Answer Happy

.4. Consider a death star under the command of Anakin Skywalkerwho wishes to target Obi-Wan’s home planet that has a mass of M andradius of R. We are assuming both celestial bodies are spherical.The death star has a mass density of ρ(r, θ, ϕ) = r3 ϕ2 and radiusr1. The distance between the death star and the planet is Z.
4. Consider a death star under the command of Anakin Skywalker who wishes to target Obi-Wan's home planet that has a mass M and radius R. We are assuming both celestial bodies are spherical. The death star has a mass density as ρ(r,θ,ϕ)=r3ϕ2 and and radius r1​. The distance between the death star and the planet is Z. (a) Find the mass of the death star. (b) The energy needed for a planet to form (or destroy) can be written as E=∫34​πρ2r3dV where the integration measure dV is just a infinitesimal volume in spherical polar coordinates. Using equation 9 find the total energy of Obi Wan's home planet. (c) Due to excessive load shedding and poor management, Anakin fired a beam with less energy from what you computed above and hence failed to destroy Obi Wan's planet. However, that event caused the planet of Mr Wan to approach the death star. Two worlds colliding, and as a curious spectator, now you will find the time for this collision by solving the following integral using the appropriate limits. T=21​∫dxm2γ​(x1​−Z1​)​ Here x is the distance between these two objects at any given time and γ=GMm and hence a constant.