Black holes

1. Black holes • Introduction to astronomy and physics

2. Astronomy - history • Astronomy is among the oldest “sciences”, if not the oldest: • Stars were always visible and became important for navigation • Phases of the moon were important for tides, calendars • Seasons were important for agriculture etc. • Eclipses were seen as important omens • Astronomy and religion were long intertwined

3. Classical Physics • Anything before 1905 can be considered “Classical” • Classical means “no quantum mechanics” and “no relativity” • Physics as a science could be tracked back to the greeks • Archimedes (buoyancy - things float) • Atoms (things cannot be made of nothing) • Geometry • “Cosmology” (science of entire universe)

4. Greek insights • The first “realistic” cosmology was derived by the greeks • Based on geometry: • Circumference of earth from distance to the horizon • Solar eclipses: size of the moon (1/4 earth) • Distance to the moon (60 earth radii) • Distance of the sun (much farther than moon) • Size of the sun (much bigger than earth)

5. Earth’s radius - the horizon Dhorizon • Greeks were sailors • They knew the earth was not flat: • You could sail beyond the horizon • They knew trigonometry • They measured the distance to the horizon • Earth’s radius Radius (6000km)

6. The size of the moon • Size of the moon: Lunar and solar eclipses (earth’s shadow is bigger than the moon’s) • Lunar phases: the sun is about 500 times farther than the moon

7. Greek cosmology • Sun and moon look like they are the same size • But the sun is 500 times more distant • It must be 500 times bigger than the moon • It must be 100 times bigger than earth

8. Greek cosmology • Sun is bigger than the earth • Earth is unlikely to be center of universe • Earth must be orbiting around the sun, not the other way around • If earth is nothing special, maybe the sun isn’t either • Maybe other stars are just like our sun?

9. Out of the dark ages... • Things were forgotten until Copernicus • First real modern breakthrough in astronomy: Tycho Brahe and Johannes Kepler • Precise measurements • A revision of theory • This is the scientific method

10. Science - what is and what isn’t • Makes testable predictions • If a prediction from a hypothesis is disproven, the hypothesis must be abandoned (it can be modified) • Experiments must be repeatable • Must not add features that are not required (this is called Okham’s razor) • Physics and astronomy are science • Evolution is science

11. A word on Astrology • Example (Hemisphere’s magazine) • Pisces (Feb 19 - March 20): • “You must be doing something right, because your financial picture looks rosy. Physically speaking, there’s no need to pretend you’re a superhero. Pace yourself. Around midmonth, lend an ear to those around you; allow ample time for those thoughts to seep into you subconsious” • This fails on all grounds

12. Some important things • Physics measures things • We measure distance, times, temperatures • We use those measurements to infer other things: • velocities (distance per time - how far can I travel in one hour?) • accelerations (velocity per time - how much faster will I be traveling in an hour?)

13. Kepler’s laws (1571-1630) • Planets orbit the sun on ellipses • Planets further out take longer (cube of the radius goes like the square of the time) • There is a relationship between how far away the planet is to how fast it is moving.

14. Saturn

15. Jupiter

16. Modern physics: • Newton could be credited with the invention of modern physics • He invented calculus (along with Leibniz), which is critical to almost all of physics • He formulated the first real theory of gravity • He invented mechanics (Newton’s laws) • He could explain Kepler’s laws

17. Gallileo (1564-1642): • Gravity is a force • Forces accelerate objects • Gravity accelerates objects • It accelerates all objects at the same rate!

18. Newton’s laws • Newtons first law • An object in motion stays in constant motion unless acted upon by a force

19. Newton’s laws • Newtons second law • A force accelerates an object and the acceleration is proportional to the force: • F=m*a • The constant m is the mass of the object Force

20. Newton’s laws • Newtons third law • An accelerated object exerts a force on the thing that is accelerating it with equal strength but opposite direction Force 1 Force 2

21. 1 3 1 1 Newton’s laws • Any object with mass M1 attracts any other object with mass M2, with a force that is • proportional to the masses (the heavier an object, the more attractive it is) • proportional to the inverse square of the distance (the further away you are, the less pull there is from the object) 2M M

22. Velocities • Consider a train with some velocity v

23. Velocities • Consider a train with some velocity v • Condider a car at rest on the train

24. Velocities • Consider a train with some velocity v • Consider a car atop the train moving backwards with the same velocity -v

25. Velocities • Consider a train with some velocity v • Consider a car atop the train moving forward with the same velocity v • It moves at twice the velocity, of course

26. Velocities • Newton and Gallileo tell us: • We are allowed to add velocities together • The car is moving twice as fast as the train • If the train is moving at the speed of light, the car is moving at twice the speed of light

27. Classical black holes

28. Escape speed • Newton predicts: massive objects have “escape speed” • If you throw a ball up, it will usually fall back down... • But: Rockets can escape earth’s gravity • Question: How fast do you have to throw the ball for it not to fall back? • Answer: 25,000 mph

29. Escape speed • The escape speed from an object is • proportional to square root of the planet mass • inversely proportional to square root of planet radius • e.g., moon: escape speed is 5,800 mph • e.g., sun: escape speed is 1,400,000 mph

30. Classical black holes • Rømer (1676): • Used Jupiter’s moons as a clock • Speed of light is finite (300,000 km/s) • Newton: • Light is a particle • presumption: it has mass

31. Classical black holes • Laplace (1795): • Make an object massive enough and small enough: escape speed faster than the speed of light • Light should not be able to escape • object would be completely dark. • It would be a “black hole”

32. No classical black holes: A particle faster than the speed of light could escape a “classical black hole”, so it would not be all-consuming. • Maxwell (1864): • Light is an electro-magnetic wave • Has no mass • No classical black hole

33. Special Relativity • Maxwell’s equations describe light as a wave • Waves propagate at some velocity • So: Light waves propagate at the speed of light • Symbol: c • c = 300000 km/s = 670000000 mph

34. Light waves

35. A moving light wave • Newton and Gallileo: • Consider a light wave moving with velocity c

36. A moving light wave • Newton and Gallileo: • Consider a light wave moving with velocity c • Consider a car moving with velocity v

37. A moving light wave • Newton and Gallileo: • Consider a light wave moving with velocity c • Consider a car moving with velocity v • To the car, the light is moving at velocity c - v

38. Michelson-Morley 1887

39. Michelson-Morley 1887 • The earth is moving around the sun with velocity v • We should be able to measure the speed of light as c-v • Experiment: Not so! • Conclusion: The speed of light is constant and always c

40. Maxwell vs. Newton • Maxwell’s theory of electro-magnetism agrees with constant, uniform c • Newton/Gallieo theory of mechanics does not agree with constant, uniform c