While looking through the Mt. Palomar telescope, you discover a large planetary

Question

While looking through the Mt. Palomar telescope, you discover a large planetary object orbited by a single moon. The moon orbits the planet every 9.10 hours with the centers of the two objects separated by a distance roughly 2.15 times the radius of the planet. Fellow scientists speculate that the planet is made of mostly iron. In fact, the media has dubbed it the "Iron Planet" and NASA has even named it Planet Hephaestus after the Greek god of iron. But you have your doubts. Assuming the planet is spherical and the orbit circular, calculate the density of Planet Hephaestus. Iron has a density of 7.87 g/cm3. Choose the best response when asked by the media whether Planet Hephaestus is appropriately named. "Iron is not the predominant mineral on this planet." "The planet could be predominantly made of iron."

Explanation / Answer

velocity of the planet
2*pie*2.15*R/(9.1*3600)

G*massof planet/(2.15*R)^2 = V^2/2.15R

putting the velocity value
mass/(2.15*R)^3= 4*pie^2/((9.1*3600)^2*G)
density= around 5000
and iron desity is 7500 so it is not iron planet

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