MEEEEEEEEE
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This one is driving me nuts
It’s very cold and dark when you crash land. You notice that the stars appear to move slowly clockwise around a location that is 40º above the horizon. Because of this apparent motion of the stars, your group chooses to declare that the crash site is in the planet’s southern hemisphere and that the stars appear to circle around the south celestial pole. Later, when the sun (smaller and redder than the Sun you are familiar with at home) rises, you notice that it rises from the southeast and passes very high in the northern sky. You record that nearly 30 hours elapse between when the sun passes highest in the sky each day, and that the sun is passing closer and closer to zenith on each successive 30-hour day. Despite the high noontime sun, the daytime remains oppressively cold. Because it’s so cold, you resolve to travel north in the hope of finding a warmer climate nearer to the equator. Some of the crash survivors choose to stay behind at the crash site, while you join a team heading north. You remain in radio contact with the crash site. One day, after you’ve traveled 150 km north, your team observes the sun to pass directly through the zenith, while the people back at the crash site observe that it passes 2º north of zenith on the same day. After that day, the sun’s noontime height in the sky as seen from the crash site begins to decrease instead of increasing like it had been before. Meanwhile, you’ve been watching the night sky and noticing two bright “stars” that have been slowly changing position compared to the other stars around them. You recognize that this must mean they are relatively nearby planets and cannot be stars. One of these planets-- very bright and yellow-- has been highest in the sky at nearly the middle of the night. The other planet-- less bright and redder-- is only visible for a few hours after sunset, and it appeared to reach a greatest height in the sky after sunset just a few days after the crash landing. Now, many days later, it appears to be moving closer to the sun and setting sooner after sunset.
a) What is the latitude of the crash site?
b) Determine the circumference of the planet that you landed on. Show your work or explain your reasoning.
c) How many kilometers from the equator is the crash site? Show your work or explain your reasoning.
d) Remembering that the circumference of a circle is equal to p times the diameter, determine the diameter of the planet. (p = 3.14…) Compare this to the diameter of the Earth.
e) What is the tilt of the planet’s equator compared to the plane of the planet’s orbit around its sun? Comment on what this implies about the seasonal extremes of weather you might expect to encounter on this planet compared to the seasonal extremes of weather back on Earth.
f) Of the two planets that you noticed in the night sky, what can you conclude about the sizes of their orbits compared to the orbit of the planet on which you crash landed? Explain the basis of your conclusions.
It’s very cold and dark when you crash land. You notice that the stars appear to move slowly clockwise around a location that is 40º above the horizon. Because of this apparent motion of the stars, your group chooses to declare that the crash site is in the planet’s southern hemisphere and that the stars appear to circle around the south celestial pole. Later, when the sun (smaller and redder than the Sun you are familiar with at home) rises, you notice that it rises from the southeast and passes very high in the northern sky. You record that nearly 30 hours elapse between when the sun passes highest in the sky each day, and that the sun is passing closer and closer to zenith on each successive 30-hour day. Despite the high noontime sun, the daytime remains oppressively cold. Because it’s so cold, you resolve to travel north in the hope of finding a warmer climate nearer to the equator. Some of the crash survivors choose to stay behind at the crash site, while you join a team heading north. You remain in radio contact with the crash site. One day, after you’ve traveled 150 km north, your team observes the sun to pass directly through the zenith, while the people back at the crash site observe that it passes 2º north of zenith on the same day. After that day, the sun’s noontime height in the sky as seen from the crash site begins to decrease instead of increasing like it had been before. Meanwhile, you’ve been watching the night sky and noticing two bright “stars” that have been slowly changing position compared to the other stars around them. You recognize that this must mean they are relatively nearby planets and cannot be stars. One of these planets-- very bright and yellow-- has been highest in the sky at nearly the middle of the night. The other planet-- less bright and redder-- is only visible for a few hours after sunset, and it appeared to reach a greatest height in the sky after sunset just a few days after the crash landing. Now, many days later, it appears to be moving closer to the sun and setting sooner after sunset.
a) What is the latitude of the crash site?
b) Determine the circumference of the planet that you landed on. Show your work or explain your reasoning.
c) How many kilometers from the equator is the crash site? Show your work or explain your reasoning.
d) Remembering that the circumference of a circle is equal to p times the diameter, determine the diameter of the planet. (p = 3.14…) Compare this to the diameter of the Earth.
e) What is the tilt of the planet’s equator compared to the plane of the planet’s orbit around its sun? Comment on what this implies about the seasonal extremes of weather you might expect to encounter on this planet compared to the seasonal extremes of weather back on Earth.
f) Of the two planets that you noticed in the night sky, what can you conclude about the sizes of their orbits compared to the orbit of the planet on which you crash landed? Explain the basis of your conclusions.