Question

Lost in the Glare.How hard would it be for an alien astronomer to detect the light from planets in our solar system compared to the light from the Sun itself?

(A)Would detecting Jupiter be easier or harder than detecting Earth? You may neglect any difference in reflectivity between Earth and Jupiter. Express your answer using three significant figures.

Answer 1

Okay, for this, we can consider a sphere around the sun whose size is same as the size of the planet’s orbit

so,

fraction of the total emitted sunlight that reaches Earth = r² / 4R²

where r is radius of earth and R is distance between sun and earth

then

fraction of the total emitted sunlight that reaches Earth = 6371000² / 4 * 1.5e11²

fraction of the total emitted sunlight that reaches Earth = 4.54e-10

and also, we know that earth's has around 29 % reflectivity

so,

fraction of total sunlight reflected by Earth = 0.29 * 4.54e-10

fraction of total sunlight reflected by Earth = 1.32e-10

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Would detecting Jupiter be easier or harder than detecting Earth

since Jupiter orbits at a greater distance from sun as compared to earth, it would reduce the chances of detection.

fraction of the total emitted sunlight that reaches Jupiter = 2.02e-9

so,

assuming same reflectivity as earth's,

fraction of total sunlight reflected by Jupiter = 6.12e-10

.