- #1
Eitan Levy
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Homework Statement
A satellite with mass of m is circling a star. The radius of the circle is R.
At some moment the mass splits to 2 equal masses (the tangential velocity of the masses doesn't change). As a result of the split the kinetic energy in the system is multiplied by k (k>1). What will be the minimal distance of the masses from the star?
Answer: R/(1+√(k-1)).
Homework Equations
Ueff=L2/2mr2+V(r)
The Attempt at a Solution
I have honestly never seen a problem similar to this, and have never used effective potential to solve a problem (not saying it's necessary here).
I tried to solve the problem by saying that the energy before the split is -GMm/2R, because the potential energy is -GMm/R and the kinetic energy is GMm/2R. Then I tried to say that the new kinetic energy is kGMm/2R, and that the potential energy stays the same.
Then I wrote the equation -kGMm/2R-GMm/R=-GMm/rmin which gave the wrong answer.
Any help please?