Questions on Early Models of the Universe

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  1. What differentiates the models developed by the Ionians from earlier, prehistoric conceptions of the Universe?

    The Ionians, an early school of classical Greek philosophy, removed the need for supernatural or mystical explanations for the Universe and tried to develop explanations based on reason and natural and observable events.
  2. Identify three observations that any mechanistic model of the Universe has to account for.

    1. The observed daily motion of the Sun across the sky. 2. The phases of the Moon. 3. The motion of the stars, fixed relative to one another, across the sky at night. (There are numerous other ones possible including retrograde motion of the planets, why Venus and Mercury are always near the Sun and changes in brightness of the planets).
  3. What is meant by the retrograde motion of the planets?

    Retrograde motion refers to the apparent backward path that planets sometimes take across the celestial sphere, that is relative to the background of fixed stars.

    Retrograde motion of Mars in 2003.
    Credit: Image was generated using Starry Night Pro software.
    Figure 1.1 From mid-July to mid-September 2003 the planet Mars appeared to backwards relative to the stars on the celestial sphere. This is an example of retrograde motion.
  4. How would an observer in antiquity have distinguished a planet from a star?

    Planets move over time relative to the background of fixed stars. Indeed this is where the term "planet" originates, from the classical Greek for "wanderer". Planets also change in brightness over time. Visually, planets sometimes appear to "twinkle" less than stars when close to the horizon.
  5. Describe one of Pythagoras' contributions to the advancement of our understanding in astronomy.

    Pythagoras and his followers used geometry in their models and measurements. They also emphasised the importance of the sphere as a shape in the heavens.
  6. In what way was the model developed by Aristarchus fundamentally different from that of his contemporaries?

    Aristarchus' model placed the Sun at the centre of the Universe and was thus heliocentric. Other models in antiquity were either geocentric or geostatic.
  7. Explain how Aristarchus' model could account for:
    1. Day and night on Earth.
    2. Why Venus always appeared near the Sun
    3. The Retrograde motion of planets.

    1. Day and night were caused by the fact that the spherical Earth rotated once on its axis every 24 hours. As a given point on its surface moved around, it swept past the Sun which thus appeared to move overhead.
    2. Venus' orbit was closer to the Sun than that of Earth. An observer on the Earth therefore always saw Venus close to the Sun as an imaginary line form Earth to Venus must pass near the Sun.
    3. Retrograde motion was explained by the relative motion between the Earth and the planet being observed. Sometimes Earth would be moving around the Sun faster in a prograde direction than the other planet which would therefore appear to move backwards relative to the background fixed stars.
  8. Outline two reasons why Aristarchus' model was rejected by his contemporaries?

    1. In Aristarchus' model the Earth must be moving. Common sense tells us that the earth does not move and we do not feel it moving.
    2. His model predicts annual stellar parallax. This was not observed (nor could it have been given the technology available at the time).
  9. Summarise Plato's contributions to the development of cosmology and models of the Universe.

    Plato founded the Academy, a forerunner of modern universities and had Aristotle and Eudoxus as students. He viewed the Universe as eternal and unchanging. Divine, eternal stars were fixed on a rotating sphere. Heavenly motions were circular and the sphere was the perfect shape. Models only needed to "save appearances" and were always destined to be dim representations of the "real world" which therefore could never properly perceive.
  10. How did Aristotle's ideas of motion explain planetary motion?

    Planets orbited the Earth on combinations of rotating transparent, crystalline spheres. They were beyond the sub-lunary sphere thus all their motion was circular and "unforced".
  11. Suggest a reason why Aristotle's model was able to be incorporated into Western Christian theology.

    Aristotle had the Earth at the centre of the Universe, that is a "special place". The heavens were perfect and unchanging whilst Earth was subject to decay and corruption.
  12. What device/s did Ptolemy use to explain retrograde motion?

    Ptolemy used a combination of epicycles and deferents to explain retrograde motion. The diagram below shows this: A planet orbits point x in a circular path called the epicycle. The deferent is the circular path that point x takes around the centre of motion, C.

    The epicycle, deferent and eccentric as used in Ptolemy's model.
    Credit: R. Hollow CSIRO
  13. State three reasons why Ptolemy's model lasted for so long.

    1. It worked, ie it could be used to predict planetary positions to within 2°.
    2. It was theologically acceptable as the Earth was near the centre of all motions.
    3. It accounted for the observed planetary motions, retrograde motion and variations in brightness.
  14. Describe one contribution of Islamic astronomers prior to Copernicus?

    Islamic astronomers, apart from making their own observations, preserved and translated many of the original classical Greek manuscripts into Arabic, thus saving them from destruction so they were later available to Western European scholars.
  15. What reason did Copernicus provide for the failure of astronomers to observe any annual stellar parallax?

    Copernicus stated that the stars must be much further away from us than previously believed hence the parallax of a star would too small to be detected.
  16. Compare Copernicus' model with that of Ptolemy.

