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.

Answer 1

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.