The mean diameters of X and Y, two planets in the same solar system, are 6.2 103

Question

The mean diameters of X and Y, two planets in the same solar system, are 6.2 103 km and 2.0 104 km, respectively. The mass of X is 0.23 times the mass of Y. The value of g on Y is 8.6 m/s2.

only question (c)

The mean diameters of X and Y, two planets in the same solar system, are 6.2 x 10 km and 2.0 x 104 km, respectively. The mass of X is o.23 times the mass of Y. The value of g on Y is 8.6 m/s (a) What is the ratio of the mean density ofX to that of Y? px 7.7 py (b) What is the value of g on X? 20.24 m/s (c) The mass of Y is 1.289 x 1025 kg. What is the escape speed on x? 3.64 10* 5 X m/s 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 kinetic energy equals the magnitude of the initial gravitational potential energy.

Explanation / Answer

Vesc(x) / Vesc(y)= sqrt[(M(x)/M(Y) * R(Y)/R(X)]

(M(x)/M(Y) = 0.23 (given in question)

R(Y)/R(X) =2.0x104 / 6.2 103 =3.225

Vesc(x) / Vesc(y) =0.23*3.225 =0.7419

Vesc(y) =sqrt[2GM(y)/R(y)]

= sqrt((2*6.673*10-11*1.289*1025) / ( 1*104) )

Vesc(y) =4.147*105

Vesc(x) =0.7419* Vesc(y) =0.7419*4.147*105 =3.0766*105 m/s

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