Assignment #11

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Case Western Reserve University *

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406

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Astronomy

Date

Dec 6, 2023

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Assignment #11 (1) Volcanoes on Jovian Moons (6 pts.) In another solar system, we discover two Jovian moons that have very different levels of volcanism. Propose three hypotheses for possible causes and explain how each of them could account for this difference. Hypothesis 1: The moon with more volcanisms might have more active core which creates a liquid surface. It will result to the more active volcanic activities than the other moon with less active core and solid frozen surface. Hypothesis 2: The moon with more active volcanisms could store more sulphuric or chlorinated resource that can be released out to cause active volcanic activities than the other. Hypothesis 3: The moon with more active volcanisms might be closer to the Jovian planet and easier to be affected by the pull of the planet than the other moon with less active volcanisms. (2) Regular vs. Irregular (2 pts.) (a) Give 3 properties of a regular satellite, that is, a satellite with a regular orbit: Have low eccentricity Have small inclination orbits Tend to be large and bright Their orbit is closed to their parent planet. (1 pt.) (b) Provide an example of a regular satellite: One example of a regular satellites are the Earth and Moon. (1 pt.) (c) Provide an example of an irregular satellite:

Sinope, which is an irregular satellite, is the moon of Jupiter. (2 pts.) (d) What is inferred about the origin of a satellite from the regularity/irregularity of its orbit? Regular orbits indicate that the satellite is formed in orbit, while the irregular orbits suggest that the satellite is captured by the planet’s gravity. (3 pts.) (e) Suppose we find a moon orbiting around a planet at a distance of 100,000 km, and a student says: "Perhaps this moon was originally an asteroid orbiting the Sun, and it just happened to drift close to the planet until it as only 100,000 km away from it, where it was caught by the planet's gravity, and it has been orbiting here ever since." Using the law of conservation of energy, explain why this scenario is physically impossible, and why a capture process must be more complicated than this. Please ignore the effect of the Sun's gravity in your analysis. It is irrelevant. According to the law of conservation of energy, the total energy of an isolated system remains constant, which means this scenario is impossible unless the total energy of the system changes. The moon will keep original movement and will not be captured by a different gravitational pull unless collision happens that change the total energy of the system. (3) Titan (6 pts.) Astronomers were amazed to discover evidence of rain, rivers, lakes, seas, and river deltas on Saturn's moon Titan. However, many astrobiologists are still skeptical that we will find living organisms in the lakes and seas on the surface of Titan. Write a paragraph discussing this issue and explaining the source of this skepticism. There are couple of reasons to support this skepticism. Firstly, the temperature of Titan is much lower than the temperature of Earth, which means no liquid water would present on its surface. Secondly, the orbit and rotation indicate that it is not solid all the time, making subsurface liquid water like. Even there existed some sort of life on the planet in some form, it is hard to sustain the life itself on this frozen moon. (4) Making a Model of Planetary Rings

(3 pts.) (a) The rings of Saturn are about 70,000 kilometers across but only 20 meters thick. Suppose you wanted to build a model of Saturn's rings out of a sheet of plastic that is 1.5 mm thick. To keep the proportions right, how large a sheet of plastic would you need to make the scale model realistic? Show your work. The proportion between the diameter to thickness: 70000km/0.02km=3500000, Since the thickness of the sheet of plastic is 1.5mm, the diameter for this sheet should be: 1.5*3500000=5250000mm=5250000*10 -6 km=5.25km (3 pts.) (b) To model Uranus' thin rings, strings of spaghetti (or perhaps, strictly speaking, linguini) would be more appropriate than sheets of plastic. Uranus' rings are also only about 20 meters thick and extend around the planet in a thin ring at a radius of about 50,000 km. If you wanted to build a model of Uranus' ring using 3 mm thick pasta - how long a piece of spaghetti would you need? Show your work. The ratio between radius and thickness of Uranus’ ring is: 50,000km/0.02km=2,500,000 So the radius of this model made by this spaghetti should be 3*2,500,000=7,500,000mm=7.5km, To calculate how long this spaghetti is, we need to calculate its circumference: 2*pi*7.5=47.12km (5) Rings (4 pts.) In another solar system we discover two Jovian planets which are very similar, yet one has an extensive icy ring system, while the other has negligible rings. Propose a hypothesis to explain why this difference might exist. Your hypothesis should be consistent with the ring systems in our own solar system. The planet with extensive icy ring system has stronger gravitational pull than the planet with negligible rings. The planet with stronger gravity will have more moons and because of its stronger gravity, it will capture rocks and

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debris for collision and generate more debris to attribute to the ring formation, compared to the planet with weaker gravity. (6) Distances and Velocities (3 pts.) (a) A space probe is launched on a mission requiring it to travel a distance of 3.5 AU in 14 months. What must be this space probe's average speed? Give your answer in kilometers per second. As we all know, 1AU=1.496*10 8 km, So 3.5AU=5.24*10 8 km. Since speed=distance traveled/time elapsed, v=5.24*10 8 km/ (365+30+31)days*24h*60min*60s=14.2km/s (3 pts.) (b) A space probe is 16 AU from the Earth. How much time will it take its radio signals to travel through space to reach us? Give your answer in hours. As we all know, 1AU=1.496*10 8 km, So 16AU=2.4*10 9 km. 2.4*10 9 km/(300,000km/s) =8000s=2.2h (3 pts.) (c) If it takes 4.78 hours for light from a comet to reach us, what is its distance? Give your answer in AU. The distance = 4.78h*60min*60s*300,000km/s=5162400000km Since 1AU=1.496*10 8 km, the distance=5162400000km/ (1.496*10 8 )=34.51AU

Assignment #11

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