2016年IOAA理论第8题-U波段测光 - 版本历史

2019年9月15日 (日) 11:11 Sqr.pi

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创建页面，内容为“==英文题目== '''(T8) U-Band photometry''' A star has an apparent magnitude 𝑚U = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfe…”

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==英文题目==
'''(T8) U-Band photometry'''

A star has an apparent magnitude 𝑚U = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfect
(100%) transmission within the band and is completely opaque (0% transmission) outside the band. The
filter is centered at 360 nm, and has a width of 80 nm. It is assumed that the star also has a flat energy
spectrum with respect to frequency. The conversion between magnitude, 𝑚, in any band and flux density,
𝑓, of a star in Jansky (1 Jy = 1 × 10−26 W Hz
−1 m−2
) is given by

𝑓 = 3631 × 10−0.4𝑚Jy

(T8.1) Approximately how many U-band photons, 𝑁0
, from this star will be incident normally on a
1 m2
area at the top of the Earth's atmosphere every second?

This star is being observed in the U-band using a ground based telescope, whose primary mirror has a
diameter of 2.0 m. Atmospheric extinction in U-band during the observation is 50%. You may assume
that the seeing is diffraction limited. Average surface brightness of night sky in U-band was measured to
be 22.0 mag/arcsec2
.

(T8.2) What is the ratio, 𝑅, of number of photons received per second from the star to that received
from the sky, when measured over a circular aperture of diameter 2′′?
(T8.3) In practice, only 20% of U-band photons falling on the primary mirror are detected. How many
photons, 𝑁t
, from the star are detected per second?

[[分类:星等]]

←上一版本		2019年9月15日 (日) 11:11的版本
第31行：		第31行：
	, from the star are detected per second?		, from the star are detected per second?

		+	==中文翻译==
		+
		+	'''(T8) U波段测光'''
		+
		+	恒星在U波段的视星等为$$m_{\rm U} = 15.0$$。U波段是理想的，也就是说，这一波段的透明度是完美的（100%）并且在该波段外完全不透光（透明度0%）。滤波器的中心是$$360 \rm{nm}$$，宽度为$$80 \rm{nm}$$。假设恒星在这一频率的能谱是平坦的。在任意波段下，星等$$m$$和恒星通量密度$$f$$（单位为央斯基，$$1 \rm{Jy} = 1\times 10^{-26} \rm{W} \cdot \rm{Hz}^{-1} \cdot \rm{m} ^{-2} $$）的转换关系为
		+	\[
		+	f = 3631 \times 10^{-0.4m} \rm{Jy}
		+	\]
		+
		+	(T8.1) 每秒来自这颗恒星的U波段光子垂直入射到地球大气层顶部$$1 \rm m^2$$的区域的数目$$N_0$$大约为多少？
		+
		+	这颗恒星是用一台直径为$$2.0 \rm m$$的地面望远镜在U波段观测到的。观测期间U波段的大气消光率为50%。假设视宁度达到衍射极限。实测U波段夜空表面平均亮度为22.0等。
		+
		+	(T8.2) 当从一个直径为2"的圆形小孔中观测时，每秒从恒星接收到的光子数与从天空接收到的光子数之比$$R$$是多少？
		+
		+	(T8.3) 实际上，只有20%的U波段光子落在主镜上。每秒检测到的来自恒星的光子的数目$$N_{\rm t}$$是多少？
		+
	[[分类:星等]]		[[分类:星等]]

←上一版本		2019年9月11日 (三) 09:45的版本
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		+	{{需要解答}}
	==英文题目==		==英文题目==
	'''(T8) U-Band photometry'''		'''(T8) U-Band photometry'''

@@ 第12行： / 第12行： @@
 𝑓 = 3631 × 10<sup>−0.4𝑚</sup>Jy
-(T8.1) Approximately how many U-band photons, 𝑁0
+(T8.1) Approximately how many U-band photons, 𝑁<sub>0</sub>
 , from this star will be incident normally on a
 m<sup>2</sup>
@@ 第25行： / 第25行： @@
 (T8.2) What is the ratio, 𝑅, of number of photons received per second from the star to that received
 from the sky, when measured over a circular aperture of diameter 2′′?
 (T8.3) In practice, only 20% of U-band photons falling on the primary mirror are detected. How many
 photons, 𝑁<sub>t</sub>

2016年IOAA理论第8题-U波段测光 - 版本历史

2019年9月15日 (日) 11:11 Sqr.pi

2019年9月11日 (三) 09:45 Quan787

2019年9月11日 (三) 09:40 Quan787

Quan787：创建页面，内容为“==英文题目== '''(T8) U-Band photometry''' A star has an apparent magnitude 𝑚U = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfe…”

Quan787：创建页面，内容为“==英文题目== '''(T8) U-Band photometry''' A star has an apparent magnitude 𝑚_U = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfe…”