PHYS 420: Astrophysics & Cosmology

Transcription

1 PHYS 420: Astrophysics & Cosmology

2 Dr Richard H. Cyburt Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) My My webpage: In person or is the best way to get a hold of me.

3 My Office Hours TR 5:30-17:00am W 5:00-5:00pm Meetings may also be arranged at other times, by appointment

4 Douglas Adams Hitchhiker s Guide to the Galaxy

5 Kudos to Kepler Several points worth noting... oan amazing discovery mathematics underlies the workings of the cosmos! oorbits have a simple geometry...but not simplest: ellipse not circle okepler s laws remain (almost) perfectly accurate to this day indeed, in slightly generalized form will show up in many (most!) situations where motions are controlled by gravity oyet note what we still don t have: an understanding of why Kepler s laws hold that is, what is the mechanism that makes planets move this way...for that, need to wait for Kepler s successors...

6 Galileo Galilei: Astronomer First to use telescope in Astronomy Contributions omountains on the moon omoons of Jupiter osunspots These are bad for Ptolemy (but maybe not deadly) Q: how? Galileo reporting to the funding agency

7 Galileo Galilei: Astronomer Crucial, decisive experiment: Phases of Venus Ptolemaic Predictions Capernican Predictions Observed Phases observations contradicted Aristotle, supported Copernicus paradigm shift (Kuhn) radical change in outlook/conceptual framework

8 Galileo Galilei: Astronomer Note: Galileo put on trial, forced to recant heliocentrism ohis work, Copernicus, Kepler banned until 1832 oofficial semi-apology ( mistakes were made ) 1992 complex: crackdown as much political as theological shows view of the world people had 1. really not at all obvious that sun at center 2. the paradigm shift difficult, challenged outlook

9 What are your thoughts?

10 Description of Motion Want precise language not just for planets but all objects Speed: rate of motion speed = '()*+, -*.-/0)*', '()*+, -* 0-1, mathematically: v = d/t (more technically v = dx/dt ) d = vt, distance traveled = speed x travel time Velocity: both speed and direction of travel Example: 10 mi East in ½ hour, velocity = 10/(½) = 20 mph East Q: can two objects have same speed, different velocities? Q: does car speedometer really measure speed or velocity? Q: turn corner in car, speedometer pegged at 20 mph-whassup?

11 Description of Motion Acceleration: Change in velocity Change in speed Change in direction of motion Speed up rate Slow down rate Q: What kind(s) of motion(s) have zero acceleration? Intuitively: acceleration is rate of speeding up or slowing down Sometimes it s useful to distinguish: Acceleration = speeding up Deceleration = slowing down

12 Galileo Galilei: Physicist Studied motion of objects on earth two important cases: Special Motion I: Free Body moving with no external influences (including friction, gravity) moves in straight line, constant speed constant velocity Galileo finds this is the natural motion of an object keeps constant speed & direction unless something happens to change this Contrary to Aristotle: natural motion is to come to rest Q: Why did Aristotle think this?

13 Galileo Galilei: Physicist Galilean Relativity o Motion of objects is always described as relative to something else. For example: oyou walk on the road relative to Earth, but Earth is moving relative to the Sun. oso your motion relative to the Sun is different from your motion relative to Earth.

14 Galileo Galilei: Physicist Galilean Relativity ovelocity is only meaningful wrt a frame of reference oi.e. a body is moving relative to another body othere exists an absolute space (i.e. the Universe) oall reference frames are moving relative to this absolute frame othere is a universal time oall clocks tick at the same rate in all reference frames The fundamental laws of physics are the same in all frames of reference moving with constant velocity with respect to one another.

15 Reference frames Coordinate transformation t = t x = x Vt y = y z = z Velocity transformation v x = v x V v y = v y v z = v z Time is absolute V

16 Galileo Galilei: Physicist Acceleration Formulated by Galileo based on his experiments with inclined planes. Galileo increased the inclination of inclined planes. Steeper inclines result in greater accelerations. When the incline is vertical, acceleration is at maximum, the same as that of a falling object. When air resistance is negligible, all objects fall with the same unchanging acceleration. Special Motion II: Free Fall Motion due to gravity only

17 Galileo Galilei: Physicist Q: in free fall, is velocity constant? Even if falling in a straight line, speed changes Gravity causes acceleration Same acceleration for ALL objects Independent of size, mass Feather vs Hammer Einstein called this independence the equivalence principle crucial in his invention of General Relativity Note: Galileo describes motion (mathematically) but to explain with a theory fell to...

18 Issac Newton Why Kepler s laws for planets? Are they special? Can we understand using general rules for all motion? New concepts Mass: amount of stuff measure in kg 1 kg of anything has the same mass Force: push or pull on object can have more that one acting, in different directions Motion & Forces linked

19 Newton s Laws: First Law Newton I: Law of Inertia an object at rest stays at rest if no net force acts on it an moving object goes in straight line w/ const speed if no forces act on it i.e., free body as per Galileo so we say: objects have inertia or momentum will keep their state of motion (i.e., velocity) unless and until a net force acts

20 Newton s Laws: Second Law Newton II: F=ma a net force acting on an object causes it to accelerate a F : a stronger force will cause an object to accelerate faster a 1/m: a more massive object will be more difficult to accelerate F i i = ma 2nd Law a mathematical machine which predicts future!

