IAO 2002, Теория, Група β, английски — Задача 6

The same intensity of light should be registered by the telescope form the asteroid of the main asteroid belt with size $D=5$ km and unknown yet asteroid of the Kuiper belt. The following aspects should be taken into account:

1. R. Distance from the Sun: 2.8 a.u. for the asteroid of the main belt and about 40 a.u. for the asteroid of the Kuiper belt. The intensity of light coming to the asteroids is reverse proportional to the square of these distances.
2. D. Size (diameter) of the body. The intensity of light reflecting by the body is proportional to the square of these sizes.
3. $\alpha$. Albedo. Albedo of Mars is about 0.15 and one of Pluto is 0.65. The intensity of light reflecting by the body is proportional to the albedos.
4. L. Distance from the observer (i.e. from the Earth): 1.8 a.u. for the asteroid of the main belt (in opposition) and about 40 a.u. for asteroid of Kuiper belt. The intensity of light coming to the telescope is reverse proportional to the square of these distances.

So $I\sim R^{-2}\cdot D^2\cdot\alpha\cdot L^{-2}$. And for $I_1=I_2$ we have to write: