2012年CNAO决赛第15题-星等
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15、（低年组和高年组）星等
某中学有一台口径60厘米的天文望远镜，如果用它来观测冥王星轨道附近的柯伊伯带天体，并认为这些天体大致呈球状，且反照率和冥王星接近，那么理论上这台望远镜能看到的冥王星轨道附近的最小天体的直径为多少？已知冥王星直径为2300千米，视星等约为14等。
解答
英文解答：
Assume brightness F follows:
Where Fsun is the total brightness of the sun, R is the distance between the celestial object and the sun, r is the radius of the celestial object, k1 is the ratio of reflection and k2 is the ratio of light of reflection which reaches the earth. Then, the ratio of brightness of two celestial objects F1 and F2 of same distance from the sun is given by:
Thus, the magnitude difference between object 1 and 2 is given by:
The extreme magnitude of a telescope is given by:
Where [D] = mm. Thus, the extreme magnitude of the given telescope with D = 600 is:
Assume that the smallest object that can be observed has magnitude m2 = 15.66, and Pluto has magnitude m1 = 14, we have:
As given that r1 = 2300km/2 = 1150 km, we have:
Parameter d is:
