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Home Q & A Board Science-Related Homework Help Physics
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12 years ago
HD 209458b was the first extrasolar planet whose size was measured. It has a radius of 1.43 Jupiter radii and mass of 0.63 Jupiter masses. Calculate its average density in grams per cubic centimeter. How does this compare with Jupiter?
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12 years ago
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12 years ago
The volume of a sphere with radius R is V =  (4/3)piR3 and the density is M/V.
We are asked for the density in grams per cubic centimeter so must convert the radius to centimeters and the mass to grams. We find the radius and mass of Jupiter in these units from Appendix E so find, for HD 209458b,
R=1.43 × 71,492 km = 102,230 km = 1.02 × 1010 cm
and therefore V =  (4/3)piR3 = 4.48 × 1030 cubic centimeters
M=0.63 × 1.90 × 1027 kg = 1.20 × 1030 g
so the density is M/V = 0.27 grams per cubic centimeter.

The average density of Jupiter is 1.33 grams per cubic centimeter, so HD 209458b is five times less dense. This is due to it being "puffed up" from the high temperatures in such a close orbit around its host star.
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