Atmospheric Retention – Student Guide

QUESTION

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

Object

Mass
(Mearth)

Radius
(Rearth)

vesc
(km/s)

vesc (km/s) calculation
(optional)

Mercury

0.055

0.38

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Uranus

15

4.0

Io

0.015

0.30

Vesta

0.00005

0.083

Krypton

100

10

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.

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
vmp and average velocity vavg, and d) shade in the region
corresponding to the fastest moving 3% of the gas particles.

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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)

vmp (m/s)

300

200

100

Question 4: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 and vmp.

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?

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

Gas

Mass (u)

vmp (m/s)

H2

NH3

CO2

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.

Run

T (K)

vesc (m/s)

Description of
Simulation

1

500

1500

H2 is very quickly lost
since it only has a mass of 2u and its most probable velocity is greater than
the escape velocity, NH3 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, CO2 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?
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×vavg) 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 vesc over 10×vavg of a gas, it will certainly
retain that gas over time intervals on the order of the age of our solar
system.
o
If vesc is roughly 5
to 9 times vavg, the gas will be partially retained and the color
fades into white over this parameter range.
o
If vesc < 5 vavg, 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. · 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. 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? Question 12:Most nitrogen atoms have a mass of 14u (hence 28u for N2), 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.)   ANSWER: REQUEST HELP FROM A TUTOR