Black holes Introduction to astronomy and physics

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

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)

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)

Earth’s radius - the horizon Radius (6000km) 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 D horizon

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

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

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?

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

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

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

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?)

Kepler’s laws ( ) 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.

Saturn

Jupiter

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

Gallileo ( ): Gravity is a force Forces accelerate objects Gravity accelerates objects It accelerates all objects at the same rate!

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

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 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 1Force 2 Newton’s laws

Any object with mass M 1 attracts any other object with mass M 2, 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 3111 Newton’s laws

Velocities Consider a train with some velocity v

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

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

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

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

Classical black holes

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 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

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 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”

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

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 = km/s = mph

Light waves

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

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

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

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

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