__Gravitational Field Experiment__

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**with(plots):
with(linalg):**

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**Two body case.**

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

**Two Dimensional Gravitational Potential for three body problem.**

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

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

**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?**

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

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