GEOL212 Due 10/29/18 Homework VIII

Transcription

1 GEOL212 Due 10/29/18 Homework VIII General instructions: Although you are allowed to discuss homework questions with your classmates, your work must be uniquely your own. Thus, please answer all questions in your own intelligible words. (When in doubt, use complete sentences.) If calculations are involved, show all work (so that I will have some basis for giving partial credit.) Be sure to use appropriate units and significant figures, where appropriate. Igneous rocks: Scenario: It is 2680 and you are on a new geologic survey assignment to (the fictional) GJ504e, an Earth-like exoplanet that is the moon of a GJ504a, a jovian planet (with roughly one Jupiter mass) orbiting GJ504, a sun-like star. You have access to physical specimens from three locations, which have been thin-sectioned and examined in your orbiting laboratory. The following items provide information on the mineral content of the specimens, the size of their crystals (Note: any smaller than 1 mm are considered "small"), and the general locations from which they were taken. For each one, indicate: Its rock name (granite, andesite, etc.) Its general chemistry (ultramafic, mafic, intermediate, or felsic) Its manner of formation: Intrusive or extrusive (we will regard any crystal grain smaller than 1 mm as being "small.")

2 1.) Mineral: Percent in sample: Deep ocean floor Orthoclase 0 Quartz 0 Avg. Crystal width: Plagioclase mm Muscovite 0 Biotite 0 Radiometric age: Amphibole 0 8 million years Pyroxene 10 Olivine 90 2.) Mineral: Percent in sample: Slope of a highland Orthoclase 5 mountain Quartz 25 Avg. Crystal width: Plagioclase mm Muscovite 2 Grains are spheroidal, very loosely cemented and flattened in one direction Biotite 3 Amphibole 15 Pyroxene 0 Olivine 0

3 3.) Mineral: Percent in sample: Rolling hills in a Orthoclase 50 landmass Quartz 25 Avg. Crystal width: Plagioclase mm Muscovite 3 Grains are strongly Biotite 2 interlocking Amphibole 10 Pyroxene 0 Olivine 0 4.) Mineral: Percent in sample: Large shield Orthoclase 0 volcano on lone oceanic island Quartz 0 Avg. Crystal width: Plagioclase mm Muscovite 0 Grains are strongly Biotite 0 interlocking Amphibole 0 Pyroxene 75 Olivine 20

4 5.) Recall that the surface area and volume of a sphere is given by: Surface area: A = 4πr 2 Volume: V = 4/3πr 3 Earth s mean radius is 6371 km. Calculate the ratio of its surface area to its volume. (Four significant figures in scientific notation, please!) 6.) At 0.9 Earth-masses, GJ504e has a radius of 6151 km. Calculate the ratio of its surface area to its volume. 7.) Based on your answer above, should GJ504e be losing its heat faster or more slowly than Earth? Based on your observation of specimens, has GJ504e had more or less internal heat than Earth in the recent geologic past (roughly the last 100 Ma)? Which specimen provides the key information?

5 8.) GJ504e's orbital period around GJ504a is four Earth days, and it's semimajor axis is 700,000 km. It's orbital eccentricity is 0.006, and it is locked in a 2:1 orbital resonance with GJ504h, the next large moon out from GJ504a. Do these parameters closel match any of the Galilean moons of Jupiter? What is the likely cause of the difference between GJ504e's internal temperature as predicted by your calculation of its volume, and what the rocks seem to be telling you? 9.) The maximum height of a "plinian column" a rising column of volcanic ash produced by an eruption is given by: HT = k(mδt) 1/4 Where: HT = maximum height k = constant of proportionality, an indicator of atmospheric density. This value is higher for thinner atmospheres. M = Mass eruption rate - a function of the gas content of the magma and the diameter of the volcanic vent. Larger vents erupting gassier lava have larger values. ΔT = Temperature contrast between erupting magma and air. Al other things being equal greater temperature contrast yields taller columns. Your team s observations indicate that on GJ504e, values of M on GJ504e are similar to those on Earth. It has roughly the same proportion of ocean surface to land area. Its other physical properties are slightly different. Its atmospheric pressure at sea level is only 0.89 bars. It s average surface temperature is 277 K (as opposed to 288 for Earth). Would you expect ΔT to be greater or less than on Earth? What two factors in the data you have uncovered in this homework would lead you to expect ΔT to be different on GJ504e and Earth? 10.) Given the foregoing, would you expect plinian columns to reach, on average, greater or lesser height than they do on Earth?