lab 6

Name: NAME_____________Sami Frost CLASS_________ Instructions: Go to web site http://astro.unl.edu . Click on the Nebraska astronomy applet project and then go to NAAP Modules(at top of screen) and pick Atmospheric Retention Lab . Read the materials and complete the guide below and complete the exercises and complete the document below—the background materials will help you answer the questions—the flash demonstration will help you complete the rest. ON LINE LAB 06 Nebraska Astronomy Applet Project Student Guide to the Atmospheric Retention Atmospheric Retention – Student Guide Background Information Work through the background sections on Escape Velocity, Projectile Simulation, and Speed Distribution. Then complete the following questions related to the background information. Question 1: Imagine that asteroid A that has an escape velocity of 50 m/s. If asteroid B has twice the mass and twice the radius, it would have an escape velocity ______________ the escape velocity of asteroid A. a) 4 times b) Twice c) the same as d) half e) one-fourth Object Mass Radius v esc v esc (km/s) calculation NAAP – Retention of an Atmosphere 1/7

(Mearth) (Rearth) (km/s) (optional) Mercury 0.055 0.38 4.3 Uranus 15 4.0 22 Io 0.015 0.30 2.7 Vesta 0.00005 0.083 .4 Krypton 100 10 36 Question 2: Complete the table below by using the Projectile Simulator to determine the escape velocities for the following objects. Since the masses and radii are given in terms of the Earth’s, you can easily check your values by using the mathematical formula for escape velocity. Question 3: Experiment with the Maxwell Distribution Simulator. Then a) draw a sketch of a typical gas curve below, b) label both the x-axis and y-axis appropriately, c) draw in the estimated locations of the most probable velocity v mp and average velocity v avg , and d) shade in the region corresponding to the fastest moving 3% of the gas particles. NAAP – Retention of an Atmosphere 2/7     0.055 11.2 4.3 0.38 km km s s       

Exercises  Use the pull-down menu to add hydrogen to the chamber. Question 4: Complete the table using the draggable cursor to measure the most probable velocity for hydrogen at each of the given temperatures. Write a short description of the relationship between T and v mp . The higher temperature, the faster the escape speed (low curve), so the faster molecules move. The lower temperature, the slower the escape speed (high curve), so slower molecules movement. Question 5: If the simulator allowed the temperature to be reduced to 0 K, what would you guess would be the most probable velocity at this temperature? Why? It would be very close to 0 because it would become a solid.  Return the temperature to 300 K. Use the gas panel to add Ammonia and Carbon Dioxide to the chamber. Question 5: Complete the table using the draggable cursor to measure the most probable velocity at a temperature of 300 K and recording the atomic mass for each gas. Write a short description of the relationship between mass and vmp and the width of the Maxwell distribution. The higher the mass, the less Vmp the narrower the curve (low temperature). When the mass is a much lower number, Vmp is much higher, and the curve is wider (high temperature). Question 6: Check the box entitled allow escape from chamber in the chamber properties panel. You should still have an evenly balanced mixture of hydrogen, ammonia, and carbon dioxide. Run each of the simulations specified in the table below for the mixture. Click reset proportions to restore the original gas levels. Write a description of the results similar to the example completed for you. NAAP – Retention of an Atmosphere 4/7 T (K) v mp (m/s) 300 1600 200 1300 100 900 Gas Mass (u) v mp (m/s) H2 2 1541 NH3 17 543 CO2 44 339

Run T (K) v esc (m/s) Description of Simulation 1 500 1500 H 2 is very quickly lost since it only has a mass of 2u and its most probable velocity is greater than the escape velocity, NH 3 is slowly lost since it is a medium mass gas (18u) and a significant fraction of its velocity distribution is greater than 1500 m/s, CO 2 is unaffected since its most probable velocity is far less than the escape velocity. 2 500 1000 H 2 and NH 3 are moving very quickly, and CO 2 is visibly starting to move as well. Overall, still not affected much. H 2 is still moving the fastest for same reason it started. 3 500 500 They all 3 are moving quickly now, H 2 is still the fastest, but CO 2 is now moving along much quicker than before. 4 100 1500 Almost the same result as Run 1. H 2 is lost very quickly and NH 3 is much slower while Co 2 is unaffected as many particles are moving slowly. 5 100 1000 Only H 2 was affected, CO 2 and NH 3 were not affected. 6 100 500 H 2 wins the prize again for escaping quickly, NH 3 was 2 nd place and CO 2 had little escape but slow. Question 7: Write a summary of the results contained in the table above. Under what circumstances was a gas likely to be retained? Under what circumstances is a gas likely to escape the chamber? Gas was likely retained when the temperature and escape velocity were high. Gas was able to escape the chamber when temperatures and escape velocity were the same. Gas Retention Plot This simulator presents an interactive plot summarizing the interplay between escape velocities of large bodies in our solar system and the Maxwell distribution for common gases. The plot has velocity on the y-axis and temperature on the x-axis. Two types of plotting are possible:  A point on the graph represents a large body with that particular escape velocity and outer atmosphere temperature. An active (red) point can be dragged or controlled with sliders. Realize that the escape velocity of a body depends on both the density (or mass) and the radius of an object.  A line on the graph represents 10 times the average velocity (10×v avg ) for a particular gas and its variation with temperature. This region is shaded with a unique color for each gas. o If a body has an escape velocity v esc over 10×v avg of a gas, it will certainly retain that gas over time intervals on the order of the age of our solar system. NAAP – Retention of an Atmosphere 5/7

atmospheric retention plot? Explain. (Make sure that show icy bodies and moons is checked as well as the gasses methane and nitrogen.) No, its not consistent because Titan has a temperature of 90K and density of 1.9g/cm 3 . Farths temperature is 280K and has a density of 5.5g/cm 3 . NAAP – Retention of an Atmosphere 7/7