Escape Speed Calculation for Identical Planets

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The discussion centers on calculating the escape speed of a rocket launched from the midpoint between two identical planets. Initially, a user suggests that the escape speed should be zero due to gravitational potentials canceling each other out. However, this is corrected by noting that the total gravitational potential energy at that midpoint is not zero, as it requires energy to escape to infinity. The proper approach involves calculating the gravitational potential energy needed to move the rocket from infinity to the midpoint and equating it to kinetic energy to find the escape speed. Thus, the escape speed is derived from the difference in gravitational potential energy, confirming it is not zero.
zhen
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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?
 
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You need to calculate the difference in total gravitational potential between the starting point and infinity. It's not zero.
 
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.
 
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