Tutorial 8 As we approach the final exam, the following is a collection of problems taken from past papers. A great strategy is to only skip the ones in which you feel most confident and to ask for help for the ones about which you are less sure. Please also note, that there are 70 Review Questions in ‘Our Place in the Universe”, following Appendix L, (Pg 241 in the Print Edition). Discussion of solutions will appear on Moodle only after the final tutorial as it is much more useful to attempt the to answer these questions when a solution is unavailable. 2020 Tycho Brahe is remembered for his careful measurements of objects in this sky, including the Great Comet of 1577, and for his popular model of the solar system in which Mercury, Venus, Mars, Jupiter and Saturn orbit the Sun while the Moon and Sun orbit the Earth. Why do you think he chose to propose this model instead of accepting Copernicus’ model in which the Earth also orbits the Sun? Tycho Brahe was a careful observer of the sky and was known to challenge existing notions about the structure of the universe as evidenced by his observations and conclusions regarding the a new star (nova) in 1572 and a comet in 1577. Because of this, it may seem counter-intuitive that he was unwilling to accept Copernicus’ model. The Copernican and Tychonic systems are very similar. The major difference being whether the Earth was in motion. As a careful observer, one might speculate that Tycho sought evidence of the Earth’s movement by looking for changes in our perspectives on stars (parallax) over the course of a year. No such change would be able to be observed with technology available to him, (or anyone for the next few centuries). Tycho seemed able to dismiss the notion that the celestial bodies were seated in immutable or unchanging spheres composed of ether when his observations seemed to contradict that notion. However, without observations in support of the Earth’s motion, he seems unable to reject that the Earth is fixed. 2019 What evidence supports the understanding that all objects in the sky are made up of the elements found on the periodic table? In what ways is this important to our current understanding of the structure of the universe? The biggest tool to support this is the use of spectroscopy in astronomy. Spectroscopy makes use of atomic and molecular fingerprints to identify the chemistry of distant objects. Once we know the chemistry of those objects we can use our understanding of physics on Earth to develop ideas about star formation, solar system formation, galaxy formation etc. 2017 Galileo’s telescopic observations helped heliocentrism gain wider support amongst astronomers and the educated in Europe. Do any of his observations disprove geocentrism? If so, how? If not, in what ways do they lend support to a heliocentric model. None of Galileo’s telescopic observations directly contradict the notion that the Earth is the unmoving center of the solar system. In fact, evidence of the Earth moving only comes much later. However, geocentrism as modelled in the tradition of Ptolemy was based on an understanding of the structure of the cosmos going back to Aristotle. • • • • • From the phases of Venus, we must conclude that the Sun is in the center of Venus’ epicycle. The phases of Venus are easily explained if it orbits the Sun. If the Earth is the center, why does Venus orbit the Sun (which in turn orbits the Earth)? If the Sun is the center, there’s no need to answer this question. The moons of Jupiter also fit more easily into the Copernican idea. Our moon orbits the Earth in the same way Jupiter’s moons orbit Jupiter. In a geocentric idea, you’re left with the question of why those other planets are central for other celestial objects. Whatever adaptation would allow Venus to orbit the Sun could probably also allow for Jupiter, and later other planets, to have moons. However, this explanation is getting complicated. The surface of the moon has features as if it is made of dirt and rocks, (the element earth). Aristotle tells us that the reason that celestial objects have predictable patterns is due to their nature as objects made of ether constructed in perfect spherical shells. The reason why the Earth is in the centre, is that the nature of earth (the element) is to tend towards the centre. If the Moon is made of earth, why does it not have this tendency? If it is still made of ether, they why does it have surface features? In Copernicus’ system, these questions need not be asked. The moon has a sphere around the Earth as the Earth has a sphere around the Sun. Similarly, spots appearing on the Sun’s surface contradict the nature of ether as it was understood. Also, these spots change their appearance in time. The nature of ether should be that it is perfect and unmutable (unchanging). Observing stars not visible to the naked eye, may have the least to say about geocentrism, but