A total solar eclipse occurs when the moon passes
between the earth and the sun, and the darkest
shadow cast by the moon, called the umbra, hits the surface of the earth. If the umbra does not hit the surface, as shown in the following figure, then a total solar eclipse is not possible. In other words, for a total solar eclipse to occur, point P must lie inside the circle for the earth.Assume the diameter of the sun is 870,000 miles, the diameter of the moon is 2160 miles, the diameter of the earth is 7920 miles, and the distance from the center of the sun to the center of the earth is approximately 93,000,000 miles. The distance from the moon to the earth varies, but the maximum distance from the center of the moon to the center of the earth is 252,700 miles, and is called the lunar apogee. How far is P from the center of the earth during lunar apogee?
To calculate the distance "P" from the center of the earth during lunar apogee, we can use the given information and basic geometry principles.
First, let's draw the diagram to understand the scenario better. Here, the sun, earth, and moon are aligned, and the distance from the center of the sun to the center of the earth is approximately 93,000,000 miles.
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Now, let's calculate the distance from "P" to the center of the earth.
1. Calculate the distance from the center of the moon to the center of the earth:
The maximum distance from the center of the moon (lunar apogee) to the center of the earth is given as 252,700 miles.
2. Calculate the distance from the center of the moon to the point where the umbra of the moon does not hit the earth's surface:
Since the diameter of the moon is given as 2160 miles, we can conclude that the distance from the center of the moon to the edge of the umbra is half its diameter, which is 2160/2 = 1,080 miles.
3. Determine the distance from point "P" to the center of the earth:
Subtract the distance calculated in step 2 from the distance calculated in step 1 to find the distance from point "P" to the center of the earth during lunar apogee.
Distance from P to the center of the earth = Maximum distance from the center of the moon to the center of the earth - Distance from the center of the moon to the edge of the umbra
= 252,700 miles - 1,080 miles
= 251,620 miles
Therefore, during lunar apogee, point "P" is approximately 251,620 miles away from the center of the earth.