NAAP – Retention of an Atmosphere 4/7

NAAP – Retention of an Atmosphere 4/7

NAAP – Retention of an Atmosphere 4/7

Name:Atmospheric Retention – Student GuideBackground InformationWork through the background sections on Escape Velocity, Projectile Simulation, andSpeed Distribution. Then complete the following questions related to the backgroundinformation.Question 1: Imagine that asteroid A that has an escape velocity of 50 m/s. If asteroid Bhas twice the mass and twice the radius, it would have an escape velocity______________ the escape velocity of asteroid A.a) 4 timesb) Twicec) the same asd) halfe) one-fourthObjectMass(Mearth)Radius(Rearth)Mercury0.0550.38Uranus154.0Io0.0150.30Vesta0.000050.083Krypton100vesc(km/s)vesc (km/s) calculation(optional)100.0550.3811.2kmkm4.3ssQuestion 2: Complete the table below by using the Projectile Simulator to determine theescape velocities for the following objects. Since the masses and radii are given in termsNAAP – Retention of an Atmosphere 1/7of the Earth’s, you can easily check your values by using the mathematical formula forescape velocity.Question 3: Experiment with the Maxwell Distribution Simulator. Then a) draw a sketchof a typical gas curve below, b) label both the x-axis and y-axis appropriately, c) draw inthe estimated locations of the most probable velocity v mp and average velocity vavg, and d)shade in the region corresponding to the fastest moving 3% of the gas particles.Maxwell Speed DistributionNAAP – Retention of an Atmosphere 2/7Gas Retention SimulatorOpen the gas retention simulator. Begin by familiarizing yourself with the capabilitiesof the gas retention simulator through experimentation.The gas retention simulator provides you with a chamber in which you canplace various gases and control the temperature. The dots moving inside thischamber should be thought of as tracers where each represents a large number ofgas particles. The walls of the chamber can be configured to be a) impermeable sothat they always rebound the gas particles, and b) sufficiently penetrable so thatparticles that hit the wall with velocity over some threshold can escape. You canalso view the distributions of speeds for each gas in relation to the escape velocityin the Distribution Plot panel.The lower right panel entitled gases allows you to add and remove gases in theexperimental chamber. The lower left panel is entitled chamber properties. In itsdefault mode it has allow escape from chamber unchecked and has atemperature of 300 K. Click start simulation to set the particles in motion in thechamber panel. Note that stop simulation must be clicked to change thetemperature or the gases in the simulation.The upper right panel entitled distribution plot allows one to view the Maxwelldistribution of the gas as was possible in the background pages. Usage of theshow draggable cursor is straightforward and allows one to conveniently read offdistribution values such as the most probable velocity. The show distribution infofor selected gases requires that a gas be selected in the gas panel. Thisfunctionality anticipates a time when more than one gas will be added to thechamber.ExercisesUse the pull-down menu to add hydrogen to the chamber.Question 4: Complete the table using the draggableT (K)cursor to measure the most probable velocity for300hydrogen at each of the given temperatures. Write a200short description of the relationship between T and v mp.100vmp (m/s)NAAP – Retention of an Atmosphere 3/7Question 5: If the simulator allowed the temperature to be reduced to 0 K, what wouldyou guess would be the most probable velocity at this temperature? Why?Return the temperature to 300 K. Use the gas panel to add Ammonia and CarbonDioxide to the chamber.Question 6: Complete the table using the draggableGascursor to measure the most probable velocity at aH2temperature of 300 K and recording the atomic massNH3for each gas. Write a short description of theCO2Mass (u)vmp (m/s)relationship between mass and vmp and the width of the Maxwell distribution.Question 7: Check the box entitled allow escape from chamber in the chamberproperties panel. You should still have an evenly balanced mixture of hydrogen,ammonia, and carbon dioxide. Run each of the simulations specified in the table belowfor the mixture. Click reset proportions to restore the original gas levels. Write adescription of the results similar to the example completed for you.NAAP – Retention of an Atmosphere 4/7RunT (K)vesc (m/s)Description of SimulationH2 is very quickly lost since it only has a mass of 2u and itsmost probable velocity is greater than the escape velocity,NH3 is slowly lost since it is a medium mass gas (18u) and asignificant fraction of its velocity distribution is greater than1500 m/s, CO2 is unaffected since its most probable velocityis far less than the escape velocity.1500150025001000350050041001500510010006100500Question 8: Write a summary of the results contained in the table above. Under whatcircumstances was a gas likely to be retained? Under what circumstances is a gas likelyto escape the chamber?NAAP – Retention of an Atmosphere 5/7Gas Retention PlotThis simulator presents an interactive plot summarizing the interplay between escapevelocities of large bodies in our solar system and the Maxwell distribution for commongases. The plot has velocity on the y-axis and temperature on the x-axis. Two types ofplotting are possible:A point on the graph represents a large body with that particular escape velocityand outer atmosphere temperature. An active (red) point can be dragged orcontrolled with sliders. Realize that the escape velocity of a body depends on boththe density (or mass) and the radius of an object.A line on the graph represents 10 times the average velocity (10×v avg) for aparticular gas and its variation with temperature. This region is shaded with aunique color for each gas.o If a body has an escape velocity vesc over 10×vavg of a gas, it will certainlyretain that gas over time intervals on the order of the age of our solarsystem.o If vesc is roughly 5 to 9 times v avg, the gas will be partially retained and thecolor fades into white over this parameter range.o If vesc < 5 vavg, the gas will escape into space quickly.ExercisesBegin experimenting with all boxes unchecked in both the gasses and plotoptions.Question 9: Plot the retention curves for the gases hydrogen, helium, ammonia, nitrogen,carbon dioxide, and xenon. Explain the appearance of these curves on the retention plot.Check show gas giants in the plot options panel.Question 10: Discuss the capability of our solar system’s gas giants to retain particulargases among those shown.Question 11: Drag the active point to the location (comparable with the escape speed andtemperature) of Mercury. The gases hydrogen, helium, methane, ammonia, nitrogen, andcarbon dioxide were common in the early solar system. Which of these gases wouldMercury be able to retain?NAAP – Retention of an Atmosphere 6/7Question 12: Most nitrogen atoms have a mass of 14u (hence 28u for N 2), but a smallpercentage of nitrogen atoms have an extra neutron and thus an atomic mass of 15u. (Werefer to atoms of the same element but with different masses as isotopes of that element.)Recently, scientists studying isotope data from the Cassini spacecraft have noticed thatthe ratio of 15u nitrogen to 14u nitrogen is much larger than it is here on earth. Assumingthat Titan and the earth originally had the same isotope ratios, explain why the ratiosmight be different today.Question 13: Other observations by the Cassini probe have confirmed that Titan has athick atmosphere of nitrogen and methane with a density of about 10 times that of theEarth’s atmosphere. Is this finding completely consistent with Titan’s position on theatmospheric retention plot? Explain. (Make sure that show icy bodies and moons ischecked as well as the gasses methane and nitrogen.)NAAP – Retention of an Atmosphere 7/7

 

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