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Announcements Website http: //casa. colorado. edu/~wcash/APS 1020. html First Homework Due January 31 First observatory session January 31 at 7 pm, weather allowing.
Motion • x=v*t • v=a*t • x = ½ * a * t 2
Question A spaceship accelerates from rest at 20 gees (200 m/s/s) steadily for 1. 2 days (105 seconds). How far has it travelled? a) 2 x 107 m b) 5000 m c) 1012 m d) 104 m
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.
Law #1 A body in motion remains that way unless acted upon by an outside force. No Forces Contact Forces (electrical) Gravity
Law #2 F=ma a=F/m F = Force m = mass a = acceleration • Have a mass • Apply a force • Acceleration Results Note: Law #1 is special case of Law #2 (F=0 a=0)
Question A force of 250 Newtons is applied to a 100 kg object. How fast does it accelerate? a) 2. 5 m/s/s b) 25 m/s/s c) 0. 4 m/s/s d) 4 m/s/s
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
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
Newton’s Law of Universal Gravitation (Law #3 Satisfied) G = 6. 7 x 10 -11 in mks units Value of G is measured. Nobody knows why it is the value it is. Electrical Force Equation Similar
Question What is the weight of a 100 kg person standing on the surface of the Earth. (in Newtons) M=6 x 1024 kg. R=6000 km a) 6. 7 x 1021 N b) 1. 6 x 108 N c) 1000 N d) 6. 7 x 10 -3 N
But What is a Force? Newtons Laws Give Value, and Show what to do. Force is an Exchange of Virtual Particles
Orbits Falls Freely Hits Surface Misses Surface From Sideways Motion
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
Circular Orbit circle implies Kepler’s Law
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. 5 x 1013 cm G=6. 7 x 10 -8 M=4 x 1033 g About 9 Months
Non-Circular Formula 2 r Focus Same Formula for P Use half orbit length for r Fast Slow
Escape Velocity R 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.
Example Earth R=6 x 108 cm M=5 x 1027 g
Question What is the escape velocity of the Moon? M=7. 35 x 1022 kg, R=1738 km a)2000 km/s b)200 km/s c)20 km/s d)2 km/s e)0. 2 km/s
Answer: D Moon R=1700 km M=7 x 1022 kg
Surface Gravity Force of Gravity at Surface of Body is So or The acceleration of a body near the surface. Independent of mass. Remember Galileo and the Leaning Tower of Pisa
Gravity on Earth 1 gee is 9. 8 m/s per second
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
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
Most of Mass Forms Ball in Center A Star Is a Hot Ball of Hydrogen (plus 11% Helium) One Million Miles
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
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.
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?
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.
Question What is the surface gravity of the Moon in gees? R=. 01 Re, M=. 25 Me? a). 04 b)4 c)16 d). 16
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.
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 is Force per Unit Area
Pressure is Proportional to Temperature Low Temperature Atoms Move Slowly High Temperature Atoms Move Fast
A Star Is Held Up By Thermal Pressure From Below Outer Mass Gravity Individual Atoms Don’t Orbit Entire Inside of Star Like This They Jostle Each Other But Effect Is The Same
Temperature Scales • Fahrenheit – – 0=salt water freeze 100=human body • Celsius – – 0=pure water freeze 100=water boil (sea level) C=(F-32)x 5/9 • Kelvin – – – 0=absolute zero 100 degrees between freeze and boil K=C+273 -273 C = 0 K = Absolute Zero Atoms Stop Moving
Thermal Pressure Ideal Gas Law Chemistry Style Ideal Gas Law Physics Style P V n R T Pressure Volume # moles Constant Temperature (K) P V N k T Pressure Volume # atoms Constant Temperature (K) Pressure Is Proportional to Temperature x Density
Pressure Balance A Star Always Balances Gravitational Pressure with Thermal Pressure At Each Point Inside Thermal Pressure (Jostling) Gravity
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?
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
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.
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 K. At 15, 000 K in the core nuclear power generated finally balanced the luminosity from the surface. That’s the equilibrium we are still in.
The Nuclear Core Envelope 1 Million K core 15 x 106 K Photosphere 5000 K At Surface
Cosmic Composition • • • H He O C N hydrogen helium oxygen carbon nitrogen 89% by number 11% 0. 06% 0. 015% Pretty much the composition of the entire universe. Sun and Jupiter have this composition Earth does not.
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
Proton-Proton Chain Bottom Line: H+H+H+H He 1 H 1+ 1 H 2 He 3+ 1 H 2+ 2 He 3 1 1 H 2 + e + + n 1 H 1 2 He 3 + g 2 He 4 + 1 H 1 5 x 106 < T < 2 x 107 K
CNO Cycle 6 C 12 + 7 N 13 6 C 7 N 13 + 15 15 + 1 7 N 13 + g 6 C 13 + e+ + n 14 + 8 O 7 N 1 H 1 H 1 H 1 1 7 N 14 + g 8 O 15 + g 7 N 15 + e+ + n 1 H 1 2 x 107 < T < 108 K 6 C 12 + 2 He 4 Net: 1 H 1 +1 H 1 2 He 4 + 2 e+ + 4 g +2 n hydrogen -> helium + energy
Triple-a Reaction 2 He 4 Be 4+ 8+ 2 He 4 4 4 Be 8 + g T < 108 K 6 C 12 + g Must be very dense for this to work Be 8 decays back into helium very quickly unless struck by another He 4 Net: 2 He 4 +2 He 4 6 C 12 + 2 g helium -> carbon + energy Too low density in Big Bang
Sunspots Seen by Ancient Persians (and me!)