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Calculating the Radius for Pluto

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Spectroscopic observations suggest that Pluto is covered with icy frost and thus has a high albedo (0.5). The brightness of Pluto at opposition (38 AU from the Earth) is 2 x 10^-17 as bright as the Sun (1 AU from the Earth). From these two observations, calculate a radius of Pluto.

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This solution assists in calculating the radius of Pluto.

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Let, radius of the Pluto is R km.
Radius of sun is 7*10^5 km
brightness of the Pluto = brightness of the Sun * 2*10^(-17)
=>brightness of the Pluto = L_pluto/(4pi*38^2 ...

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