orbits

#!/usr/bin/zsh

zmodload zsh/mathfunc

imgsize=400
pi=$((4*atan(1.0)))
a=149.6
b=147
c=$((sqrt(a*a-b*b)))

for ((i=0;i<101;i++)); do
        tg=$((sin(2.0*pi*i/101)/cos(2.0*pi*i/101)))
        xa=$((sqrt(1.0/(1.0/(a*a)+tg*tg/(b*b)))))
        [[ $((2.0*pi*i/101)) < $((pi/2.0)) ||  $((2.0*pi*i/101)) > $((3*pi/2.0)) ]] && xa=$((-xa))
        ya=$((xa*tg))
        xb=$c
        yb=0
        [ -n "$1" ] && {
                xb=$((c-xa))
                yb=$((-ya))
                xa=0
                ya=0
        }
        # translate spatial coords in to display coords
        xa=$((imgsize/2+xa))
        ya=$((imgsize/2-ya))
        xb=$((imgsize/2+xb))
        yb=$((imgsize/2-yb))

        convert -size ${imgsize}x${imgsize} canvas:black \
                -stroke white -draw "rectangle 5,5 $((imgsize-5)),$((imgsize-5))" \
                -stroke black -fill blue -draw "circle $xa,$ya $((xa+5)),$ya" \
                -fill yellow -draw "circle $xb,$yb $((xb+10)),$yb" \
                draw_point$((i+10000)).gif
done

convert -loop 0 -delay 20 *.gif points.gif
rm draw_point*.gif