7. This question shows an example of how you can test the predictions of competing astronomical hypotheses against obser

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7. This question shows an example of how you can test the predictions of competing astronomical hypotheses against observations. In class, we discussed an explanation of moon phases in relation to the angle at which sunlight hits the moon, and the angle at which we see the moon. In understanding moon phases, we made the assumption that the sun is much farther from the earth than the moon is, without really talking about how we have come to believe that. In this question, you'll be asked to imagine an alternative scenario where the sun and moon are at nearly the same distance from us instead, and imagine what moon phases would look like in that world. To start with, let's recall how we described the configuration of the Moon, Sun and Earth when the Moon is at first quarter:
Sunlight Line of sight To moon To Sun Figure 1: First quarter moon, viewed from above north pole In this case, we imagine the sun to be far away off the right side of the page, so the light from it comes from the right. This means that the right half of the moon is illuminated. Since the moon is at an angular distance of 90 degrees from the sun, this means when we look at the moon from the earth, we are viewing the terminator head on, and we see equal amounts of the light and dark side of the moon. a) Now, let's imagine an alternate reality where the sun is only a little bit farther from us than the moon, but the Moon still revolves around the earth with the same period. You might think of this as a kind of alternative hypothesis to the generally accepted view, and we want to see which matches our observations better. Let's look at what would happen when the moon was 90° away from the sun, as shown in the diagram (figure 2) below:
Sunlight To Moon To Sun Figure 2: An alternate universe where the sun is only slightly farther from us than the moon. Draw a copy of this diagram showing the Moon's terminator and the light and dark half of the moon based on the direction of sunlight hitting the Moon in this configuration. (Remember that the terminator should be at right angles to the direction of sunlight). Based on that answer, describe what the moon would look like from earth when it was 90° away from the sun. (Would it be half illuminated, or crescent, or gibbous, etc.? A drawing would help.) (2pts) b) Considering this same alternate universe, can you sketch a position of the Moon where it would appear half lit as seen from Earth? In reality, it takes about a week (1/4 of a lunar cycle) for the Moon to go from new (close to the Sun) to a first quarter (half lit) phase. In this alternate reality, would the Moon take less, more, or the same amount of time to reach this half-lit phase? (2pts) c) Now, let's go back to the configuration of figure 2, where the Moon and Sun are 90 degrees apart as seen from Earth. If you now began to move the Sun further away from the Earth-Moon system, briefly describe how that would change the appearance of the moon? (How would the angle of the terminator change? Would the moon appear more or less fully lit? A series of drawings might help illustrate your answer.) (2pts)