21 Newton s Laws: Second Law Input: at initial time, need to know/specify object mass m all of forces acting on m 1. Find net force F 2. Turn the math crank: a = F /m 3. Find acceleration = change in velocity 4. Use this to find new position, new velocity at at moment a little later 5. At new time and position, find new net force...lather, rinse, repeat Result: find particle path in future! But also: can mathematically run the movie backwards and predict the past history as well!

22 Newton s Laws: Third Law Newton I: Law of Inertia a rule about how forces behave between two objects if 2 bodies interact: the force exerted by object 1 on object 2 is equal and opposite to the force exerted by object 2 on object 1

23 Explaining Kepler Kepler s Laws I. Law of Ellipses: Planet orbits are ellipses with the Sun at a focus II. Law of Equal Areas: Equal areas of the ellipse are swept through in equal times III. Law of Harmonies: P 2 yrs = a 3 AU Laws I and II say a planet s velocity changes planets accelerate Need a force gravity

24 Universal Gravitation gravity is a force the force of gravity on you is your weight gravity acts beyond earth gravity directed on line connecting centers of bodies gravity strength decreases with distance all objects with mass are sources of gravity everything attracts everything else

25 Universal Gravitation Can summarize mathematically compact way: for 2 bodies, masses m 1, m 2 centers separated by distance R F grav m 1 gravitational force: F grav m 2 F grav 1/R 2 Newton s Universal Law of Gravitation F grav = Gm 1m 2 R 2 where G is just a fixed, constant number, same always: G = YZZ inverse square law m3 kg s 2

26 Gravity and Planetary Motion Newton 2 nd Law: input is force, output is motion For planets around Sun, force is gravity (free fall!) Given Newton s Universal Law of Gravity, what are the planets motion? Newton s 2 nd Law + Gravity: Properties of Predicted Orbits Orbit is elliptical, with Sun at one focus Equal areas in equal times P 2 yrs = a 3 AU, actually Newton does better: P 2 = 4π2 GM a 3

27 Gravity and Planetary Motion Theory agrees with Observations!! All Kepler s Laws verified! Only force acting on a planet is gravity m bc)*,0 a bc)*,0 = F bc)*,0 = de 1 fghijk l m a bc)*,0 = de l m Free fall acceleration only depends on mass of Sun, M and Sunplanet orbital distance R. Independent of planet mass and size! At same R, all objects accelerate same way Equivalence Principle pops out of Newton s Gravity!!! Wooo-hooo!!!

28 Testing Newton s Gravity Moons of Jupiter: orbits obey Kepler s laws but in Newton s more general form, using M Jupiter Jupiter s gravity works like the Sun s and Earth s.. Gravity is Universal 1830 s: Uranus obsersed orbit did NOT follow predictions of Newtonian solar system model The death of Newton s gravity? Remember: Have to agree with ALL data, not just some even one clear failure is enough to kill theory e.g., Kepler and Mars: just a small discrepancy from circular but still had to throw out circular orbits

29 What are your thoughts?

30 19 th Century Dark Matter to save Newton s gravity: need unseen massive object could have been called dark matter! whose gravity is altering Uranus motion based on Uranus known path, can use Newton s gravity to predict where the dark matter should be! Crucial experiment: go look there with telescope! This was done, in 1846.

31 Newton Triumphs! planet Neptune found at dark matter position predicted by Newton s gravity! Other more recent tests: Binary Stars: two stars orbiting each other move in ellipses, obey Kepler s laws Binary Stars Orbit Gravity theory works outside solar system

32 Cosmology: Progress Report after Newton Recall: Cosmology is a mystery story Based on evidence we can observe, want to understand: structure of Universe: how big? map of contents across space? contents of Universe: what ingredients is it made of? origin & evolution of Universe: birth? past? future? rules of the game: what makes the Universe this way? Cosmological progress so far: Copernicus Sun-centered Universe Kepler precisely described planetary motion Newton explained planetary motion, agrees w/ observations

33 Lessons from Newtonian Triumph Lesson from Newtonian success: insight into rules of the game powerful laws exist explaining all motion due to forces planetary motion is due to force of gravity gravity determines behavior of the cosmos! Also important implications for structure of Universe

34 What are your thoughts?

35 Lessons from Newtonian Triumph Recall: to naked eye, stellar parallax is undetectable stars don t seem to wiggle annually on sky so if parallax exists, wiggle must be small stars must be very far away! But if stars hugely far away, and can still be seen they must emit a lot of light perhaps stars are like the Sun!

36 Where do we go from here?