The mean diameters of planets A and B are 9.3 × 103 km and 1.8 x 104 km, respect

Question

The mean diameters of planets A and B are 9.3 × 103 km and 1.8 x 104 km, respectively. The ratio of the mass of planet A to that of planet B is 0.57. (a) What is the ratio of the mean density of A to that of B? (b) What is the ratio of the gravitational acceleration on A to that on B? (c) What is the ratio of escape speed on A to that on B? B (a) Number (b) Number (c) Number Units Units Units Click if you would like to Show Work for this question: Open Show Work SHOW HINT SHOW SOLUTION By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor

Explanation / Answer

a) ratio of mean density of A(m1) and B(m2)

d1/d2 = (m1/v1)/(m2/v2) = (m1/m2)*(v2/v1) = 0.57*(R2/R1)^3 = 0.57*(0.9*10^4/(0.465*10^4))^3 = 4.129

b) gravitational acceleration

g = GM/r^2

=> g1/g2 = (m1/m2)*(R2/R1)^2 = 0.57*(0.9*10^4/(0.465*10^4))^2 = 2.134

c) escape speed V = (2GM/R)^0.5

=> v1/v2 = ((m1/m2)*(R2/R1))^0.5 = (0.57*0.9*10^4/(0.465*10^4))^0.5 = 1.050

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