GATE-2018 (24) :Wyllie – Time average equation

CSIR-NET 2013

118. The orbital radius of Venus around the Sun is about two-thirds of the orbital radius of the Earth around the Sun. Find the ratio of solar constants on the two planets.

A) 2.25                         B) 0.67                        C) 1.5                          D) 1.0

solution

Solar constant S = ER² / r²

R – radius of the Sun 

r – radius of the earth’s orbit around the sun 

(Sun – Earth distance )

Radius of Venus orbit around the Sun = (2 / 3) r_E

Radius of Earth’s orbit around the Sun =r_E

Therefore , the ratio of the Solar constants

S₁ = (ER²) / (2/3 *r_E )² ---------(1)

S₂ =( ER²) / ( r_E)² ------------(2)

equation (1) / (2)

S₁ / S₂ =( ER² / 4/9*r_E²) / (ER² / r_E²)

S₁ / S₂ = (1) / (4/9)

            = 9/4

The ratio of solar constant = 2.25