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 7.85 hours with the centers of the two objects separated by a distance roughly 1.90 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.

density= kg/m3

Explanation / Answer

Here,

let the density of the planet is p

let the radius of planet is R

time period , T = 7.85 hours

radius of orbit , r = 1.90 * R

T^2/r^3 = 4 * pi^2/(G * Mass of planet)

(7.85 * 3600)^2/(1.90 * R)^3 = 4 * pi^2/(6.673 *10^-11 * (4/3) *pi * R^3 * p)

(7.85 * 3600)^2/(1.90)^3 = 4 * pi^2/(6.673 *10^-11 * (4/3) *pi * p)

solving for p

p = 1213 Kg/m^3

the density of the planet is 1213 Kg/m^3

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