Quiz 1 Study Guide Astronomy 1101: Planets to Cosmos Astronomical Numbers, Scientific Notation, Metric system, Weight vs. Mass The Night Sky: The Constellations, true motions of the stars in the galaxy Measuring the Earth Aristarchus's derivation of the distance to the Moon and the distance to the Sun. Example of early heliocentrism The Spherical Earth Appeal to perfect symmetry Aristotle's arguments The circumference of the Earth Method of Eratosthenes Ptolemy's estimate and its influence Daily & Annual Motions Motions due to Earth's Daily Rotation, and due to Earth's orbit around the Sun. The latter gives us a different persepctive on the Sun and planets with respect to background stars. Motions of the inferior planets: always tied to the Sun Motions of the superior planets: not tied to the Sun Retrograde Motion: What is it, when does it occur for different planets? The Phases of the Moon The moon rotates synchronously: it rotates once for every orbit around the Earth. Main Phases of the Moon: Moonrise & Moonset times at the different Moon phases The orientation of the Earth-Moon-Sun system in different phases. Some important equations: F = ma (Newton's 2nd law) P^2 = a^3 (Kepler), and Newton's generalization. V_circ = (G M / r)^1/2 (M is the central mass, r is the distance to its center) V_escape = 2^1/2 V_circ (velocity needed to escape the gravity of a body) a_1/a_2 = M_2/M_1 (determines center of mass between M_1 and M_2) L = m v r (the angular momentum of a body in orbit is conserved: L = constant) In practice, I am more likely to ask you a question like "All else being equal, if the mass of a body increases, its escape velocity _____" (A) increases (B) decreases (C) stays unchanged than I am to ask you about the actual scaling of the escape velocity equation. Nevertheless, I will sometimes put in harder questions that ask you about the scaling, and the consequences of an equation. For example, "All else being equal, if the mass of a body were to increase by a factor of 4, its escape speed would (A) increase by a factor of 2. (B) increase by a factor of 4. (C) decrease by a factor of 2. (D) decrease by a factor of 4 Short review of gravity and orbits: Two bodies with masses M1 and M2 are separated by a distance d. If M1 increases by a factor of 4, the force increases by a factor of ____. If M2 increases by a factor of 4, the force increases by a factor of ____. If d increases by a factor of 4, the force decreases by a factor of ____. If d decreases by a factor of 4, the force increases by a factor of ____. The above can be understood knowing the equation F = G M1 M2 / d^2. Two bodies with masses M1 and M2 are in a gravitationally bound orbit. All else held equal, if either M1 or M2 increases, the period of the orbit ____. A small asteroid is in orbit around the Sun with semi-major axis A and period P. All else being equal, if A is increased by a factor of 4, the P increases or decreases by a factor of 2, 4, 8, 16, 32? Aristotelian World View Assumptions (uniform circular motion, fixed unmoving earth) Early Geocentric Systems Eudoxus, Pythagoras, Aristotle Epicyclic Systems Hipparchus & Ptolemy Early Heliocentric System Aristarchus Ptolemaic Geocentric System Epicycles and so on. Preserving Appearances - especially the retrograde motion & change in brightness of superior planets at "opposition." Opposition is when we are closest to asuperior planet in its orbit. It is the same configuration for the superior planet as it is for the Full Moon: The planet, the Earth, and the Sun lie on a line, in that order. Problems: complex, no way to measure planetary distances with epicycles. Copernicus Motivations & Assumptions (disliked equant, wanted to **restore** Aristotelian ideal of uniform circular motion) Copernican Heliocentric System Sun at the center! Earth rotates on its axis every 24 hours! Earth orbits (revolves) around the sun once a year! His use of epicycles and why he used them. Successes: a) explains superior & inferior planets b) explains retrograde motion c) gives a geometric way to measure planetary distances Problems: (a) the Earth is not apparently moving (b) stellar parallaxes are not observed Should they have been able to measure stellar parallaxes at that time? (c) stars do not get brighter at "opposition" It is true that we do get a bit closer to and farther away from certain stars as we orbit the Sun, but the effect is TINY since the stars are actually so far away. Tycho Brahe: his observations & their significance Johannes Kepler: his theoretical work & its significance Kepler's Three Laws of Planetary Motion First Law Second (Equal Areas) Law Third (Harmonic) Law Galileo's telescope observations & their significance The Moon Sunspots Phases of Venus Moons of Jupiter Isaac Newton: work and its significance Laws of Motion First Law (Law of Inertia) Second Law (F=ma) Third Law (Action & Reaction) Newtonian Gravity Inverse-Square Law Force Dependence of the gravitational force on masses and distance of the two bodies. Newton's Generalized forms of Kepler's Laws Shapes of Orbits Orbit about the Center of Mass Circular and Escape Velocity Measuring Masses with Newton's form of Kepler's 3rd Law Gravitational Interactions among objects What is Stellar Parallax? General Solar System --------------------- Names of the 8 planets Dwarf Planets Order of planets in the Solar System Main types of planets & other bodies Extrasolar Planetary Systems ---------------------------- Searches for planets around other stars Doppler Wobble Planetary Transits Extrasolar planetary systems Jupiter-sized planets close to their parent stars Prospects for finding Earth-like planets Basic conditions for Life The Habitable Zone