Question 2.1

Who wrote down the equation for the law of gravitation?

• a. Copernicus
• b. Tycho
• c. Newton
• d. Galileo
• e. Kepler

Question 2.2

Which of the following most accurately describes the shape of Earth’s orbit around the Sun?

• a. circle
• b. ellipse
• c. parabola
• d. hyperbola
• e. square

Question 2.3

Of the following planets, which takes the longest time to orbit the Sun?

• a. Earth
• b. Uranus
• c. Mercury
• d. Jupiter
• e. Venus

Question 2.4

What is a Sun-centered model of the solar system called?

Question 2.5

How long does it take Earth to complete a sidereal orbit of the Sun?

Question 2.6

How did Copernicus explain the retrograde motions of the planets?

Question 2.7

Which planets can never be seen at opposition? Which planets never pass through inferior conjunction?

Question 2.8

At what configuration (superior conjunction, greatest eastern elongation, etc.) would it be best to observe Mercury or Venus with an Earth-based telescope? At what configuration would it be best to observe Mars, Jupiter, or Saturn? Explain your answers.

Question 2.9

What are the synodic and sidereal periods of a planet?

Question 2.10

What are Kepler’s three laws? Why are they important?

Question 2.11

In what ways did the astronomical observations of Galileo support a heliocentric cosmology?

Question 2.12

How did Newton’s approach to understanding planetary motions differ from that of his predecessors?

Question 2.13

What is the difference between mass and weight?

Question 2.14

Why was the discovery of Neptune a major confirmation of Newton’s universal law of gravitation?

Question 2.15

Why does an astronaut have to exert a force on a weightless object to move it?

Question 2.16

From the definition KE = ½mv², derive the equation KE = p²/2m, as discussed in An Astronomer’s Toolbox 2-2.

Question 2.17

* Convert:

• a. 8.3 pc (parsec) into light-years
• b. 6.52 ly into parsecs
• c. 8450 AU into kilometers
• d. 2.7 × 10³ Mpc into kiloparsecs

Question 2.18

Is it possible for an object in the solar system to have a synodic period of exactly 1 year? Explain your answer.

Question 2.19

Describe why there is a systematic decrease in the synodic periods of the planets from Mars outward, as shown in Table 2-1.

Question 2.20

* A line joining the Sun and an asteroid was found to sweep out 5.2 square astronomical units of space in all of 2012. How much area was swept out in 2013? In the five years from 2008 to 2013?

Question 2.21

* A comet moves in a highly elongated orbit (e ≈ 0.95) around the Sun, with a period of 1000 years. What is the length of the semimajor axis of the comet’s orbit? Referring to Figure 2-8b, estimate the farthest distance that the comet can travel from the Sun.

Question 2.22

* The orbit of a spacecraft around the Sun has a perihelion distance of 0.5 AU and an aphelion distance of 3.5 AU. What is the spacecraft’s orbital period?

Question 2.23

Make diagrams of Jupiter’s phases as seen from Earth and as seen from Saturn.

Question 2.24

In what direction (left or right, eastward or westward) across the celestial sphere do the planets normally appear to move as seen from Australia? In what direction is retrograde motion as seen from there?

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Question 2.25

The dictionary defines astrology as “the study that assumes and attempts to interpret the influence of the heavenly bodies on human affairs.” Based on what you know about scientific theory, is astrology a science? Why or why not? Feel free to further explore astrology, if you wish, before answering this question.

Question 2.26

Which planet would you expect to exhibit the greatest variation in apparent brightness as seen from Earth? Explain your answer.

Question 2.27

Use two thumbtacks (or pieces of tape), a loop of string, and a pencil to draw several ellipses. Describe how the shapes of the ellipses vary as you change the distance between the thumbtacks.

Question 2.28

* Earth were 2 AU from the Sun? What would be the length of the year? Assuming that such physical properties as rotation rate were as they are today, what else would be different here?

Question 2.29

* Earth were ½ AU from the Sun? What would be the length of the year? Assuming that such physical properties as rotation rate were as they are today, what else would be different here?

Question 2.30

* Earth were 10 AU from the Sun? How much stronger or weaker would the Sun’s gravitational pull be than it is on Earth today?

Question 2.31

* Earth had twice its present mass? Assume that all other properties of Earth and its orbit remain the same. What would be the acceleration of the more massive Earth due to the Sun compared to the present acceleration of Earth from the Sun? Hint: Try combining F = m₁a and the force equation in An Astronomer’s Toolbox 2-3, where m₁ is the mass of Earth in both equations. Given that acceleration determines the period of the planet’s orbit, how would the year on the more massive Earth compare to a year today?

Question 2.32

The Sun suddenly disappeared? What would Earth’s path in space be in response to such an event? Describe how Earth would change, as a result, and how humans might survive on a Sunless planet.

Question 2.33

The skies of Earth were perpetually cloudy? How might that have changed the history of our understanding of the cosmos, and how might humans under such conditions eventually learn what is really “out there”?

Question 2.34

Scientists remained believers in the first theory of the cosmos that they decided was correct? How might that change the dynamics by which science evolves in the face of new data that conflict with earlier theories?

Question 2.35

Search the Web for information about Galileo. What were his contributions to physics? Which of Galileo’s new ideas were later used by Newton to construct his laws of motion? What incorrect beliefs about astronomy did Galileo hold?

Question 2.36

Search the Web for information about Kepler. Before he realized that the planets move on elliptical paths, what other models of planetary motion did he consider? What was Kepler’s idea of the “music of the spheres”?

Question 2.37

Search the Web for information about Newton. What were some of the contributions that he made to physics other than developing his laws of motion? What contributions did he make to mathematics?

