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Question
Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about 1/2 A.U. from the earth. Calculate what size it will appear when seen through the same telescope.
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Solution
Given that `D_("mars")/D_("earth") = 1/2` .....(i)
Where D represents the diameter.
We know that, `D_("earth")/D_("sun") = 1/100`
∴ `D_("mars")/D_("sun") = 1/2 xx 1/100` ......[From equation (i)]
At 1 A.U sun's diameter = `(1/2)^circ`
∴ Diameter of mars = `1/2 xx 1/200 = (1/400)^circ`
At `1/2` A.u, Mar's diameter
= `1/400 xx 2^circ = (1/200)^circ`
With 100 magnification mar's diameter
= `1/200 xx 100^circ = (1/2)^circ` = 30
This is larger than the resolution limit due to atmosphere fluctuations.
Hence, it looks magnified.
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