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2017年IOAA理论第6题-超新星1987A - 版本历史
2026-04-29T14:07:57Z
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Caroldong：增加了中文标题
2019-08-08T07:30:43Z
<p>增加了中文标题</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">2019年8月8日 (四) 07:30的版本</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{需要解答}}IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{需要解答}}IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>= 英文原题 =</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=英文原题=</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(T6) Supernova 1987A [15 marks]'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(T6) Supernova 1987A [15 marks]'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>b) Find the last day that observers could have seen the supernova if they had a 6-inch (15.24cm) telescope with transmission efficiency ''T''=70%. Assume that the average diameter of the human pupil is 0.6 cm. [10]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>b) Find the last day that observers could have seen the supernova if they had a 6-inch (15.24cm) telescope with transmission efficiency ''T''=70%. Assume that the average diameter of the human pupil is 0.6 cm. [10]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>= 中文翻译 =</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=中文翻译=</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">'''超新星1987A'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>超新星1987A爆发于1987年5月15日，爆发最亮时的视星等达到+3等。随后，它逐渐变暗，直到1988年2月4日，减为裸眼不可见。假设它的亮度为 B，随着时间 t 的变化趋势为指数变化''B=B<sub>0</sub>e<sup>-t/τ</sup>''，其中''B<sub>0</sub>''和''τ''是常数。裸眼的极限星等为+6等。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>超新星1987A爆发于1987年5月15日，爆发最亮时的视星等达到+3等。随后，它逐渐变暗，直到1988年2月4日，减为裸眼不可见。假设它的亮度为 B，随着时间 t 的变化趋势为指数变化''B=B<sub>0</sub>e<sup>-t/τ</sup>''，其中''B<sub>0</sub>''和''τ''是常数。裸眼的极限星等为+6等。</div></td></tr>
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Caroldong
https://www.astro-init.top/index.php?title=2017%E5%B9%B4IOAA%E7%90%86%E8%AE%BA%E7%AC%AC6%E9%A2%98-%E8%B6%85%E6%96%B0%E6%98%9F1987A&diff=383&oldid=prev
Caroldong：创建IOAA2017T6
2019-08-08T07:25:59Z
<p>创建IOAA2017T6</p>
<p><b>新页面</b></p><div>{{需要解答}}IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题<br />
<br />
= 英文原题 =<br />
'''(T6) Supernova 1987A [15 marks]'''<br />
<br />
Supernova SN 1987A was at its brightest with an apparent magnitude of +3 on about 15th May 1987 and then faded, finally becoming invisible to the naked eye by 4th February 1988. It is assumed that brightness ''B'' varied with time ''t'' as an exponential decline, ''B=B<sub>0</sub>e<sup>-t/τ</sup>'', where ''B<sub>0</sub>'' and ''τ'' are constant. The maximum apparent magnitude which can be seen by the naked eye is +6.<br />
<br />
a) Determine the value of ''τ'' in days. [5]<br />
<br />
b) Find the last day that observers could have seen the supernova if they had a 6-inch (15.24cm) telescope with transmission efficiency ''T''=70%. Assume that the average diameter of the human pupil is 0.6 cm. [10]<br />
<br />
= 中文翻译 =<br />
超新星1987A爆发于1987年5月15日，爆发最亮时的视星等达到+3等。随后，它逐渐变暗，直到1988年2月4日，减为裸眼不可见。假设它的亮度为 B，随着时间 t 的变化趋势为指数变化''B=B<sub>0</sub>e<sup>-t/τ</sup>''，其中''B<sub>0</sub>''和''τ''是常数。裸眼的极限星等为+6等。<br />
<br />
（a）求''τ''的值，以天为单位。<br />
<br />
（b）如果观测者有一台传输效率''T''=70%，口径为6英寸（15.24cm）的望远镜，求他能用望远镜观测到1987A的最终日期。假设人眼的平均直径为0.6cm。</div>
Caroldong