2019年IOAA理论第7题-太阳黑子对太阳辐照度的影响

英文题目

7. Effect of sunspots on solar irradiance (20 p)

Since 1978, the solar constant has been almost continuously measured by detectors on-board artificial satellites. These accurate measurements revealed that there are seasonal, monthly, yearly, and longer timescale variations in the solar constant. While the seasonal variations have their origins in the periodically varying Earth–Sun distance, the decade-long quasi-cyclic variations mainly depend on the activity cycle(s) of the Sun.

a) Calculate the value of the solar constant at the top of the Earth's atmosphere, when the Earth is 1 au from a perfectly quiet Sun, assuming that Sun emits as a perfect black-body. (4 p)

b) Calculate the solar constant of this perfectly quiet Sun in early January and early July, and find their ratio. (4 p)

c) Calculate the solar constant again at 1 au in the presence of a near equatorial sunspot with mean temperature of $$𝑇_{sp}=3300K$$ and diameter of sunspot, $$𝐷_{sp}=90 000 km$$. Calculate the ratio - blank Sun to Sun with sunspot. (7 p)

Assume the sunspot is circular and ignore the effects of its spherical projection. Neglect any other activity features. Also assume that the Sun is rotating fast enough, hence solar irradiance is still isotropic。

d) In reality solar irradiance is no longer isotropic. Calculate the ratio of solar irradiance for the cases when the sunspot is not visible from the Earth to the case when it is fully visible. (5 p)

中文题目

从1978年开始，太阳常数几乎被搭载在人造卫星上的探测器连续测量。这种精确的测量揭示了太阳常数有季度、月度、年度、以及更长时间尺度上的变化。其季度变化的来源是周期性变化的日地距离，而其约十年长的拟周期性的变化主要原因是太阳的活动周期。

a）计算在地球大气层顶的太阳常数，假设地球距离一个绝对平静的太阳1au远，并且太阳是一个绝对黑体。

b）计算完美的平静太阳在一月份和七月份的太阳常数，并求出它们的比值。

c）计算一个在接近赤道有一个温度$$𝑇_{sp}=3300K$$,直径$$𝐷_{sp}=90 000 km$$的黑子，计算此时的太阳常数并求出其与原来的比值。假设黑子是圆形并忽略球形投影的影响。忽略其他的活动点，并假设太阳自转足够快使得太阳辐照依然是各向同性的

d）在事实上太阳辐照不是各向同性的。计算这个黑子在完全可见与完全不可见的情况下太阳常数的比值。