Question 2.38

A comet coming inward from the Kuiper Belt, outside the orbit of Neptune, experiences a gravitational force from the Sun. Does the presence of the planets affect the comet’s orbit? Explain your reasoning.

Question 2.39

How would the weight of an astronaut on the Moon compare to her weight on Earth?

Question 2.40

How would the mass of an astronaut on the Moon compare to his mass on Earth?

Question 2.41

An astronomer observes a new comet and calculates that it will exit the solar system and not return. Which of the following best describes the path of the comet?

• a. a nearly straight line
• b. a circle
• c. an ellipse
• d. a hyperbola
• e. some other shape

Question 2.42

It is quite probable that, within a few weeks of your reading of this chapter, one of the planets visible to the unaided eye (all the planets out as far as Saturn) will be in opposition or at greatest eastern elongation, making it visible in the evening sky from your location. Using the Starry Night™ computer program, the Internet, or a reference book such as the current issue of the Observer’s Handbook of the Royal Astronomical Society of Canada, the Astronomical Almanac, or the pamphlet Astronomical Phenomena (both of the latter published by the U.S. Naval Observatory), select a planet that is at or near such a configuration. To use Starry Night™, launch the program and click the Sunset button in the toolbar. Open the Options side pane and expand the Solar System layer. Click on both boxes in the Planets-Moons row to show and label the planets in the view and click on left-hand boxes for all other objects to remove them from view. Use the hand tool to search the sky for planets as far away as Saturn. Change the date by a few days if your search is unsuccessful. Repeat this step until you have found one or two visible planets up at night. Plan to make your observations at that time. Make a sketch to show the positions of planets with respect to nearby stars, noting the time and date of this observation. If possible, confirm that your observation is a planet by observing a few days later and showing that the object has moved. (This kind of procedure is vital in confirming the discovery of new bodies in the solar system.) If a small telescope or spotting scope is available, make a drawing of what you see through it, being careful to include planet phases, moons, surface features, and nearby stars.

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Question 2.43

Use the Starry Night™ program to observe retrograde motion. Select Favourites > Explorations > Retrograde from the menu. The view from Earth is centered upon Mars, shown against the background of stars and the framework of star patterns within the constellations. The Time Flow Rate is set to 1 day. Start time flow and observe Mars as it moves against the background constellations. An orange line traces Mars’s path in the sky from night to night. Watch the motion of Mars for at least 2 years of simulated time. Since the view is centered upon and tracks Mars in the view, the sky appears to move but the relative motion of Mars against this sky is obvious. (a) For most of the time, does Mars move generally to the left (westward) or to the right (eastward) on the celestial sphere? Select File > Revert from the menu to return to the original view. Use the Time controls in the toolbar (Play, Step time forward and Step time backward) along with the Zoom controls (+ and − buttons at the right of the toolbar or the mouse wheel) to determine when Mars’s usual direct motion ends, when it appears that Mars comes to a momentary halt in the west-east direction, and retrograde motion begins. On what date does retrograde motion end and direct motion resume? (b) You have been observing the motion of Mars as seen from Earth. To observe the motion of Earth as seen from Mars, locate yourself on the north pole of Mars by selecting Favourites > Explorations > Retrograde Earth from the menu. The view is centered upon and will track Earth as seen from the north pole of Mars, beginning on June 23, 2010. Click the Play button. As before, watch the motion for 2 years of simulated time. In which direction does Earth appear to move for most of the time? On what date does its motion change from direct to retrograde? On what date does its motion change from retrograde back to direct? Are these roughly the same dates as you found in part (a)? (c) To understand the motions of Mars as seen from Earth and vice versa, observe the motion of the planets from a point above the solar system. Select Favourites > Explorations > Retrograde Overview from the menu. This view, from a position 5 AU above the plane of the solar system, is centered upon the Sun, and the orbits and positions of Mars and Earth on June 23, 2010, are shown. Click Play and watch the motions of the planets for 2 years of simulated time. Note that Earth catches up with and overtakes Mars as time proceeds. This relative motion of the two planets leads to our observation of retrograde motion. On what date during this 2-year period is Earth directly between Mars and the Sun? How does this date compare to the two dates you recorded in part (a) and the two dates you recorded in part (b)? Explain the significance of this.

Question 2.44

Use Starry Night™ to observe the phases of Venus and of Mars as seen from Earth. Select Favourites > Explorations > Phases of Venus and click the Now button in the toolbar to see an image of Venus if you were to observe it through a telescope from Earth right at this moment. (a) Draw the current shape (phase) of Venus. With the Time Flow Rate set to 30 days, step time forward, drawing Venus to scale at each step. Make a total of 20 time steps and drawings. (b) From your drawings, determine when the planet is nearer or farther from Earth than is the Sun. (c) Deduce from your drawings when Venus is coming toward us or is moving away from us. (d) Explain why Venus goes through this particular cycle of phases. Select Favourites > Explorations > Phases of Mars and click the Now button in the toolbar. With the Time Flow Rate set to 30 days, step time forward, and observe the changing phase of Mars as seen from Earth. (e) Compare this with the phases that you observed for Venus. Why are the cycles of phases as seen from Earth different for the two planets?

Question 2.45

Use Starry Night™ to observe the orbits of the planets of the inner Solar System. Open Favourites > Explorations > Kepler. The view is centered upon the Sun from a position in space 2.486 AU above the plane of the solar system and shows the Sun and the inner planets and their orbits, as well as many asteroids in the asteroid belt beyond the orbit of Mars. Click the Play button and observe the motions of the planets from this unique location. (a) Make a list of the planets visible in the view in the order of increasing distance from the Sun. (b) Make a list of the planets visible in the view in the order of increasing orbital period. (c) How do the lists compare? (d) What might you conclude from this observation? (e) Which of Kepler’s laws accounts for this observation?