Some demonstrations of the relation between the behavior of the relative coordinate betwen two masses,

    and the motion of each of the two masses themselves,

       all with respect to the CM, which is at rest.

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>	with(plots);

Warning, the name changecoords has been redefined

>	with(plottools);

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   Below the write out the equation for the relative motion of objects undergoing elliptical motion, with q as the eccentricity of the orbit.

>	rrr:=(1-q^2)/(1+q*cos(phi));

  and here we decide the eccentricity should be 3/4.

>	rrr34:=subs(q=3/4,rrr);

  So first we just see what the graph actually should look like, in the relative coordinate.

>	plot([rrr34,phi,phi=0..2*Pi],scaling=constrained,coords=polar);

NOW we begin plotting all 3 pertinent motions on the same graph, and also animating them so we can watch their relative behaviors:

This example has a mass ratio of 1 to 2

>	beli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[rrr34*cos(phi)/3,rrr34*sin(phi)/3,phi=0..2*Pi*t/50],[-2*rrr34*cos(phi)/3,-2*rrr34*sin(phi)/3,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(beli,insequence=true,scaling=constrained);

This example has a mass ratio of 2 to 1; all that means is that which one is particle 1 and which one is particle 2 has been reversed.

>	meli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[2*rrr34*cos(phi)/3,2*rrr34*sin(phi)/3,phi=0..2*Pi*t/50],[-1*rrr34*cos(phi)/3,-1*rrr34*sin(phi)/3,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(meli,insequence=true,scaling=constrained);

This example has a mass ratio of 9 to 1

>	eeli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[9*rrr34*cos(phi)/10,9*rrr34*sin(phi)/10,phi=0..2*Pi*t/50],[-1*rrr34*cos(phi)/10,-1*rrr34*sin(phi)/10,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(eeli,insequence=true,scaling=constrained);

This example has a mass ratio of 4 to 1

>	neli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[8*rrr34*cos(phi)/10,8*rrr34*sin(phi)/10,phi=0..2*Pi*t/50],[-2*rrr34*cos(phi)/10,-2*rrr34*sin(phi)/10,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(neli,insequence=true,scaling=constrained);

This example has a mass ratio of 17 to 3.

>	noeli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[8.5*rrr34*cos(phi)/10,8.5*rrr34*sin(phi)/10,phi=0..2*Pi*t/50],[-1.5*rrr34*cos(phi)/10,-1.5*rrr34*sin(phi)/10,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(noeli,insequence=true,scaling=constrained);

Here is an example for a mass ratio of 3 to 1.

>	aeli:=[seq(plot({[rrr34*cos(phi),rrr34*sin(phi),phi=0..2*Pi*t/50],[3*rrr34*cos(phi)/4,3*rrr34*sin(phi)/4,phi=0..2*Pi*t/50],[-1*rrr34*cos(phi)/4,-1*rrr34*sin(phi)/4,phi=0..2*Pi*t/50]},scaling=constrained,color=[red,blue,green],thickness=3),t=1..50)]:

>	display(aeli,insequence=true,scaling=constrained);

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