Gravitational Field Experiment

> with(plots):

Warning, the name changecoords has been redefined

Warning, the protected names norm and trace have been redefined and unprotected

Two body case.

> g:=1*(1/sqrt(x^2+y^2)+4/sqrt((2-x)^2+y^2));

g := 1/(sqrt(x^2+y^2))+4/(4-4*x+x^2+y^2)^(1/2)

Two Dimensional Gravitational Potential for three body problem.

Unit mass at (0,0) and (1,1). Mass 4 at (2,0).

> f:=1*(1/sqrt(x^2+y^2)+4/sqrt((2-x)^2+y^2))+1/sqrt((1-x)^2+(1-y)^2);

f := 1/(sqrt(x^2+y^2))+4/(4-4*x+x^2+y^2)^(1/2)+1/(s...

After you execute this worksheet (including the with(plots) line above),

below will be the level curves of f for the values 2 and 10.

You can add other comma separated values for f between 2 and 10 to see more level sets.

What happens in between 2 and 10?
Are there values when the level sets change their shape?

If so can you find them? Accurately?

What happens to the level sets of the function g?

> contourplot(f,x=-4..5,y=-4..4,grid=[100,100],contours=[2,10],coloring=[red,blue],thickness=2);

[Maple Plot]