# trig

The sun of galaxy X has a diameter of about 25,000 mi with a maximum distance from Planet​ X's surface of about 47,700,000 mi. Planet​ X's moon has a diameter of 6,603 mi. For a total solar eclipse to​ occur, the moon must pass between the sun and Planet X. The moon must also be close enough to Planet X for the​ moon's umbra​ (shadow) to reach the surface of Planet X.

The maximum distance that the moon can be from Planet X and still have a total solar eclipse occur is approximately how many miles? And can an eclipse occur?

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1. for an eclipse to occur , the moon must appear large enough to "cover" the sun

for the sun and moon to appear to be the same size
... the smaller moon, must be closer to the planet

apparent size / distance = constant

2.5E4 / 4.77E7 = 6603 / d

solve for d

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