Planetary Atmosphere worksheet

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Clemson University *

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1030

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Physics

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Dec 6, 2023

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docx

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3

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Planetary Atmosphere Worksheet These lab activities have evolved over many years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include, in chronological order, Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Steven Bromley, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. Student Name: _________________________________________________Section: _______ For the following questions, use the equations given in the instruction document to do the calculation and answer the questions. You may use trial and error, a range of values in a spreadsheet, or algebra! For any question where you use an equation be sure to give the equation (the number from the instructions is acceptable) and the values of the variables that you plugged into the equation. Every question should have complete sentence answers. 1) What is the velocity of a hydrogen molecule in a planet’s atmosphere at 1 AU from the Sun? (remember to provide the equations you use and the numbers you plug into the equation) Using the equation for the velocity of gas, (160*sqrroot(400/2)), the velocity of a hydrogen molecule in a planets atmosphere 1au from the sun would be 2262.7417 m/s 2) Can the Earth hold onto an atmosphere of hydrogen? Explain why or why not. No, Earth cannot hold onto this atmosphere of hydrogen, using equation #2, the escape velocity (11200) multiplied by 1/6 is 1866.667 which is less than the velocity of gas which is 2262.7417 m/s 3) What is the velocity of a nitrogen molecule at 1 AU? Using the first equation, (160*Sqrroot(400/28)) the velocity of a nitrogen molecule at 1au is 604 . 7432 m/s 4) Can the Earth hold onto an atmosphere of nitrogen? Explain why or why not.
Yes, using the second inequality equation, earth can hold onto an atmosphere of nitrogen because the vgas is less than the escape velocity multiplied by 1/6 which is 1866.667 m/s 5) Estimate how far the Moon would have to be from the Sun before it would be cool enough to retain a nitrogen atmosphere. Right now the equation stands at 160*sqrroot(400/28) which gets 604. Vesc is equal to 2300 for the moon. 2300/6 is 383.3. to make these numbers close we must change the distance thus changing the temp. if we try 6 for example, the temp would change to 163 thus changing vgas to 385.99 m/s. This number is extremley close to the number we need to be able to contain a nitrogen atmosphere, thus my estimation would be around 6au 6) What gasses from Table 3 could Mars retain in its atmosphere? The maximum mass that mars would be able to retain in its atmosphere would be 12.0217 amu using the average between 1 and 2. To find which gasses would work, you must repeat the first equation for each gas to find a amu that is less than 12.0217. After doing the formula for each gas, the only gas that mars could contain in its atmosphere would be hydrogen. 7) What gasses from Table 3 could Ceres retain? Since the escvelocity of ceres is is 510, divided by 6 is 90. We must do the first formula for each gas and find which one is less than 90. We must find the temp at 2.8 which would be roughly 220. 220/each gas’ mass one by one> hydrogen doesn’t work, Methane doesn’t work, ammonia doesn’t work, water doesn’t work, nitrogen doesn’t work, carbon dioxide doesn’t work. After doing the math for each gas, Ceres could retain none of these gasses. 8) Jupiter formed at and currently orbits at a distance of about 5 AU from the Sun. Could Jupiter hold onto an atmosphere of hydrogen molecules if you moved it to 0.5 AU from the Sun? Yes, Jupiter would be able to hold on to an atmosphere of hydrogen molecules if you moved it to .5au due to the escape velocity (9916.667 m/s) being greater than the vgas from this same scenario with all the values plugged in 9) Given what you currently know about the formation of the planets in the Solar System, could Jupiter have formed at 0.5 AU from the Sun? Explain your answer. No, given Jupiter’s mainly gas makeup, its large size, being a gas giant it would be impossible unlike the rest of the planets which are terrestrial planets. Look up, either in your textbook or online, the dominant composition of the atmospheres of Ceres, Earth, and Jupiter. Are these consistent with your calculations? Explain your answer for each.
10) Ceres:From my research, Ceres has a thin, almost non existent atmosphere composed mainly of water vapor. This does line up and support my observations as we found that none of the molecules would be able to be held in the atmosphere. 11) Earth:Earths atmosphere is mostly nitrogen, meaning this is consistent and supports our calculations, because from what I said, earth would be able to hold on to nitrogen in its atmosphere 12) Jupiter: Yes, this is also consistent with my calculations bc Jupiter’s atmosphere consists mostly of hydrogen. When answering questions, I said Jupiter could hold an atmosphere of hydrogen.
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