(2) What was the actual motions in the models of (a) Ptolemy and (b) Copernicus that explained these apparent motions? Ptolemy argued that the loop was due to Mars having a circular orbit about the Earth, but also moving on a smaller circle - so that the net result is a looping, epicycle motion around the Earth. Copernicus argued that Mars and Earth orbitted the Sun on circles but the the retrograde motion is due to the Earth moving faster and closer to the Sun, overtaking Mars on the inside track.
(3) Why was the distance of the stars an important issue in resolving the geocentric vs. heliocentric issue? The lack of parallax motion of the stars could be explained by either the Earth being motionless (the geocentric view) or by the stars being very far (a necessary implication of the heliocentric view).
(4) Why did the early astronomers want to make the planets move in circles (rather than any other shapes)? It was entirely esthetic. They wanted the heavens to be perfect and circles seemed appropriately pure.
(5) Why did he not have musical tones for Uranus, Neptune or Pluto? These outer planets had not been discovered in Kepler's time.
(6) If the Sun is at one focus, what is at the other? Anything? NOTHING! It is just an empty location in space.
(7) Measure the Major Axis (A) and the Minor Axis (B) of each of your ellipses: The fattest and thinnest dimensions.
(8) What is the value of each of the Semi-Major and Semi-Minor Axes? Half the value of each of the Major and Minor Axes.
(9) Sketch ellipses with eccentricities of e = 0 and e=10. The first is a circle - the second a cigar.
(10) Halley's Comet has a very eccentric orbit (e = 0.983). It orbits between 35 and 0.6 A.U, being visible for only about a year, when it is inside about 2 A.U. How does Kepler's 2nd law of planetary motion explain that the comet spends most of its 76 year orbit outside 5 A.U. and only a couple of years inside 5 A.U.? Kepler's second law says that an object in orbit around the Sun (such as a comet) moves faster when closer to the Sun and slower when farther away. Since a comet is only visible when close to the Sun, it will spend a short time visible in the sky and then spend the rest of the time slowly moving along the parts of the cigar-shaped orbit far from Earth.
(11) (a) A new asteroid (called Redloub) is discovered with a roughly circular orbit of radius 3 A.U. Use Kepler's 3rd law to derive its orbital period (in years). Kepler's 3rd law says that the orbital period squared equals the cube of the semi-major axis. So, if we take the semi-major axis to be 3AU (same as radius for a circular orbit), cube it to make 3x3x3=27 AU3. This is equal to P2. So, P equals the square root of 27 = 5.2 years.
(12) The table below tests Kepler's 3rd law with current measurements of the planet's orbits. How accurate is Kepler's 3rd law? At which significant figure does the law fail? For which planet is it least accurate? Any guesses why? For all the planets except Pluto the values of P2 and a3 are close to equal - to 4 significant figures. Pluto has a high eccentricity, its orbit is poorly determined, and it is small so that it is more easily pushed and pulled about by the neighboring giant planets.
(13) How did these discoveries provide supporting evidence for the Copernican (heliocentric) universe rather than the Ptolemaic (geocentric) universe? Galileo's observations of the imperfections of the heavenly bodies (e.g. mountains on the Moon, sunspots on the Sun) suggested that they are not so perfect or devine - they are just objects which should obey the same as everyday objects on Earth. The discovery of the phases of Venus showed that the illumination of Venus was not consistent with Venus orbiting the Earth but had to be orbiting the Sun. The discovery of moons around Jupiter showed that not EVERYTHING orbited the Earth - perhaps only the Moon could be orbiting the Earth - like the moons of Jupiter.
(14) You take a trip from Boulder to Santa Fe, roughly 600 kilometers (km). You have exceeded the speed limit at times, going 140 km/hr, and you have been stopped by the police, during which time your speed was 0 km/hr. But you made the trip in 6 hours overall.
(b) You are driving a new Honda VX (it does 55 miles to the gallon!) and, for a small engine, it has good acceleration: You can accelerate from 0 MPH to 60 MPH (100 km/hr) in 8 seconds. Explain how this is a measure of acceleration. It is a change in speed with time.
(c) If you accelerate from 0 to 100 km/hr, at a constant acceleration for 8 seconds, it is pretty easy to believe that your average speed is 50 km/hr (just (0+100)/2). How far did you travel in those 8 seconds? At an average speed of 50 km/hr then in 1 hour you travel 50 km. In one second you travel 50km/60/60 = 50,000meters / 60 / 60 = 14 meters. In 8 seconds you travel 14 x 8 = 111 meters.
(16) Did the Copernican revolution take place overnight? If not, how long would you say it took? Why? Copernicus' book came out in 1543, Newton's Principia, published in 1687, pretty much put the last nail in the coffin of the Ptolemeic view. That's 144 years. (Though Galileo was not forgiven by the Pope until the 1980s. )
(17) Woops! There is a mistake in the lower picture - is this sunSET or sunRISE? The sun is just below the horizon and we are looking East. If it's looking at the Sun in the EAST then it much be sunRISE.
(18) Note that when Mercury is at greatest elongation, the Earth-Mercury-Sun angle is a right-angle.