Earth’s umbra: Earth has a shadow in space, just as people do on a sunny day. The darkest part1 of that shadow is a conical region in space known as the umbra. A representation of Earth’s umbra is...

Earth’s umbra: Earth has a shadow in space, just as people do on a sunny day. The darkest part1 of that shadow is a conical region in space known as the umbra. A representation of Earth’s umbra is shown in Figure 3.39. Earth has a radius of about 3960 miles, and the umbra ends at a point about 860,000 miles from Earth. The moon is about 239,000 miles from Earth and has a radius of about 1100 miles. Consider a point on the opposite side of Earth from the sun and at a distance from Earth equal to the moon’s distance from Earth. What is the radius of the umbra at that point? Can the moon fit inside Earth’s umbra? What celestial event occurs when this happens?