Phys 171 Midterm Review

Scientific Reasoning

• A scientific hypothesis should be falsifiable.
• A successful scientific hypothesis should be consistent with previously accepted theories and or experimental results.
• A scientific hypothesis should have predictive power.
• Science prefers simpler and/or "more elegant" hypotheses.
• Experiments and observations are the final arbiter of scientific questions. A scientific theory must make successful predictions of experimental or observational results in order to be believable.

Brahe, Kepler, Galileo, and Newton

• Brahe's main contributions were his accurate observations which laid the observational foundation for Kepler's laws and his rejection of Aristotelean dogma when contradicted by observational evidence.
• Kepler's main contribution was his laws of planetary motion:
  • The planets orbit in elliptical paths with the Sun located at one focus of the ellipse.
  • A planet speeds up when it is closer to the Sun such that the "pie shaped" area swept out by the line connecting the planet to the Sun traces out equal areas in equal times.
  • A planet which is closer to the Sun will have an orbital period that is shorter than the orbital period of a more distant planet. The orbital radius (or semi-major axis) cubed times the period squared is a constant.
• Galileo's accomplishments included:
  • The "establishment" of the scientific method.
  • The first use of the telescope as an astronomical instrument which led to discovery of mountains and craters on the moon, thousands of stars invisible to the naked eye, sunspots, Venus' phases, Saturn's "ears" (now known to be rings), the 4 large moons of Jupiter, the observable angular size of the planets, and the fact that the Milky Way is composed of many thousands of faint stars.
  • His famous book: "A Dialog on the Two Chief World Systems, Copernican and Ptolemaic" which helped establish the correctness of the Copernican model but also led to Galileo's arrest and incarceration by the Roman Catholic Church.
• Newton is generally considered (by physicists, at least) to be the greatest scientist that ever lived. His accomplishments included:
  • The theory of dynamics which explains the motion of bodies and forces.
  • His universal law of gravitation which explained both terrestrial gravity and the forces affecting celestial bodies with a single theory. One puzzle was the concept of "action at a distance" that this theory required.
  • The invention of the reflecting telescope.

Distance Measurements

• The size of the Earth and the distance to the moon can be determined
• The measurement of stellar parallax allowed the accurate determination of the distances to nearby stars.
• The distances of more distant objects can only be determined if we have some physical understanding of what they are.

Electromagnetic Radiation and Atoms

• electrons in atoms have decrete energy levels
• only one electron is allowed in each "state"
• spectral lines are caused by photon emission or absorption when an electron changes energy levels.
• spectral lines can be seen in emission when observing a diffuse hot gas
• spectral lines can be seen in absoption when observing a diffuse backlit gas
• a solid or dense gas radiates a continuous spectrum of radiation.
  • this radiation has the "black body" form
  • with _max proportional to 1/T (temperature).

Stellar and Galactic Astronomy

• The use of spectroscopy in astronomy allowed astronomers to determine both the chemical composition and the radial velocity of distant astronomical objects. Students should know how this works and they should know about the Doppler effect.
• Normal stars are supported by the pressure generated by the heat from nuclear reactions
• "Dead stars"
  • electron or neutron degeneracy pressure gives a maximum mass which controls the fate of "dead stars"
  • stars like the Sun die as white dwarfs supported electron degeneracy pressure.
  • more massive stars explode as type II Supernovae
  • Type I supernovae are caused by the explosion of white dwarfs in binary star systems.
• Cepheid variable stars were found to be a particularly useful distance indicator through the Cepheid "period-luminosity" relation.
• Using Cepheid variable stars discovered in nearby Galaxies, Hubble discovers that spiral nebulae are actually external galaxies. Spectra of these external galaxies leads Hubble to propose "Hubble's law" which states that galaxies are receding from us at a velocity proportional to their distance.

Einstein's Theory of Gravity

• the speed of light is the "universal speed limit"
  • space-time diagram: only the "past" light-cone can affect a space-time point.
• General Relativity: Einstein's Theory of Gravity
  • Equivalence Principle: gravity = acceleration
  • curved space-time
  • explains details of Mercury's orbit
  • gravitational redshift
  • gravitational bending of light rays
• Black Holes
  • escape velocity > c (the speed of light)
  • Event Horizon at the Schwartschild Radius, R_sch
    • Light rays emitted from inside the event horizon cannot escape.
    • Observer will have no escape once inside the event horizon.
    • Observer may not notice falling through the event horizon unless the black hole is small so that tidal forces are large.
    • An outside observer never sees anything move beyond the event horizon.
  • singularity: a black hole's mass is all at this point
  • photon sphere: at R = 1.5 R_sch light rays are bent so that photons can orbit the star in circular orbits.
  • Dead stars with masses above 3M_sun are too massive to be neutron stars, and so they are expected to become black holes. (Note that stars more massive than 3M_sun do often create neutron stars because most of their mass is lost in a supernova explosion.)
  • Black holes can be very bright because the matter falling into them can release a lot of energy.
  • The centers of most galaxies are thought to have black holes of 10⁶ - 10⁸ M_sun.

The Expanding Universe

• Hubble discovered the apparent expansion of the Universe.
  • velocities easy to determine
  • distances difficult
• Interpretation of Hubble's result
  • expansion with no center
• Cosmology with Einstein's Theory of gravity
  • predicts expanding or contracting Universe
  • Einstein fudged with "cosmological constant"
• homogeneous and isotropic - assumptions
• Olber's paradox

Possible Calculation Problems

• The equation describing the relationship between brightness, luminosity, and distance:
  • The 1/d² dependence of brightness on distance, d, is the crucial feature.
• The equation for the Doppler shift of light given in the class notes for Thursday, Feb. 25.