2015IOAA理论短问题第3题-小行星掩星 - 版本历史

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某九流辣鸡民科：创建页面，内容为“==英文题目== On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, wh…”

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创建页面，内容为“==英文题目== On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, wh…”

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==英文题目==
On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, which was located at the center of the asteroid shadow path. It lasted for only 6.201 s. Assume that Earth’s orbit is circular and the orbit of Julietta is on the ecliptic plane and revolves in the same direction as Earth. At the occultation, Julietta is near its aphelion. At the time of the occultation the distances of Julietta from the Sun and the Earth are 3.076 AU and 2.156 AU respectively. Find the approximate diameter of asteroid Julietta, if the semi major axis of Julietta is 𝑎 = 2.9914 AU.

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 ===官方答案===
 '''（20%）''' Calculate the Earth revolution speed
 Earth revolution speed is
 \[v_E = \frac{2\pi \bar{r}_E}{T_E} = \frac{2\pi a_E}{T_E} = 29805 m/s\]
 '''（25%）''' Calculate Julietta revolution speed
 Julietta revolution is (since the given data is semimajor axis, the orbit of Julietta is ellipse)
 \[v_J = \sqrt{GM \left( \frac{2}{r_J} - \frac{1}{a} \right)} = 16742.9 m/s\]
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 '''（15%）''' Hence, the approximate dimension of Julietta is
 \[l_J = v_{J,rel} t_{occul} = 86701.8 m\]

←上一版本		2026年7月30日 (四) 04:12的版本
第5行：		第5行：
	AI翻译		AI翻译
	2015年5月27日02:18:49，从婆罗浮屠寺（Borobudur temple）观测到了小行星1285 Julietta对恒星HIP 89931（δ-Sgr）的掩星现象，该寺位于小行星阴影路径的中心。掩星仅持续了$$6.201$$秒。假设地球轨道为圆形，Julietta的轨道位于黄道面上，且公转方向与地球相同。在掩星发生时，Julietta正处于其远日点附近。掩星发生时，Julietta到太阳和地球的距离分别为$$3.076 AU$$和$$2.156 AU$$。若Julietta的半长轴$$ a = 2.9914 AU$$，求小行星Julietta的近似直径。		2015年5月27日02:18:49，从婆罗浮屠寺（Borobudur temple）观测到了小行星1285 Julietta对恒星HIP 89931（δ-Sgr）的掩星现象，该寺位于小行星阴影路径的中心。掩星仅持续了$$6.201$$秒。假设地球轨道为圆形，Julietta的轨道位于黄道面上，且公转方向与地球相同。在掩星发生时，Julietta正处于其远日点附近。掩星发生时，Julietta到太阳和地球的距离分别为$$3.076 AU$$和$$2.156 AU$$。若Julietta的半长轴$$ a = 2.9914 AU$$，求小行星Julietta的近似直径。
		+	==解答==
		+	===官方答案===
		+	'''（20%）''' Calculate the Earth revolution speed
		+	Earth revolution speed is
		+	\[v_E = \frac{2\pi \bar{r}_E}{T_E} = \frac{2\pi a_E}{T_E} = 29805 m/s\]
		+
		+	'''（25%）''' Calculate Julietta revolution speed
		+	Julietta revolution is (since the given data is semimajor axis, the orbit of Julietta is ellipse)
		+	\[v_J = \sqrt{GM \left( \frac{2}{r_J} - \frac{1}{a} \right)} = 16742.9 m/s\]
		+
		+	Calculate the approximate dimension of Julietta
		+	[[文件:IOAA2015_ShortProblem_T3_solution_step3.png\|无框\|左]]
		+	From the geometry
		+	\[\cos\alpha = \frac{r_E^2 + r_J^2 - r_{J-E}^2}{2 r_E r_J} = 0.995\]
		+	'''（40%）''' Thus, Julietta's relative projected speed to Earth is
		+	\[v_{J,rel} = v_E - v_J \cos\alpha = 13984.16 m/s\]
		+
		+	'''（15%）''' Hence, the approximate dimension of Julietta is
		+	\[l_J = v_{J,rel} t_{occul} = 86701.8 m\]

←上一版本		2026年7月30日 (四) 03:54的版本
第1行：		第1行：
		+	{{需要解答}}
	==英文题目==		==英文题目==
	On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, which was located at the center of the asteroid shadow path. It lasted for only 6.201 s. Assume that Earth’s orbit is circular and the orbit of Julietta is on the ecliptic plane and revolves in the same direction as Earth. At the occultation, Julietta is near its aphelion. At the time of the occultation the distances of Julietta from the Sun and the Earth are 3.076 AU and 2.156 AU respectively. Find the approximate diameter of asteroid Julietta, if the semi major axis of Julietta is 𝑎 = 2.9914 AU.		On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, which was located at the center of the asteroid shadow path. It lasted for only 6.201 s. Assume that Earth’s orbit is circular and the orbit of Julietta is on the ecliptic plane and revolves in the same direction as Earth. At the occultation, Julietta is near its aphelion. At the time of the occultation the distances of Julietta from the Sun and the Earth are 3.076 AU and 2.156 AU respectively. Find the approximate diameter of asteroid Julietta, if the semi major axis of Julietta is 𝑎 = 2.9914 AU.
		+	==中文翻译==
		+	AI翻译
		+	2015年5月27日02:18:49，从婆罗浮屠寺（Borobudur temple）观测到了小行星1285 Julietta对恒星HIP 89931（δ-Sgr）的掩星现象，该寺位于小行星阴影路径的中心。掩星仅持续了$$6.201$$秒。假设地球轨道为圆形，Julietta的轨道位于黄道面上，且公转方向与地球相同。在掩星发生时，Julietta正处于其远日点附近。掩星发生时，Julietta到太阳和地球的距离分别为$$3.076 AU$$和$$2.156 AU$$。若Julietta的半长轴$$ a = 2.9914 AU$$，求小行星Julietta的近似直径。

←上一版本		2026年7月30日 (四) 05:38的版本
第1行：		第1行：
−	~~{{需要解答}}~~
	==英文题目==		==英文题目==
	On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, which was located at the center of the asteroid shadow path. It lasted for only 6.201 s. Assume that Earth’s orbit is circular and the orbit of Julietta is on the ecliptic plane and revolves in the same direction as Earth. At the occultation, Julietta is near its aphelion. At the time of the occultation the distances of Julietta from the Sun and the Earth are 3.076 AU and 2.156 AU respectively. Find the approximate diameter of asteroid Julietta, if the semi major axis of Julietta is 𝑎 = 2.9914 AU.		On 27 May 2015 at 02:18:49, the occultation of the star HIP 89931 (𝛿 −Sgr) by the asteroid 1285 Julietta was observed from Borobudur temple, which was located at the center of the asteroid shadow path. It lasted for only 6.201 s. Assume that Earth’s orbit is circular and the orbit of Julietta is on the ecliptic plane and revolves in the same direction as Earth. At the occultation, Julietta is near its aphelion. At the time of the occultation the distances of Julietta from the Sun and the Earth are 3.076 AU and 2.156 AU respectively. Find the approximate diameter of asteroid Julietta, if the semi major axis of Julietta is 𝑎 = 2.9914 AU.