Lab 13

Name: NAAP – Retention of an Atmosphere 1/7 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 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 ± ² ± ² 0.055 11.2 4.3 0.38 km km s s § · ¨ ¸ © ¹ Uranus 15 4.0 Io 0.015 0.30 Vesta 0.00005 0.083 Krypton 100 10 • 4. 3 YI 21.7k ¥ (11.2+7)=21.7*7 0.56 KF F, (11.2*7)=0.56*7 0.275K ¥ FÉ (112+7)=0.2 > sky 35.4*75%(11.2*7)=3%4 ' %

NAAP – Retention of an Atmosphere 2/7 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. Maxwell Speed Distribution 1 Most Probable 1 ✓ Velocity & average n velocity A ¥ É ¥ 1 fastest 1 moving i Particle speed / mutant "

NAAP – Retention of an Atmosphere 4/7 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? x 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. 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 of the results similar to the example completed for you. Gas Mass (u) v mp (m/s) H2 NH3 CO2 The most probable velocity would be DK Since molecular speed decreases when the temperature is lowered 2. 0603g 4556 My 17.23449 538 MI } 44.9855g 333mi If the mass of the gas molecule increases , Then the Vmp Lmao ) would decrease

NAAP – Retention of an Atmosphere 5/7 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 3 500 500 4 100 1500 5 100 1000 6 100 500 Question 8: 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? 11-2 Molecules would escape . Nltj is slowly 10s * because it is close to the escape velocity . Due to low probable Velocity , it will not affect CO2 . All the molecules are able to escape because the most Probable velocity is higher for all molecules than the escape velocity . No molecule would escape . They don't have enough energy to escape . Most probable velocity is less than the escape velocity . Ha molecules would escape ; CO2 and NH } will Remain . A2 will escape quickly . probable velocity of NH } is less . However , Some molecules will escape slowly . No molecules of CO2 will be able to escape . Most probable velocity is less than the escape velocity . Gas is likely to be retained if the temperature is low , and escape velocity is higher than most of the gas molecules . Gas is likely to escape if the molecules have enough energy and the most probable velocity is high .

NAAP – Retention of an Atmosphere 7/7 Mercury be able to retain? Question 12: Most nitrogen atoms have a mass of 14u (hence 28u for N 2 ), but a small percentage of nitrogen atoms have an extra neutron and thus an atomic mass of 15u. (We refer 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 that the ratio of 15u nitrogen to 14u nitrogen is much larger than it is here on earth. Assuming that Titan and the earth originally had the same isotope ratios, explain why the ratios might be different today. Question 13: Other observations by the Cassini probe have confirmed that Titan has a thick atmosphere of nitrogen and methane with a density of about 10 times that of the Earth’s atmosphere. Is this finding completely consistent with Titan’s position on the atmospheric retention plot? Explain. (Make sure that show icy bodies and moons is checked as well as the gasses methane and nitrogen.) Mercury can retain carbon dioxide . The others will escape quickly because of Mercury 's slow speed . Both gases will be retained on Earth because it has a larger escape velocity than Titan . The higher the temperature , the higher the velocity . Titan is a lot cooler than Earth , so the velocity of the gases will be slower than that of Earth ] Velocity . Titan will not have an atmosphere according to the atmosphere retention plot . Therefore , the finding is not completely consistent .