Questions on Planetary Science - Homework 3 - Fall 2009 | EART 160, Assignments of Geology

Download Questions on Planetary Science - Homework 3 - Fall 2009 | EART 160 and more Assignments Geology in PDF only on Docsity! EART160 Homework #3 Due Friday 30 th Jan 2009 Show all your working for full credit 1. The figure above shows a topographic profile across part of a corona (a circular feature with a trench surrounding it) on Venus. We are going to interpret the trench and rise as a flexural feature due to loading. a) Mark on the figure the approximate distance over which flexure is deforming the lithosphere [1] b) Assuming that this distance is the flexural parameter, use the expression given in your notes to determine the elastic thickness of the lithosphere on Venus. You may assume that g=9 ms-2, =0.3, the density contrast is 500 kg m-3 and E=100 GPa [3]. c) How does the elastic thickness on Venus compare with that of continents on Earth? Why might this be a surprising result? [2] d) The base of the elastic layer is determined by a temperature of about 1000 K and the surface temperature of Venus is 700 K. What is the thermal gradient on Venus? [1] e) Thermal gradients on Earth are about 25 K/km. What does this result imply about the relative rates at which the Earth and Venus are cooling down? [2] f) How might you explain this difference in cooling rates? [1] [10 total] 2. Here we’re going to consider volcanism on Io. a) The velocity u of magma traveling upwards through a dike of width w is given by    gw u 2 where g is gravity,  is the density contrast between magma and the surrounding rock, and  is the viscosity. Examine the effect of each variable in turn and explain why this equation makes physical sense [4]. b) If the total height of the dike is d, write down an expression for the time taken for a packet of magma to get from the bottom to the top of the dike [1] c) Also write down an expression for how long it takes the material in the dike to cool by conduction [1]. d) By comparing the expressions for the cooling time and the transit time, derive an expression for the minimum width of a dike which will allow magma to ascend all the way to the surface [3] e) On Io, let’s assume that we have d=20 km, =100 kg m-3, g=1.8 ms-2, =10-6 m2s-1 and  =103 Pa s. Using this information, what is the minimum dike width? [1] f) If the total horizontal length of the dikes on Io is L and they all have a constant width w, write down an expression for the magma discharge rate (in m 3 s -1 ) from these dikes in terms of u, L and w [1] g) The magmatic resurfacing rate on Io is about 1 cm/yr. If the radius of Io is 1800km, what is the corresponding magma discharge rate (in m 3 s -1 )? [2] h) If dikes on Io are 1m wide, use the information given above to determine what the total length of dikes L has to be in order to produce the observed resurfacing rate [4] i) How easy would it be to spot these dikes from a spacecraft? [1] [18 total] 3 Here we’re going to consider compressive stresses on Mercury. a) The figure below shows a fault dipping at 30 o and extending to depth h. Write down an expression for the vertical (lithostatic) stress on the bottom of the fault. The crustal density is  and the gravity is g. [1] b) Write down an expression for the stress acting perpendicular to the fault plane [1] h 30o