# Geol 116 The Planet Class 7-1 Feb 28, Exercise 1, Calculate the escape velocities of the nine planets in the solar system

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1 Exercises/Discussions Atmospheric Composition: Escape Velocities and Surface Temperature Objectives Escape velocity and the mass and size of a planetary body The effect of escape velocity and surface temperature on the oss/retention of gases by a planetary body The atmospheric compositions of terrestrial planets Exercise 1, Calculate the escape velocities of the nine planets in the solar system Escape velocity: the minimum speed needed before a body has enough kinetic energy to escape from the surface of a planet (i.e. overcome its gravitational field). v esc = sqrt(2gm/r), G is the gravitational constant. G = 6.67x10-11 Nm 2 kg -2 Name of your planet Find the mass and mean radius data for your planet in Table A1. mass radius Using the formula given above, calculate the escape velocity for your planet. Give the answer in both SI unit (m/s) and in mph (1mile ~ 1600m, 1 hour = 3600seconds) escape velocity in m/s escape velocity in mph Arrange the following bodies a) All bodies have the same mass. A B C Order in increasing escape velocities: Order in increasing bulk density: b) All bodies have the same size. Darker bodies are denser Order in increasing escape velocities: 1

2 Exercise 2, Locate all planets on an escape velocity-temperature plot Write down all the escape velocities you and your classmates have calculated. Find the mean surface temperature of each planetary body in Table A1 (for the giants, use the effective cloud-top temperature) and complete the table below. V, m/s V, 1/6 V, T, K Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto Locate all planets and the Moon on the following plot: The plot uses base 2 log scales. Roughly estimate the locations based on the labeled ticks. Why do the giant planets have lots of hydrogen and helium while the atmosphere of terrestrial planets are rich in carbon dioxide, nitrogen etc.? Why is the Moon so dry? Do you expect the atmosphere of Pluto rich in hydrogen and helium like the giant planets? Why or why not? 2

3 Exercise 3, Composition of the atmospheres of terrestrial planets Read Figure 5.15 and complete Table 5.2 (there are three blanks for Venus, four for Earth, and four for Mars). Match the following Mercury Venus Earth Mars Thickness of atmosphere Dense Normal (from our perspective, of course) Tenuous Sparse Why is the concentration of carbon dioxide in the terrestrial atmosphere so much lower than that in Martian or Venusian atmosphere? Why is the terrestrial atmosphere so rich in oxygen compared with Venus and Mars? Why is the terrestrial atmosphere so rich in nitrogen compared with Venus and Mars? 3

4 \ 4

5 Keys Exercise 1 Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto mass, kg radius, km V, m/s V, mph Note that kg, m, s, and N are SI units. When you use SI unit for each quantity, your result will also be in SI unit. a) B C A (mass being the same, the smaller the radius, the higher the escape velocity) B C A (massing being the same, the smaller the radius, the higher the density) b) B C A (radius being the same, the denser the body, the larger its mass, hence the higher the escape velocity) Exercise 2 Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto V, m/s V, /6V, T, K According to the Y-axis from bottom up: P, Mo, Me, Ma, (V left, E right), U, N, S, J 5

6 The giant planets are more massive than terrestrial planets. Despite their larger radius, the escape velocities on these planets turn out to be much higher than that on terrestrial planets. They are colder than terrestrial planets so that gas molecules on the giant planets move a lot slower than they do on terrestrial planets. With these two factors combined, the giant planets can retain hydrogen and helium while the terrestrial planets have lost most of them to the space through its 4.6 Ga history. The plot shows that the velocities of hydrogen and helium are well below the one-sixth escape velocities of the giant planets. In contrast, most terrestrial planets plot below the hydrogen and helium line except for the Earth. The Earth plots between the hydrogen and helium line: it can retain helium but not hydrogen. The Moon is small and relatively warm. The one-sixth escape velocity on the Moon is smaller than the velocity of water vapor at lunar surface temperature. Hence the Moon has dried out over its history. Since Pluto plot way below the hydrogen and helium lines, we do not expect that the atmosphere of Pluto contain much hydrogen or helium. Exercise 3 Venus: CO 2, N 2, SO 2 Earth: N 2, O 2, Ar, H 2 O Mars: CO 2, N 2, Ar, O 2 6

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