The mean diameters of X and Y, two planets in the same solar system, are 6.8 Tim

Question

The mean diameters of X and Y, two planets in the same solar system, are 6.8 Times 10^3 km and 1.8 Times 10^4 km, respectively. The mass of X is 0.15 times the mass of Y. The value of g on Y is 8.1 m/s^2. What is the ratio of the mean density of X to that of Y (rho_x/p_y)? What is the value of g on X? The mass of Y is 9.837 Times 10^24 kg. What is the escape speed on X? Density is the ratio of mass to volume. Do you recall how to calculate the volume of a sphere? The gravitational acceleration is the ratio of the gravitational force on a particle to the particle's mass. The escape speed is the speed when the escape kinetieenergy equals the magnitude of the initial gravitational potential energy.

Explanation / Answer

b)

gx = (Mx/My) (Ry/Rx)^2 gy

gx = (0.15/1) * (1.8e7/6.8e6)y2 * (8.1)

gx = 8.51 m/s^2

c)

Mx = 0.15 (9.837e24) = 1.476e24 kg

vx = sqrt(2 G Mx/rx) = sqrt((2)*(6.67e-11)*(1.476e24)/(6.8e6)) = 5380 m/s

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