Escape energy multiples for Earth, Moon, and Jupiter

[popo902]

Homework Statement

What multiple of the energy needed to escape from Earth gives the energy needed to escape from (a) the Moon and (b) Jupiter? Use the Table (link below) if necessary

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c13/fig13-19.gif

Homework Equations

1/2mv^2 - GMm/r = 0 (energy)
v = sqrt(2GM/R)

The Attempt at a Solution

for the potential energy, do i put in the radius of the planet instead of the distance between it and something? because there's nothing else there...

at first i figured that the potential will be zero anyway because once you escape, r would be infinity and make the potential 0
then i fiugured that only v mattered in comparing the amount of energy because the mas of the projectial would be the same, the only difference would be escape speed.
but i got it wrong

these are supposedly the rigth answers
a)0.0451
b) 28.5

im very confused...

 

[tiny-tim]

hi popo902!

the energy needed to escape is defined as the energy needed to reach infinite distance at zero speed (ie at KE = 0) …

(of course, it's 1/2 mv², where v is escape velocity )

since KE + PE = constant, that means that the escape KE is the difference in PE between the planet's surface and infinity.