Part A: While looking through the Mt. Palomar telescope, you discover a large pl
ID: 1434334 • Letter: P
Question
Part A: While looking through the Mt. Palomar telescope, you discover a large planetary object orbited by a single moon. The moon orbits the planet every 8.35 hours with the centers of the two objects separated by a distance roughly 2.20 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.
Part B: Iron has a density of 7.87 g/cm3. Choose the best response when asked by the media whether Planet Hephaestus is appropriately named...yes or no?
Explanation / Answer
8.35hr = (8.35 x 3600)s .. T = 3.0060 *10^4 s
Moon's ang velocity, = 2 rad (1 rev) / 3.0060 *10^4s .. = 2.25*10^-4 rad/s
Moon's centripetal force (Mm.R.²) = grav attraction (G.Mm.Mp / R²)
Planet mass .. Mp = R³² / G
R = 2.2r .. (r = planet radius) .. Mp = 2.2³.r³.²/G ----- (1)
Planet volume (sphere) .. Vp = 1.33r³ ---- (2)
Planet density = Mp/Vp (kg/m³) ... = (1)/(2) .. .. r³ cancels out
D = 2.2³.² / (1.33.G)
D = 2.2³ x (2.25*10^-4 rad/s)² / (1.33 x 6.67*10^-11) ..
D 1.935 * 10^3 kg/m³ = 2.0 g/cm³ .. .. looks like planet is not mostly made of iron (7.80 g/cm³)