The escape velocity for your rocket leaving the Earth is vE

The escape velocity for your rocket leaving the Earth is v_E = v₀. What is the escape velocity for your rocket leaving a planet with a mass of m_P = 9 m_E? Assume your rocket\'s mass is now half of its original mass to account for the spent fuel. Answer in _____ v₀.

Solution

The expression for the escape velocity is

V_E = sqrt (2G M_E /R_E ) = Vo

We replace the mass of the new planet in the expression

V_P= sqrt (2G M_P/R_P)

we must assume that the radius of the plant is the same

V_P= sqrt (2G 9M_E/R_E)

V_P = sqrt (9) sqrt (2G M_E/R_E )

V_p= 3 vo