Question

A) In the x y-plane, a planet is at the origin, and there is a moon at x=5. The planet has mass 100, and the moon has mass 10. Find the potential energy for a satellite of mass 1 in the x y-plane due to the planet and the moon (hint: if V1(x,y) is the potential of the planet, V1 100(x-5,y) will be the potential due to the moon). Plot the potential V (x,y) for -10<x<10 and -10<y<10 by setting G=1.

B)  Next, ?nd the force due to the two bodies. The function should have the form F[x,y]={... , ...}; that is, it should be a vector with the x component in the ?rst space of the curly brackets and the y component in the second space of the curly bracket. Plot the vector ?eld F(x,y) for -10<x<10 and -10<y<10 by again setting G=1.

C) Finally, calculate the work done by gravity if the satellite moves from point (x1,y1) to (x2,y2).

Answer 1