The escape velocity of a bullet from the surface of planet Y is 1727 m/s. Calculate the escape velocity from t

Question

The escape velocity of a bullet from the surface of planet Y is 1727 m/s. Calculate the escape velocity from the surface of the planet X if the mass of planet X is 1.63 times that of Y, and its radius is 0.927 times the radius of Y (in m/s).

Answer 1

For this question start with the Escape velocity formula:

v = sqrt( 2GM / r)

therefore, when u remove the constants, you have the proportionality:

v ~ sqrt(M) / sqrt(r)

The mass increases by 1.63 and radius decreases 0.927.

therefore,

v = (1727) * sqrt(1.63) / sqrt(0.927)

v = 2290.06 m/s

Answer 2

v = √(2GM/r)
√(2G) = v√(r/M)
v2√(r2/M2) = v1√(r1/M1)
v2 = v1√(r1M2)/√(r2M1)
v2 = 1,727√(r1*1.63M1)/√(0.927r1M1)
v2 ≈ 2,290 m/s