Lab 4 Atmospheric Retention

Atmospheric Retention Remember to type your answers in blue text 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 10 m/s. If asteroid B has four times the mass and the same radius, how would its escape velocity compare to the escape velocity of asteroid A? Highlight the correct answer in blue. a) Four times as much b) Twice as much c) It would be the same d) Half as much e) One fourth as much Object Mass (Mearth) Radius (Rearth) v esc (km/s) v esc (km/s) calculation Mercury 0.055 0.38 4.3 Venus 0.82 0.95 Jupiter 318 11.2 Saturn 95.2 9.4 Pluto 0.0022 0.19 Question 2: Complete the table below by determining the escape velocities for the listed objects. Since the masses and radii are given in terms of Earth, you can use the simplified mathematical formula for escape velocity shown in the example for Mercury. You must multiply the √(M/R) ratio by 11.2 km/s since that is Earth’s escape velocity. Question 3: Experiment with the Maxwell Distribution Simulator found in the Speed Distribution background reading section. NAAP – Retention of an Atmosphere 1/8     0.055 11.2 4.3 0.38 km km s s       

Particle speeds Number of Particles a) Using the Scribble drawing tool found in Shapes under the Insert tab, sketch a Maxwell distribution curve for a typical gas in the box below. b) Using the Line drawing tool found in Shapes under the Insert tab, draw in the estimated location of the most probable velocity (v p ). You do not need to label the line. c) Using the Scribble drawing tool, outline and shade in the region corresponding to the fastest moving 3% of the gas particles. Maxwell Speed Distribution NAAP – Retention of an Atmosphere 2/8

Question 5: If the simulator allowed the temperature to be reduced to 0 K, what do you think would be the most probable velocity at this temperature? Why?  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 record the atomic mass for each gas. Write a short description of the relationship between mass and v mp , and between mass and the width of the Maxwell distribution. Question 7: Check the box titled 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 on the next page 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 4/8 Gas Mass (u) v mp (m/s) H2 NH3 CO2

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? NAAP – Retention of an Atmosphere 5/8

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, if any, of these gases would Mercury be able to retain to the present day? 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 on Titan 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. Hint: note the location of Titan and Earth relative to the Nitrogen retention curve, and remember how gas velocity is affected by particle mass. NAAP – Retention of an Atmosphere 7/8

Summary/Conclusion (5 points): Using what you have learned in this lab, describe why most of the inner planets have relatively thin atmospheres of heavy gases , and the outer planets have very thick atmospheres of light and heavy gases . In your answer, you should address how atmosphere retention is affected by temperature, mass of gas particles, and the escape velocity of a planet. NAAP – Retention of an Atmosphere 8/8