?
The Sun collapsed until a new source of energy offset the losses
to radiation.
NUCLEAR FUSION IT’S BURNING HYDROGEN
As long as it burns H at this rate, it will be stable.

44. Fusion Increases with T
As T in core of Sun increases so does energy production
Sun shrank steadily, with T rising until, about 10 million years
after it started to form, it reached its current size
There is a VERY fast increase in nuclear energy production
above 1,000,000K.
At 15,000,000K in the core nuclear power generated finally balanced
the luminosity from the surface.
That’s the equilibrium we are still in.

45. The Nuclear Core Envelope 1 Million K core 15x106K
Photosphere 5000K At Surface

46. Cosmic Composition H hydrogen 89% by number He helium 11%
O oxygen 0.1%
C carbon 0.06%
N nitrogen %
Pretty much the composition of the entire universe.
Sun and Jupiter have this composition
Earth does not.

47. Fusion vs. Fission Fusion: Atoms unite and release energy (Fuse)
New atom must be no heavier than iron z=26
Fission: Heavy atoms split to release energy
Initial atom must be heavier than iron
WWII Nukes were fission bombs made of U and Pu
Sun works on FUSION of H into He

48. Proton-Proton Chain Bottom Line: H+H+H+H  He 1H1 +1H1  1H2 + e+ + n
1H2 +1H1  2He3 + g
2He3 +2He3  2He4 + 1H1 + 1H1
5x106 < T < 2x107K

49. CNO Cycle 6C12 +1H1  7N13 + g 7N13  6C13 + e+ + n
7N14 +1H1  8O15 + g
8O15  7N15 + e+ + n
2x107 < T < 108K
7N15 +1H1  6C12 + 2He4
Net: 1H1 +1H1 + 1H1 +1H1  2He4 + 2e+ + 4g +2n
hydrogen -> helium + energy

50. Triple-a Reaction 2He4 +2He4  4Be8 + g 4Be8 +2He4  6C12 + g
T < 108K
4Be8 +2He4  6C12 + g
Must be very dense for this to work
Be8 decays back into helium very quickly
unless struck by another He4
Too low density
in Big Bang
Net: 2He4 +2He4 + 2He4 +2He4  6C12 + 2g
helium -> carbon + energy

51. Solar Schematic

52. Seen by Ancient Persians
Sunspots
Seen by Ancient Persians
(and me!)