Escape Speed Calculation for Identical Planets

[zhen]

the question is : there are two identical planets of mass M and radius R spaced 6R apart. What is the escape speed of a rocket launched from the mid-point (3R) between two planets?

I use the energe conservation law. K1 + Ua1 + Ub1 =K2 + Ua2 + Ub2 = 0 to get the Vi
because the rocket is in the middle, the U1 and U2 should be opposite sign, which will cancel out each other. In this case the escape speed should be 0, why that is not true?

 

[Tide]

You need to calculate the difference in total gravitational potential between the starting point and infinity. It's not zero.

 

[Kenny Lee]

The way I would do it is calculate the total GPE that is required to bring the rocket from infinity to that point, using the equation (GMm/R)... assuming the rocket has no KE to begin with, I would equate (1/2)mv^2 with the resulting expression and solve for v. That's how I would do it.