    There were several advantages of Copernicus' model over that of Ptolemy:

    1. It could predict planetary positions to within 2°, the same as that of Ptolemy.
    2. Retrograde motion of planets was explained by the relative motion between them and the Earth.
    3. Distances between planets and the Sun could be accurately determined in units of the Earth-Sun distance (ie Astronomical Units).
    4. Orbital periods could be accurately determined.
    5. It explained the difference between the inferior planets (Mercury and Venus) that were always observed close to the Sun and the superior ones (Mars, Jupiter and Saturn).
    6. It preserved the concept of uniform circular motion without the need for equants.
    7. It preserved Aristotle's concept of real spheres nestled inside one another.
    8. Unlike Ptolemy's model it did not require the Moon to change in size.

    Copernicus' model also had several problems which contributed to its failure to immediately supplant Ptolemy's model:

    1. No annual stellar parallax could be detected. Copernicus explained this as due to the fact that the stars were a vast distance hence any parallax would be very small and difficult to detect.
    2. It required a moving Earth, This would contradict Aristotelian physics and Copernicus presented no new laws of motion to replace Aristotle.
    3. By removing the Earth from its natural place it was philosophically and theologically unacceptable to many scholars.
    4. It was no more accurate than Ptolemy's in predicting planetary positions.
    5. It was actually more complicated then Ptolemy's model. In his efforts to avoid the equant but retain uniform circular motion he had to introduce more devices to fit his observations.
  17. What techniques allowed Tycho Brahe to make such accurate observations with the unaided eye?

    Brahe built a dedicated observatory that contain purpose-built, state-of-the-art instruments. His instruments were large and made of quality wood and brass. Their size and rigidity enabled him to have accurate scales on them. He was a careful, methodical observe who spent years studying and recording the night sky.
  18. What was Brahe's most important contribution to the development of models of the Universe?

    His accurate, detailed, long-term records of observations of planetary motions, particularly that of Mars. They were used by Kepler to determine the true nature of planetary orbits.
  19. Why was Kepler's first law of planetary motion so radical?

    By showing that planets all orbited the Sun in elliptical, not circular, orbits Kepler overthrew more than two thousand years of the pervasive use of circular motion as espoused by Plato and subsequent philosophers.
  20. State Kepler's three laws of planetary motion?

    1. Kepler's 1st Law: The Law of Ellipses.
      All planets orbit the Sun in elliptical orbits with the Sun as one common focus.

      Kepler's 1st Law: The Law of Ellipses.
    2. Kepler's 2nd Law: The Law of Equal Areas.
      The line between a planet and the Sun (the radius vector) sweeps out equal areas in equal periods of time.
      In the diagram, the time interval t2-t1 = t4-t3 so the areas swept through in equal times are equal,
      that is A1 = A2.
      Kepler's 2nd Law: The Law of Equal Areas.
    3. Kepler's Third Law: The Law of Periods or the Harmonic Law*.
      The square of a planet's period, T, is directly proportional to the cube of its average distance from the Sun, r

      or T2/r3 = k (1.1)
      where k is a constant and the same for all planets or orbital bodies (such as comets) in a given system.
  21. Identify one of Galileo's key observations with the telescope and explain how it undermined the Aristotelian-Ptolemaic system?

    Galileo observed four small stars near Jupiter. Systematic observations over many nights showed that these orbited around Jupiter and were in fact moons of Jupiter, much like our Moon orbits Earth. By showing otherwise invisible moons orbiting another object in the Universe Galileo showed that the Earth was not the centre of all motions as which contradicted Aristotle's ideas.
  22. How did Galileo's work on motion help demolish Aristotle's physics?

    Galileo rejected Aristotle's ideas of forced and natural motions after studying falling or rolling objects and projectiles and realised that gravity was some type of force acting in terrestrial situations. By rolling objects down planes he was able to study them in more detail than if they just fell. He realised that objects do not need a force to be continuously applied to keep them moving.
  23. Explain the importance of Newton's Principia.

    In his Principia Newton provided the groundwork for the science of dynamics through his three laws of motion. He then went on to describe this law of universal gravitation.He provided a rigorous mathematical foundation for his laws and showed that they applied equally to motion on Earth and in the heavens.
  24. Outline one of the early successes of Newton's Law of Universal Gravitation?

    Newton's law could successfully account for Kepler's Third Law (Law of Periods). It was also used by Halley to successfully predict the return of a comet that would thereafter be known as Comet Halley.
  25. How did Newton improve the telescope?

    Newton developed a reflecting telescope that used a parabolic primary mirror and a secondary reflecting mirror. Refracting telescopes used lenses that produced chromatic aberration when viewing bright objects. Mirrors such as those Newton used are not sunject to this aberration. Today all large optical telescopes are variations on reflecting rather than refracting telescopes.