Planetary Atmospheres Lab Handout

Name: Emma Petersen Planetary Atmospheres Instructions Then complete the following q.uestions related to the background information. Type your answers directly into this document, using bold, red text. When you are finished, save the document as a pdf and upload to Canvas. To begin this assignment, you will need to download and install the NAAP Labs software . Be sure to select “NAAP Labs – v 1.1” for whatever operating system you are using. It is also possible you already have this installed from a previous lab assignment, so check your computer before (possibly re-)installing. Once NAAP Labs is installed, launch the program and click on the “Atmospheric Retention” lab (lab #11 as of May 2021, but this may change in the future). Section 1: Background Read the background sections on escape velocity , projectile simulation , and speed distribution by clicking on those links in the left part of your NAAP Labs window. Then answer the following questions. 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. (Highlight your answer using bold, red text) 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 (M earth ) Radius (R earth ) v esc (km/s) v esc (km/s) calculation Mercury 0.055 0.38 4.3 √ 0.055 0.38 × ( 11.2 km s ) = 4.3 km s Uranus 15 4.0 21.7 √ 15 4 × ( 11.2 km s ) = 21.7 km s Io 0.015 0.30 2.5 √ 0.015 0.30 × ( 11.2 km s ) = 2.5 km s Vesta 0.00005 0.083 0.09 √ 0.00005 0.83 × ( 11.2 km s ) = 0.09 km s Krypton 100 10 35.4 √ 100 10 × ( 11.2 km s ) = 35.4 km s Question 3 : Experiment with the Speed Distribution Simulator (also called a “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. (To sketch the curve, you may either use the drawing tools available in your word processor, or alternatively draw the sketch on paper, take a picture, then insert the picture into this document.) Relative number of Particle speeds

molecular motion theoretically stops. This would imply that the most probable velocity at 0 K would be 0 m/s. This is because there is no thermal energy left to provide any kinetic energy to the particles, and they would be completely at rest. • 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 v mp and the width of the Maxwell distribution. As the mass of the gas molecules increases, the most probable velocity (vmp) generally decreases. Lighter molecules like hydrogen have higher most probable velocities, while heavier molecules like carbon dioxide have lower most probable velocities. 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. 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 H2 once again was lost very quickly, meanwhile slightly slower than before because its most probable velocity is higher than the escape velocity. NH3 was lost relatively at half the speed of H2. CO2 was lost extremely slowly Gas Mass (u) v mp (m/s) H 2 2 1500 NH 3 17 545 CO 2 44 354

3 500 500 H2 and NH3 were lost at almost the same speed, which was very quickly. CO2 was also lost very quickly only slightly slower than H2 and NH3 4 100 1500 H2 was lost at a consistent sped, meanwhile NH3 and CO2 stayed stable and were unaffected 5 100 1000 H2 was lost quicker than last time and NH3 and CO2 both stayed unaffected. 6 100 500 H2 was lost very quickly and NH3 was lost at about 1/3 the speed of H2. Meanwhile CO2 appeared to be unaffected 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? A gas is likely to be retained when its most probable velocity is significantly lower than the escape velocity. This is observed in the cases of NH3 and CO2 at low temperatures. A gas is likely to escape when its most probable velocity is close to or greater than the escape velocity. This is observed in the cases of H2 and NH3 at high temperatures. Section 3: 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.

 Helium is lighter than hydrogen, so it will have an even higher most probable velocity. The retention curve for helium will decline more rapidly than for hydrogen.  Ammonia (NH3), Nitrogen (N2), Carbon Dioxide (CO2), Xenon (Xe):  These gases are heavier, so their most probable velocities will be lower. They will tend to be retained at higher temperatures compared to hydrogen and helium.  Xenon (Xe):  Being the heaviest gas in this list, xenon will have the lowest most probable velocity. Its retention curve will show a very gradual decline, indicating that it is retained over a wide range of temperatures. • 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 (Jupiter and Saturn) primarily retain hydrogen and helium due to their massive sizes and strong gravitational fields. Uranus and Neptune, while also capable of retaining hydrogen and helium, have lower masses and therefore hold onto lighter gases less effectively. Other gases like ammonia, nitrogen, carbon dioxide, and xenon are present in trace amounts or are not significant components in the atmospheres of these planets.

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 is a small, rocky planet with a very thin atmosphere. Its low mass and weak gravity mean it has a limited ability to retain gases. Mercury would be most capable of retaining nitrogen and carbon dioxide. These gases have higher molecular masses compared to hydrogen, helium, methane, and ammonia, making them less likely to escape Mercury's gravitational pull. However, even with these heavier gases, Mercury's retention capacity would still be quite limited compared to larger planets in our solar system. . 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. The disparity in nitrogen isotope ratios between Titan and Earth may be attributed to a range of geological and atmospheric processes. Factors such as differing gravitational strengths, distinct geological histories, impact events, chemical reactions, and solar radiation interactions could have influenced the isotopic composition of each celestial body. Additionally, historical variations in Titan's environment, including changes in temperature, pressure, and chemical makeup, might have played a role. 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.)