2019年IOAA理论第7题-太阳黑子对太阳辐照度的影响

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 𝑇sp=3300 K and diameter of sunspot, 𝐷sp=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)