What is Atmospheric Retention?

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.

(1 points) 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 same as ___ the escape velocity of asteroid A.

4 times

Twice

the same as

half

One-fourth

(2 points) 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
Mercury	0.055	0.38	4.3
Uranus	15	4.0	21.7	√(15)/(4.0) (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	0.3	√(0.00005)/(0.083) (11.2 km/s) =0.3 km/s
Krypton	100	10	35.4	√(100)/(10) (11.2 km/s) = 35.4 km/s

(2 points) Experiment with the Maxwell Distribution Simulator . Then a) draw a sketch of a typical gas curve below ( use simple MS word drawing capability ), 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

Gas Retention Simulator

Open the gas retention simulator . Begin by familiarizing yourself with the capabilities of the gas retention simulator through experimentation.

The gas retention simulator provides you with a chamber in which you can place various gases and control the temperature. The dots moving inside this chamber should be thought of as tracers where each represents a large number of gas particles. The walls of the chamber can be configured to be a) impermeable so that they always rebound the gas particles, and b) sufficiently penetrable so that particles that hit the wall with velocity over some threshold can escape. You can also view the distributions of speeds for each gas in relation to the escape velocity in the Distribution Plot panel.

The lower right panel titled gases allows you to add and remove gases in the experimental chamber. The lower left panel is titled chamber properties . In its default mode it has allow escape from chamber unchecked and has a temperature of 300 K. Click start simulation to set the particles in motion in the chamber panel. Note that stop simulation must be clicked to change the temperature or the gases in the simulation.

The upper right panel titled distribution plot allows you to view the Maxwell distribution of the gas as was possible in the background pages. Usage of the show draggable cursor is straightforward and allows you to conveniently read off distribution values such as the most probable velocity. The show distribution info for selected gases requires that a gas be selected in the gas panel. This functionality anticipates a time when more than one gas will be added to the chamber.

Gas Retention Simulator 

Open the gas retention simulator . Begin by familiarizing yourself with the capabilities of the gas retention simulator through experimentation.

The gas retention simulator provides you with a chamber in which you can place various gases and control the temperature. The dots moving inside this chamber should be thought of as tracers where each represents a large number of gas particles. The walls of the chamber can be configured to be a) impermeable so that they always rebound the gas particles, and b) sufficiently penetrable so that particles that hit the wall with velocity over some threshold can escape. You can also view the distributions of speeds for each gas in relation to the escape velocity in the Distribution Plot panel.

The lower right panel entitled gases allows you to add and remove gases in the experimental chamber. The lower left panel is entitled chamber properties . In its default mode it has allow escape from chamber unchecked and has a temperature of 300 K. Click start simulation to set the particles in motion in the chamber panel. Note that stop simulation must be clicked to change the temperature or the gases in the simulation.

The upper right panel entitled distribution plot allows one to view the Maxwell distribution of the gas as was possible in the background pages. Usage of the show draggable cursor is straightforward and allows one to conveniently read off distribution values such as the most probable velocity. The show distribution info for selected gases requires that a gas be selected in the gas panel. This functionality anticipates a time when more than one gas will be added to the chamber.

Exercises

Use the pull-down menu to add hydrogen to the chamber.

T (K)	v mp (m/s)
300	1500
200	1215
100	874

(2 points) 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(K) and v mp (m/s) . Given a situation that involves a higher temperature, it consequentially affects the speed, which will be faster. 

(2 points) 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 at that temperature would be zero, given that the energy emitted at that time would be zero. It means there is the suspension of everything, and there is no movement. ______ 

Return the temperature to 300 K. Use the gas panel to add Ammonia and Carbon Dioxide to the chamber.

Gas	Mass (u)	v mp (m/s)
H2	2	1500
NH3	28	92.7
CO2	44	48.1

(2 points) 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. For both the mass and the vmp, they exhibit a correlation existing between one another. As mass nears zero, the probable velocity increases. With that in question, it impacts on the Maxwell distribution graph. Then it becomes wider to lower the mass of the gases. With a rise in mass, the probable velocity lowers and consequently the narrowing of the graph. 

(2 points) 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 first example completed for you . The table provided here should be used to record your escape velocity associations to temperature. The primary objective here is to perform an analysis using the escape velocity data as it relates to the temperature of a planet's atmosphere. This will provide some insight as to why the Jovian vs. Terrestrial planetary atmospheres differs greatly in composition.

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	Hydrogen is the first to be lost quickly due to its low mass, for Ammonia is lost at a slower rate but at a reasonable speed since about half of its velocity distribution is over the required escape velocity. On the other hand, Carbon Dioxide is lost very slowly with escape lying on the fastest particles.
3	500	500	Hydrogen escapes at a very fast rate, NH3 as well as Carbon Dioxide which also escapes after Hydrogen. This happens because of the velocity distribution having half its particles above the required escape speed.
4	100	1500	Temperature shows an impact on all the gases. The single compound that is present is Carbon Dioxide and some Ammonia. No other compound showed signs of being formed. The particles are likely going extremely slow.
5	100	1000	The changes here are the same as when you move from an escape velocity of 1500 to 100m/s. The Carbon Dioxide only, particles are very few; the particle movements is very slow.
6	100	500	At this temperature Hydrogen escapes very fast, Ammonia Evacuates at a reasonable speed because of its up to 1/3 escape velocity. The only compound is Carbon Dioxide the movement as well is very slow.

(2 points) 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? From the table above, it can be summarized that with high temperatures, and with speed maintained to be high, the retention consequently exhibited a trend that went higher as well. Additionally, with a lowering escape speed, it makes additional higher mass particles to escape while making the lower mass particles to escape quicker. 

1.  

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.

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.

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.

If v esc < 5 v avg , the gas will escape into space quickly.

Exercises Gas Retention Simulator 

Begin experimenting with all boxes unchecked in both the gasses and plot options.

(2 points) 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. The curves for the different gases are the same. The difference noted is that the heavier the molecular mass xenon (131u), it has an effect on the scale such that it is lower. On the other hand, the lightest H2 (2u) is the opposite where on the scale it is the highest. 

(2 points) Check show gas giants in the plot options panel. Discuss the capability of our solar system’s gas giants to retain particular gases among those shown. All the gases represented in the graph can be retained by the gas giants in our solar system. The gases can be retained given the fact that the speed is higher than 10x avg. With such speed, it guarantees that the gas will be retained ultimately. 

(2 points) 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 would not retain any of the gases because of the reason that Mercury is below the retention curves of the gases. Hydrogen can be positioned below 5x the average velocity, and the other gases range between 5 and 9 times the escape velocity that is required. 

(2 points) 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. Titan is characterized to have lower as speed as well as lower temperature. With that, it means it causes a drop in in the gases that can be retained within the atmosphere. And provided Earth is higher in both, its atmosphere retained the 15u and 14u nitrogen atoms. For titan the 15u atoms are retained more than the 14u atoms, giving a ratio different from the actual ratio on earth. The ratio can be figured after escape as far as Titan is concerned. 

(2 points) 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.) The results of the probe and that exhibited on the graph show disparity. According to the graph, it would be challenging for Titan to retain much methane within its atmosphere entirely. From that Nitrogen would almost be the only component appearing in the atmosphere. 

NAAP – Retention of an Atmosphere 1 / 3