- #1
addy899
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1. Description of Problem
A binary planet system comprises two identical planets of mass M and radius R with their centers a distance 10 R apart. The minimum energy that the engines of a spacecraft need to supply to get a rocket of mass m from the surface of one planet to the surface of the other is of the form XGMm/R. What is X?
Escape Velocity v= √2GM/R
Gravitational Kinetic Energy KE=GMM/2R
Gravitational Potential Energy U = GmM/R
Kinetic Energy = 1/2mv2
3. Attempt at a solution
use escape velocity to find the KE of escape velocity is KE = mMG/R
I'm not sure where to go from here...
subtract the potential energy that the second planet supplies once the rocket reaches halfway?
this gives x=.8
A binary planet system comprises two identical planets of mass M and radius R with their centers a distance 10 R apart. The minimum energy that the engines of a spacecraft need to supply to get a rocket of mass m from the surface of one planet to the surface of the other is of the form XGMm/R. What is X?
Homework Equations
Escape Velocity v= √2GM/R
Gravitational Kinetic Energy KE=GMM/2R
Gravitational Potential Energy U = GmM/R
Kinetic Energy = 1/2mv2
3. Attempt at a solution
use escape velocity to find the KE of escape velocity is KE = mMG/R
I'm not sure where to go from here...
subtract the potential energy that the second planet supplies once the rocket reaches halfway?
this gives x=.8