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A newly discovered faint asteroid and Mars are observed at opposition. Mars is discovered to be 10^8 time brighter than the asteroid. Assume that Mars and the asteroid are 1.5 and 3.0 AU from the Sun respectively. Estimate the radius of the Asteroid if it has an albedo the same as Mars.

Light from the sun travels 2 AU to get to Mars and Back to earth.
Light from the sun travels 5 AU to get to the asteroid and back to earth.

Do I assume a ratio in areas as 4/25 (inverse square) or 16/625 (inverse quartics) so have to scale up to 25 X 10^-8/4 or to 625 X 10^-8/16

This gives the ratio of radii as 5/2 X 10^-4 or 25/4 X 10^-4 respectively

So which one is correct or neither.

(Mars is 3400Km in radius which gives the radius of the asteroid as either 850m or 2.125Km - both seem reasonable)

cosmo · Accepted Answer

You must consider the lightpath from the Sun to the object separately from the lightpath from the object to the Earth.  The inverse-square law operates separately along those two paths.

First calculate the luminosity of Mars and the asteroid at the object itself, then calculate the brightness as seen from Earth.

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