Detecting planets

News flash: last week astronomers argued that Earth sized planets are pretty common. Roughly 1 in 6 stars similar to our sun may have earth size planets. Now, the planets detected are generally much closer to their stars than Earth is to the Sun, which makes it tougher (we think) for life to exist on them, but still it's pretty amazing.

Astronomers detect these planets by looking for the dimming of stars as a planet blocks some of the starlight. If a planet with eight times the Earth's volume moves in front of a star identical to our sun, by what percentage does the starlight dim?

Make sure you enter at least 4 significant digits on this problem.

Details and assumptions

• The radius of the Earth is 6370 km.
• The radius of the Sun is $$7 \times 10^5$$ km.
• Assume that if you are far away and looking at the star (so it looks like a disk) the intensity of the light from the star is even everywhere on the disk.
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