- #1
Ragnarok7
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Assume that the average distance of the sun from the Earth is 400 times the average distance of the moon from the earth. Now consider a total eclipse of the sun and state conclusions that can be drawn about:
A. The relation between the sun's diameter and the moon's diameter.
B. The relative volumes of the sun and the moon.
C. Find the angle intercepted at the eye by a dime that just eclipses the full moon and from this experimental result and the given distance between the moon and Earth (=3.80×105 km) estimate the diameter of the moon.
Here is my attempted answer to the first parts:
Part A.
Since the sun is 400 times a moon's distance from earth, that must mean it looks 400 times smaller than it would if it were a moon's distance away. If the moon eclipses the sun perfectly, then that means that the sun is 400 times larger than the moon. Therefore the diameter of the sun is also 400 times larger than the diameter of the moon.
Part B.
If the sun is 400 times bigger than the moon, then the radius of the sun is also 400 times bigger than the radius of the moon. The volume of a sphere is given by [itex]\frac{4}{3}\pi r^3[/itex]. If the moon's radius is r, then the sun's radius is 400r. The volume of the sun will then be 6.4×107 times larger than the volume of the moon.
Part C.
I am unsure how to proceed with this part. I'm not totally clear on what is meant by "the angle intercepted by the eye", for one. It says "experimental result"; does it want me to actually go out and measure this angle?
A. The relation between the sun's diameter and the moon's diameter.
B. The relative volumes of the sun and the moon.
C. Find the angle intercepted at the eye by a dime that just eclipses the full moon and from this experimental result and the given distance between the moon and Earth (=3.80×105 km) estimate the diameter of the moon.
Here is my attempted answer to the first parts:
Part A.
Since the sun is 400 times a moon's distance from earth, that must mean it looks 400 times smaller than it would if it were a moon's distance away. If the moon eclipses the sun perfectly, then that means that the sun is 400 times larger than the moon. Therefore the diameter of the sun is also 400 times larger than the diameter of the moon.
Part B.
If the sun is 400 times bigger than the moon, then the radius of the sun is also 400 times bigger than the radius of the moon. The volume of a sphere is given by [itex]\frac{4}{3}\pi r^3[/itex]. If the moon's radius is r, then the sun's radius is 400r. The volume of the sun will then be 6.4×107 times larger than the volume of the moon.
Part C.
I am unsure how to proceed with this part. I'm not totally clear on what is meant by "the angle intercepted by the eye", for one. It says "experimental result"; does it want me to actually go out and measure this angle?