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Chapter 3: Problem 43

(a) Suppose the diameter of the Moon were doubled, but the orbit of the Moon remained the same. Would total solar eclipses be more common, less common, or just as common as they are now? Explain. (b) Suppose the diameter of the Moon were halved, but the orbit of the Moon remained the same. Explain why there would be no total solar eclipses.

Short Answer

Expert verified
Doubling the diameter of the Moon would result in more frequent total solar eclipses. On the other hand, halving the Moon's diameter would result in no total solar eclipses.

Step by step solution

01

Understand Solar Eclipse

In order to answer these questions, you must understand the conditions under which a solar eclipse occurs. Solar eclipses happen when the moon passes between the sun and earth, thus blocking the sunlight
02

Analyzing the Effect of Doubling the Moon's Diameter

If the moon's diameter was doubled while its orbit remained the same, it would appear from Earth to be twice its normal size. This would make it 'bigger' than the sun from our viewpoint. Under this condition, the moon would be able to cover the Sun more often during its phases resulting in more frequent total solar eclipses.
03

Analyzing the Effect of Halving the Moon's Diameter

Conversely, if the diameter of the Moon were halved, it would appear to be only half its normal size from the viewpoint of the Earth. Were this the case, it would be 'smaller' than the Sun. Consequently, it would not be able to fully cover the Sun, which means that no total solar eclipses would occur.

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Most popular questions from this chapter

Use the Starry Night Enthusiast \({ }^{\mathrm{TM}}\) program to examine the Moon as seen from space. Select Solar System > Inner Solar System in the Favourites menu. Click the Stop button in the toolbar to stop time flow. Then, click on the Find tab and double-click on the entry for the Moon in the Find pane in order to center the view on the Moon. Close the Find pane and zoom in on the Moon by clicking and holding the mouse cursor on the Decrease current elevation button (the downward-pointing arrow to the left of the Home button in the toolbar) to approach the Moon until detail is visible on the lunar surface. You can now view the Moon from any angle by holding down the Shift key while holding down the mouse button (the left button on a two-button mouse) and dragging the mouse. This is equivalent to flying a spaceship around the Moon at a constant distance. (a) Use this technique to rotate the Moon and view it from different perspectives. How does the phase of the Moon change as you rotate it around? (Hint: Compare with Box 3-1.) (b) Rotate the Moon until you can also see the Sun and note particularly the Moon's phase when it is in front of the Sun. Explain how your observations show that the phases of the Moon cannot be caused by the Earth's shadow falling on the Moon.

Describe the cycle of lunar phases that would be observed if the Moon moved around the Earth in an orbit perpendicular to the plane of the Earth's orbit. Would it be possible for both solar and lunar eclipses to occur under these circumstances? Explain your reasoning.

How would a lunar eclipse look if the Earth had no atmosphere? Explain your reasoning.

Use the Stary Night Enthusiast \({ }^{\mathrm{TM}}\) program to observe the motion of the Moon. (a) Display the entire celestial sphere, including the part below the horizon, by moving to the Atlas mode. You do this by selecting Favourites \(>\) Guides \(>\) Atlas. Here, you will see the sky, containing the background stars and the planets, overlaid by a coordinate grid. One axis, the Right Ascension axis, is the extension of the Earth's equator on to the sky and is marked in hours along the Celestial Equator. At right angles to this equator are the Declination lines at constant Right Ascension, converging upon the North and South Celestial Poles. These poles are the extensions of the two ends of the Earth's spin axis. You can use the Hand Tool to explore this coordinate system by moving your viewpoint around the sky. (Move the mouse while holding down the mouse button to achieve this motion.) Across this sky, inclined at an angle to the celestial equator, is the Ecliptic, or the path along which the Sun appears to move across our sky. This is the plane of the Earth's orbit. (If this green line does not appear, open the Options pane and check that the Ecliptic is selected in the Guides layer.) Use the Hand Tool to move the sky around to find the Moon, which will be close to, but not on, the ecliptic plane. Once you have found the Moon, use the Hand tool to move the Moon to the right-hand side of the main window. On the toolbar across the top of the main window, click on the Time Flow Rate control (immediately to the right of the date and time display) and set the discrete time step to 1 sidereal day. Then advance time in one-sidereal-day intervals by clicking on the Step Time Forward button (the icon consisting of a black vertical line and right-pointing triangle to the far right of the time controls). You will note that the background sky remains fixed, as expected when time moves ahead in sidereal- day intervals. How does the Moon appear to move against the background of stars? Does it ever change direction? (b) Use this Step Time Forward button to determine how many days elapse between successive times when the Moon is on the ecliptic. Then move forward in time to a date when the Moon is on the ecliptic and either full or new. What type of eclipse will occur on that date? Confirm your answer by comparing with Tables 3-1 and \(3-2\) or with lists of eclipses on the World Wide Web.

How is an annular eclipse of the Sun different from a total eclipse of the Sun? What causes this difference?
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