Sarah Sherman Planetary Atmosphere

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Clemson University *

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1030

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Astronomy

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Dec 6, 2023

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docx

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Planetary Atmosphere Worksheet Student Name: Sarah Sherman Section: 4 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) The velocity of a hydrogen molecule in a planet’s atmosphere at 1 AU from the Sun is approximately 2262.74 m/s. Using equation 1, 160*the square root of 400 K/2 amu equals 2262.74 m/s. 2. Can the Earth hold onto an atmosphere of hydrogen? Explain why or why not. The Earth cannot hold onto an atmosphere of hydrogen because the velocity of hydrogen is well above Earth’s escape velocity. ⅙ 3. What is the velocity of a nitrogen molecule at 1 AU? The velocity of a nitrogen molecule at 1 AU is 604.74 m/s. Using equation 1, 160*the square root of 400 K/28 amu equals 604.74 m/s. 4. Can the Earth hold onto an atmosphere of nitrogen? Explain why or why not. The Earth can hold onto an atmosphere of nitrogen because the velocity of nitrogen is well below ⅙ Earth’s escape velocity. 5. Estimate how far the Moon would have to be from the Sun before it would be cool enough to retain a nitrogen atmosphere. The Moon would have to be 6.19 AU because using equation 1 and the escape velocity of the moon (2,300 m/s) with the mass of Nitrogen (28 amu), the temperature would equal 160.7172. Then using the equation T=To x D^-½, D=6.19 AU. 6. What gasses from Table 3 could Mars retain in its atmosphere? Plugging in the gas masses into equation 1 with Mars’ escape velocity (5,000 m/s), Mars could retain all of the gasses from Table 3 except for hydrogen. 7. What gasses from Table 3 could Ceres retain? Plugging in all the gas masses into equation 1 with Ceres escape velocity (510 m/s), Ceres could not retain any of the gasses

from Table 3. 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 can hold onto an atmosphere of hydrogen molecules if it was moved to .5 AU from the Sun. Using equation 1 with the temperature 566 K and hydrogen’s mass of 2 amu, it results in 2691.62. This is possible because the gas velocity of hydrogen is 2691.62, and 2691.62 < 9916.67. 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, Jupiter could not have formed at .5 AU from the Sun because the temperature would not be suitable for gaseous planets to form. 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: These are consistent with my calculations as Ceres does not hold any of the molecules within Table 3. 11. Earth: Earth’s atmospheres consists of nitrogen, oxygen and a small amount of carbon dioxide. This is consistent with my calculations as earth could not hold hydrogen but could hold other denser gasses. 12. Jupiter: Jupiter’s atmosphere is composed mostly of hydrogen which is consistent with my calculations because even if Jupiter’s temperature changed, it could still hold large amounts of hydrogen.

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