| What were two practical uses of astronomy in the ancient world? Solution: Astronomy allowed ancient cultures to create calendars and predict yearly events, for example for the purpose of agriculture. It also facilitated navigation using the positions of the stars (as we learned in lecture 2). List 5 different ways to prove that the Earth is round. Solution: 1. The Earth casts a round shadow on the Moon during a lunar eclipse, no matter where the Moon is relative to the Earth. 2. People observe different stars in the south compared to the north. 3. When a ship leaves a port and sails into the ocean, we see it disappear below the horizon, instead of just appearing smaller and smaller. 4. There are numerous photos and videos of Earth from all angles, taken from space, which clearly show that the Earth is shaped like a sphere. 5. More objects can be seen at higher altitudes compared to lower altitudes. What is stellar parallax? How did this concept lead the Greeks to believe, incorrectly, that the Sun was moving around the Earth? What information were they missing to conclude that the Earth actually moves around the Sun? Solution: Stellar parallax is a shift in the apparent direction of a star due to the Earth moving along its orbit. The same star should appear at slightly different places in the sky when the Earth is on one side of the Sun (e.g. in January) compared to the other side (e.g. in July). When the Greeks tried to observe this effect, they did not see it, and thus they deduced that the Earth does not move around the Sun. The information they were missing is that the stars are many light-years away, and therefore this effect is extremely small, and measuring it requires more precise instruments than they had at the time. How did Eratosthenes measure the circumference of the Earth? (Describe the experiment in words, there's no need to explain the math, unless you want to.) Solution: Eratosthenes observed that when the Sun was directly overhead (at the zenith) in one city, it was slightly south of the zenith in another city, as measured by the shadow of a stick. Using the difference in the angles of the Sun's ray at each city, and the distance between the cities, he was able to calculate the circumference of the Earth. What is precession? Why does it cause stars to appear to move around in the sky over many thousands of years? Solution: Precession is the slow change in the direction of the Earth's axis over time, similar to the slow change in the axis of a spinning top as it spins. The direction of the axis completes a full circle in approximately 26,000 years. Since the axis points in different directions over this time, we also see the stars in different places in the sky. Astrologers (but not astronomers) assign special significance to dates when planets move "in retrograde". Do the planets actually move backwards when this happens? If not, what causes this motion? Does it have any special significance? Solution: No, the planets don't actually move backwards. They always move in one direction in their orbits (counterclockwise when viewed from the north pole) and they never stop or change direction. The reason planets sometimes appear to move "in retrograde" is simply because at that time the Earth is passing by that planet, just like when you pass by a slower car it looks to you like it's moving backwards from your perspective. This motion is just an illusion, it does not have any special significance. What are epicycles? What problem did Ptolemy attempt to solve when he introduced them? Did they solve the problem? Solution: In Ptolemy's model, instead of the planets orbiting the Earth in large circular orbits, they orbit around a small circle called an epicycle, and that circle itself orbits the Earth in a large circle. Epicycles were needed because Ptolemy's model was incorrect: the Sun should be at the center, not the Earth, and the orbits should be elliptical. Because the model was incorrect, its predictions did not match observations. In particular, it could not explain retrograde motion. However, by adding epicycles, which provided additional parameters that can be tweaked, Ptolemy managed to make the model fit the observations. So in that sense the problem was solved, but only temporarily - after some time, the model again did not match observations. It is interesting to note that pretty much any incorrect theory can be made to fit all the existing observations if we add enough adjustable parameters to it, but this is bad science, because usually, making more precise measurements results in the adjusted theory again failing to fit observations. To this day, the term "epicycles" is used to describe such bad science (another term is "ad hoc hypothesis"). What are two ways in which Ptolemy's model of the solar system is incorrect? Solution: 1. Ptolemy's model assumes that the Earth is at the center and the Sun, Moon, and planets orbit around it. In reality, the Sun is at the center, the planets (including the Earth) orbit around the Sun, and only the Moon orbits the Earth. 2. Ptolemy's model assumes that the orbits of the celestial bodies are perfect circles. In reality, they are ellipses. |