lab2

ES 2232G: Exploring the Planets: Sun, Earth, Planets Laboratory 02 – Planetary Atmospheres (Materials reproduced from the Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu). INTRODUCTION This lab explores some of the elements that go into the retention or loss of an atmosphere by a planet. Open a web browser and point to: http://astro.unl.edu/naap/atmosphere/atmosphere.html . 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 4.3     0.055 11.2 4.3 0.38 km km s s        Uranus 15 4.0 21.7 √ ( 15 ) ( 4.0 ) ( 11.2 km s ) = 21.1 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 Earth Sciences 2232G: Lab 02 1

km s Krypton 100 10 35.4 √ ( 100 ) ( 10 ) ( 11.2 km s ) = 35.4 km s 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. Maxwe ll Speed Distribution Earth Sciences 2232G: Lab 02 Number of Particles Average Velocity Most probable velocity Particle Speeds Fastest 3% 2

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? Absolute 0 is when a system has little to zero thermodynamic energy and there is theoretically no atom movement. Therefore, at 0K, the most probable velocity would be zero, due to the lack of energy emitted.  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. There is a direct negative correlation between the atomic mass of the atom and the probable velocity. As the atomic mass increases from H 2 (2 u) to Carbon Dioxide (44 u), the speeds of the particles at 300 K reduce. Heavier molecules tend to travel relatively slower than lighter molecules. Looking at the width of the curves, the lower the mass, the longer the width. Ammonia and Carbon Dioxide tend to have smaller widths and more prominent bell- shaped curves, while Hydrogen has a very long width and less defined curve. 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 below of the results similar to the example completed for you (max 5 lines). Earth Sciences 2232G: Lab 02 4 Gas Mass (u) v mp (m/s) H 2 2 1555 NH 3 17 538 CO 2 44 325

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 H 2 is lost very quickly since it has a relatively low mass and since its most probable velocity is much higher than the escape velocity for this stimulation. NH 3 escapes at a medium speed, faster than at 1500 m/s escape velocity, as a more significant fraction of the distribution is greater than 1000m/s. CO 2 is lost very slowly, but faster than 1500m/s. 3 500 500 All three gases are lost relatively fast because large fractions of all three of the velocity distributions are greater than the escape speed of 500. However, H 2 is still lost the fastest, NH 3 the second fastest and CO 2 the third fastest. 4 100 1500 H 2 is the only gas that is escapes from the chamber, reducing relatively fast. Both NH 3 and CO 2 are unaffected since the most probable velocity is far less than the escape velocity and large fractions of their distribution curves are less than 1500m/s. 5 100 1000 Once again, H 2 is the only gas that is escapes from the chamber, reducing relatively fast. Both NH 3 and CO 2 are unaffected since the most probable velocity is far less than the escape velocity and majority of their distribution curves are less than 1000m/s. 6 100 500 H 2 leaves very quickly, as a large fraction of its distribution is greater than 500m/s. A quarter of the NH 3 distribution is greater than the escape velocity, hence it escapes at a medium speed. CO 2 is lost, but very slowly. 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? The gas is likely to be retained in the chamber if the most probable velocity and a large fraction of the velocity distribution is less than escape velocity, as it does not have the velocity to escape the chamber. It is likely to escape when the most probable velocity and a large portion of the curve is greater than the escape velocity, as it has the velocity to escape the chamber. A general trend was H 2 would always escape first and fastest and majority of the time CO 2 would escape very slowly, if not at all. Earth Sciences 2232G: Lab 02 5

This is why Mercury is not a gas giant, but a large metal/rock body. THINGS TO SUBMIT:  Submit this document via OWL to complete this lab. Earth Sciences 2232G: Lab 02 7