2019年USAAAO决赛第5题 - 版本历史

2020年3月7日 (六) 09:44 Jingsong Guo

2020-03-07T09:44:40Z

2020年3月7日 (六) 09:21 Jingsong Guo

2020-03-07T09:21:49Z

2020年3月7日 (六) 09:20 Jingsong Guo

2020-03-07T09:20:31Z

Jingsong Guo：创建页面，内容为“==英文题目== 5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because…”

2020-03-07T09:19:00Z

创建页面，内容为“==英文题目== 5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because…”

新页面

==英文题目==

5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because of a fortunate coincidence: its axis of rotation points directly at their home planet. That means they can have uninterrupted communication with home by planting fixed transmitters on The North Pole. But first, they need to find out if Earth’s axis will always point in the same direction or if it undergoes precession. They can’t know without years of observation, so they hope that we, its now-extinct intelligence, have left behind the answer. While orbiting Earth, they see a few remarkable structures, including the Hoover Dam in Nevada. Zooming in on the dam, a colorful plaza with peculiar markings on its floor catches their attention. Descending on the plaza, they realize the markings are a map of the sky when the dam was built, left to indicate the date to posterity. Figure 1 is an overhead architectural map of this plaza. The center-point depicts the north ecliptic pole, and the large circle represents the path of the Earth’s axis throughout its counter-clockwise procession. As they interpret the map, they’re dismayed to realize that their star has not been and will not be Earth’s north star for very long.

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 [[文件:Figure 1 for USAAAO2019 Final Q5.jpg|缩略图|Figure 1: Overhead architectural plan of the Hoover Dam plaza depicting Polaris as north star]]
-For the purpose of this question, assume that the Earth’s axial tilt is a constant i = 23.5 degrees and its axis precesses at a constant rate.
+For the purpose of this question, assume that the Earth’s axial tilt is a constant $$i = 23.5^{\circ}$$ and its axis precesses at a constant rate.
 a) Using the values on the map, and knowing that the aliens used carbon-aging to determine that the dam is 12,000 years old, find all possible values for the period of Earth’s axial precession.

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	5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because of a fortunate coincidence: its axis of rotation points directly at their home planet. That means they can have uninterrupted communication with home by planting fixed transmitters on The North Pole. But first, they need to find out if Earth’s axis will always point in the same direction or if it undergoes precession. They can’t know without years of observation, so they hope that we, its now-extinct intelligence, have left behind the answer. While orbiting Earth, they see a few remarkable structures, including the Hoover Dam in Nevada. Zooming in on the dam, a colorful plaza with peculiar markings on its floor catches their attention. Descending on the plaza, they realize the markings are a map of the sky when the dam was built, left to indicate the date to posterity. Figure 1 is an overhead architectural map of this plaza. The center-point depicts the north ecliptic pole, and the large circle represents the path of the Earth’s axis throughout its counter-clockwise procession. As they interpret the map, they’re dismayed to realize that their star has not been and will not be Earth’s north star for very long.		5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because of a fortunate coincidence: its axis of rotation points directly at their home planet. That means they can have uninterrupted communication with home by planting fixed transmitters on The North Pole. But first, they need to find out if Earth’s axis will always point in the same direction or if it undergoes precession. They can’t know without years of observation, so they hope that we, its now-extinct intelligence, have left behind the answer. While orbiting Earth, they see a few remarkable structures, including the Hoover Dam in Nevada. Zooming in on the dam, a colorful plaza with peculiar markings on its floor catches their attention. Descending on the plaza, they realize the markings are a map of the sky when the dam was built, left to indicate the date to posterity. Figure 1 is an overhead architectural map of this plaza. The center-point depicts the north ecliptic pole, and the large circle represents the path of the Earth’s axis throughout its counter-clockwise procession. As they interpret the map, they’re dismayed to realize that their star has not been and will not be Earth’s north star for very long.
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		+	[[文件:Figure 1 for USAAAO2019 Final Q5.jpg\|缩略图\|Figure 1: Overhead architectural plan of the Hoover Dam plaza depicting Polaris as north star]]

	For the purpose of this question, assume that the Earth’s axial tilt is a constant i = 23.5 degrees and its axis precesses at a constant rate.		For the purpose of this question, assume that the Earth’s axial tilt is a constant i = 23.5 degrees and its axis precesses at a constant rate.

←上一版本		2020年3月7日 (六) 09:20的版本
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	5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because of a fortunate coincidence: its axis of rotation points directly at their home planet. That means they can have uninterrupted communication with home by planting fixed transmitters on The North Pole. But first, they need to find out if Earth’s axis will always point in the same direction or if it undergoes precession. They can’t know without years of observation, so they hope that we, its now-extinct intelligence, have left behind the answer. While orbiting Earth, they see a few remarkable structures, including the Hoover Dam in Nevada. Zooming in on the dam, a colorful plaza with peculiar markings on its floor catches their attention. Descending on the plaza, they realize the markings are a map of the sky when the dam was built, left to indicate the date to posterity. Figure 1 is an overhead architectural map of this plaza. The center-point depicts the north ecliptic pole, and the large circle represents the path of the Earth’s axis throughout its counter-clockwise procession. As they interpret the map, they’re dismayed to realize that their star has not been and will not be Earth’s north star for very long.		5. (15 points) An alien spaceship from the planet Kepler 62f is in search of a rocky planet for a remote base. They’re attracted to Earth because of a fortunate coincidence: its axis of rotation points directly at their home planet. That means they can have uninterrupted communication with home by planting fixed transmitters on The North Pole. But first, they need to find out if Earth’s axis will always point in the same direction or if it undergoes precession. They can’t know without years of observation, so they hope that we, its now-extinct intelligence, have left behind the answer. While orbiting Earth, they see a few remarkable structures, including the Hoover Dam in Nevada. Zooming in on the dam, a colorful plaza with peculiar markings on its floor catches their attention. Descending on the plaza, they realize the markings are a map of the sky when the dam was built, left to indicate the date to posterity. Figure 1 is an overhead architectural map of this plaza. The center-point depicts the north ecliptic pole, and the large circle represents the path of the Earth’s axis throughout its counter-clockwise procession. As they interpret the map, they’re dismayed to realize that their star has not been and will not be Earth’s north star for very long.
		+
		+	For the purpose of this question, assume that the Earth’s axial tilt is a constant i = 23.5 degrees and its axis precesses at a constant rate.
		+
		+	a) Using the values on the map, and knowing that the aliens used carbon-aging to determine that the dam is 12,000 years old, find all possible values for the period of Earth’s axial precession.
		+
		+	b) Using the most optimistic answer (longest period) from part (a), calculate how many arcseconds the Earth’s axis precesses each day. Use the period you calculate here in the next two sections.
		+
		+	c) If they hadn’t been lucky enough to come across the star map and decided to build a radio interferometer to observe the movement of the celestial pole over the course of 30 days instead, how many kilometers would the baseline of their telescope array have to be, assuming it operated at a 20cm wavelength?
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		+	d) As a last resort, to keep Earth’s axis fixed, the aliens decide to counter the forces that cause the Earth’s precession by building giant nuclear thrusters on the Earth’s surface. Assume Earth’s precession is caused by external forces alone and calculate the average force (in kN) that a strategically positioned thruster would have to exert to counter them.