ES+2232-Lab+02-Planetary+Atmospheres

ES 2232G: Exploring the Planets: Sun, Earth, Planets Laboratory 02 – Planetary Atmospheres (Materials reproduced from the Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu). INTRODUCTION This lab explores some of the elements that go into the retention or loss of an atmosphere by a planet. Open a web browser and point to: http://astro.unl.edu/naap/atmosphere/atmosphere.html . 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 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. Object Mass (Mearth) Radius (Rearth) v esc (km/s) v esc (km/s) calculation (optional) Mercury 0.055 0.38 4.3km/s Uranus 15 4.0 21.7km/s 15/4 (11.2 km/s) = 21.7 km/s Io 0.015 0.30 2.5km/s √0.015/0.3 (11.2 km/s) = 2.5 km/s Vesta 0.00005 0.083 0.3km/s √0.00005/0.083 (11.2 km/s) = 0.3km/s Krypton 100 10 35km/s √100/10 (11.2 km/s) = 35.4km/s Earth Sciences 2232G: Lab 02     0.055 11.2 4.3 0.38 km km s s        1

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. Maxwe ll Speed Distribution Earth Sciences 2232G: Lab 02 Fastest 3% Number of Particles Molecular speed (m/s) 2

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? The most probable velocity is close to 0 m/s, due to the reason that temperature is a measure of average kinetic energy of particles, at absolute zero or 0K there is barely any movement. Question 5:  Return the temperature to 300 K. Use the gas panel to add Ammonia and Carbon Dioxide to the chamber. Question 6: 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. As mass decreases the most probable velocities increase, and the mass of the gases decrease as the Maxwell distribution becomes wider. As mass increases, the most probable velocity decrease and the Maxwell distribution gets narrower. Question 7: 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 below of the results similar to the example completed for you (max 5 lines). Earth Sciences 2232G: Lab 02 4 Gas Mass (u) v mp (m/s) H 2 2 1590 NH 3 17 538 CO 2 44 338

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 is lost quickly since its mass is only 2u and its v mp is greater than the v esc . NH 3 is lost quicker because almost half of its velocity distribution is more than 1000 m/s. So, more particles can escape. CO 2 is slowly lost because a small portion of the molecules have a v mp that is greater than the v esc 3 500 500 H2 and NH3 are lost at a higher rate because a majority of their velocity distribution are greater than 500 m/s. Both have a vmp that is greater than the vesc . CO2 is lost at a faster because half of its velocity distribution is greater than 500 m/s. 4 100 1500 H 2 is lost slower at 100 K compared to 500 K because only a small portion of its velocity distribution is larger than the escape velocity. CO 2 and NH 3 cannot escape the chamber because none of the molecules are faster than the v esc . Also, their masses of 44u and 17u are large, and their v mp is lower than the v esc 5 100 1000 H2 is escaping at a faster rate because its most probable velocity is close to its vesc and also it has a small mass is 2u. Half of its velocity distribution is greater than vesc . NH3 and CO2 don’t do much escaping as their entire velocity distribution including vmp is lower than the vesc. It also might be influenced by their large masses Earth Sciences 2232G: Lab 02 5

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. o If v esc is roughly 5 to 9 times v avg , the gas will be partially retained and the color fades into white over this parameter range. o If v esc < 5 v avg , the gas will escape into space quickly. Exercises  Begin experimenting with all boxes unchecked in both the gasses and plot options. 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. These retention curves are all linear, with increasing speed as temperature increases. Also, as the gas gets heavier, the slower the speed across all temperatures. Ex. hydrogen is the lightest and fastest, while xenon is the heaviest and slowest.  Check show gas giants in the plot options panel. Question 10: Discuss the capability of our solar system’s gas giants to retain particular gases among those shown. The gas giants can retain all of the gases on the graph because these planets have escape speeds that exceed 10 times the average molecular speed of the gases. Question 11: Drag the active point to the location (comparable with the escape speed and temperature) of Mercury. The gases hydrogen, helium, methane, ammonia, nitrogen, and carbon dioxide were common in the early solar system. Which of these gases would Mercury be able to retain? Mercury’s position on the graph is below the retention curves of all the gases therefore, it may not retain any of the gases for sure. Hydrogen, methane, helium, ammonia and nitrogen will escape into space quickly due to the fact that Mercury’s escape speed is less than 6x the average escape velocity of Earth Sciences 2232G: Lab 02 7

the gases. The shading region for carbon dioxide falls around Mercury’s vicinity, meaning that this gas could be partially retained. THINGS TO SUBMIT:  Submit this document via OWL to complete this lab. Earth Sciences 2232G: Lab 02 8