the escape velocity is = sqrt (2GM/R) but i keep getting this answer wrong. why?
ID: 1449109 • Letter: T
Question
the escape velocity is = sqrt (2GM/R) but i keep getting this answer wrong. why???/ thank you!
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/rho_r> 2-78 What is the value of g on X? 8.51 m/s^2 The mass of Y is 9.837 times 10^24 kg. What is the escape speed on X? 104573 times 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
esc speed goes as
vesc=sqrt[2GM/R]
ratios:
given D= diameter
vexc(X)/vesc(Y)= sqrt[(M(x)/M(Y) * D(Y)/D(X)] =
sqrt[0.15*(1.5e4/6.8e3)]=
sqrt[0.33]=0.575
vesc(X)=0.575 vesc(Y)
vesc(Y)=sqrt[2GM(Y)/R(Y)]=sqrt[4GM(Y)/D(Y)]=381931.64 km/s
so vesc(X)=0.575x381931.64 km/s= 279610.69km/s
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