it does begin to etch away at the concept of the celestial sphere of fixed stars. Maybe we can’t see them because they are further away? None of these in isolation would be so much to adapt, but it seems in face of all of this together that the time for putting the old ways aside is come. From a practical sense, it’s becoming simpler to accept heliocentrism than to come up with new justifications for geocentrism in light of new evidence. [The bullet points may not be required for a high scoring answer. A good strategy would be to discuss that they challenged Aristotelian physics and that geocentrist would be forced to adapt to new evidence in some ways and then perhaps choose one or two of the bullet points to illustrate how that would be the case.] Kepler’s Laws provide a model of planetary motion that can be very precise for predicting the motion of celestial objects. How do Newton’s Laws improve and expand this model? Since Kepler’s Laws are a computable consequence of Newton’s Laws, they predict the exact same motion of planets in our solar system. From a complexity standpoint, Kepler’s Laws are probably simpler to work with. If that were the end of it, people would just take Kepler’s Laws. However, identifying gravity as the cause of the motion, not only of planets but also objects on the earth, greatly increases the range of applicability. Kepler’s Laws are a consequence of gravity. Gravity is also what keeps us on the Earth. This represents a huge expansion in terms of ‘range of applicability’. The physics of Universe is just that, universal. In what ways did the invention of the spectroscope contribute to the modern dogma of our view of the universe? What the Newtonian Synthesis does for physics and motion, the spectroscope does for chemistry. Knowing the chemical composition of faraway objects allows us to create models of how stars work and change, how they are born and how they die. Since we cannot create a star in the laboratory nor can we visit one and take samples, these molecular fingerprints found in the spectra of objects are the only evidence we have on which we build up all of astrophysics. 2015 Our sense of a year is defined by the seasons. If there were no obliquity of the ecliptic (i.e., the celestial equator is aligned with the ecliptic), how would our ancestors develop a sense of a year? How would they measure the length of the year? Start by drawing a two-sphere model as it exists. Note that the seasons are caused by the sun’s annual motion on the ecliptic. The northernmost point of the ecliptic is the Summer Solstice and the Equinoxes correspond to the intersection between the ecliptic and the celestial equator. If the angle between the ecliptic and the celestial equator (obliquity) becomes zero, then it is always an Equinox. Thus there is no seasonal effect. However, the sun still has two motions! It will still move relative to the stars and it will still take a year to travel around the ecliptic. Thus years may be tracked by the stars. The ecliptic (now the same as the celestial equator) can be divided up into constellations to form a new zodiac to help track the calendar. However, one might speculate that such a society might use a purely lunar calendar. Some cultures here use a lunar calendar and they typically come from regions where the seasons are not dramatically different. Give several pieces of evidence to support the statement that "the Sun is a star". What are the philosophical and religious implications of this statement? • • • After using parallax to measure the distance to stars, we can learn how bright they actually are based on how they appear to be. Many stars have brightness (luminosity) that is similar to our sun. Looking at spectra, the spectra of other stars are not all the same as our sun but they are often similar, later fitting into a “main sequence”. In recent years, we’ve been able to observe planets around many stars. Everywhere we look, stars are plentiful. They have come to be established as the basic astronomical building block. That is, stars are the most ordinary kind of object in the cosmos. If our sun is a star, then our home can also be believed to be the most ordinary sort of location in the cosmos. This is the philosophical consequence, that there is nothing special or unique about our place in the universe. This may lead many to question the idea of our existence being designed. If we are the special creation of the Creator, then why are we located here and not in some special place? What was God thinking to put us in such an arbitrary position? That’s not to say there are no reasonable religious answers to these questions, but anything that casts doubt on faith may threaten religion. In places where religious and political power are intertwined, this can be a rebellious act. Perhaps this is why Giordano Bruno was burned alive for the audacity of suggesting that the Sun is a star.
