Questions on Planetary Science - Homework IV | EART 160, Assignments of Geology

Download Questions on Planetary Science - Homework IV | EART 160 and more Assignments Geology in PDF only on Docsity! EART160 Homework #4 Due Friday 6th Feb 2009 Show all your working for full credit Figure 1. 1. Here we are going to consider the structure of an asteroid which has a porous near- surface and a solid interior (see Figure 1). The solid density is , the porosity (i.e. the volume fraction occupied by voids) of the near-surface layer is  and the density of this near-surface layer is (1-). a) Write down an expression for the overall (mean) density of the asteroid, in terms of R,Rp,  and . [3] b) What happens to the mean density from your expression if Rp=0, Rp=R or =0? Do these behaviours make physical sense? [3] c) Write down an expression for the gravitational acceleration g at the bottom of the porous layer [2] d) Assuming that g is constant throughout the porous layer, write down an expression for the pressure at the base of the porous layer [2] e) Use differentiation to find an expression for the value of Rp which maximizes this pressure for a given value of R, and , and also write down an expression for this maximum pressure [4] f) Pores will start to close if this maximum pressure exceeds roughly 1 MPa. Assuming that =0.3, =3000 kg m-3, how big can an asteroid get before pore closure starts? [2] [16 total] solid porous R Rp