The planets with radii R₁ and R₂ have densities ₁, ₂ respectively. Their atmospheric pressures are p₁ and p₂ respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere is

Step-by-step solution

Acceleration due to gravity, aligned & g= G M R^2 = 4 3 G R & g₁ g₂ = ₁ R₁ ₂ R₂ aligned Atmospheric pressure can be given by p= W S where, W= Weight of atmosphere, S= Surface area of the planet m₁ m₂ = ₁ S₁ g₂ ₂ S₂ g₁ = p₁ (4 R₁^2 ) p₂ (4 R₂^2 ) ₂ R₁ ₁ R₁ = p₁ R₁ ₂ p₂ R₂ ₁