If we had 2 suns of the same mass, they might both move along the same circle. The gravity from one sun would provide the centripetal force needed to keep the other in orbit, and vice versa. This simple solution to the mutual gravitational effects on 2 bodies was known to Newton. Introduce a third body, like a comet or small planet, and it may move chaotically, bouncing irregularly back and forth between the 2 stars. With 3 or 4 stars, the stars can be coaxed to move along the same circle, they can orbit each other non-periodically, or they could move chaotically. This is known as the "many body" problem and suggests that any seemingly regular arrangement of heavenly bodies is temporary at best; chaos will eventually disrupt the even cycles. With these formulas, the chaotic trajectories of the stars or the comet can be plotted. The simulations only use 2 dimensions, whereas gravity is 3-dimensional. There are 3 formulas, allowing for 2, 3, or 4 stars and a comet. The comet is assumed to be small enough to not have an effect on the stars, while the stars influence each other and the comet.
GravitySample { ; copyright Kerry Mitchell 27jan2000
fractal:
title="Gravity Sample" width=480 height=480 author="Kerry
Mitchell"
created="January 27, 2000" numlayers=4
layer:
method=multipass caption="comet 3" opacity=25 visible=yes
alpha=no
mapping:
center=0/0 magn=1 angle=0
formula:
filename="lkm.ufm" entry="gravity3-comet" maxiter=628 percheck=off
p_zc0=-2/-0.2 p_vc0=1/0 p_z10=1/0 p_z20=-0.5/0.866025403784438647
p_z30=-0.5/-0.866025403784438647 p_v10=0/1
p_v20=-0.866025403784438647/-0.5 p_v30=0.866025403784438647/-0.5
p_mass1=3.466 p_mass2=3.466 p_mass3=3.466 p_timestep=0.01
p_ztype="comet position" p_bailout=1000
inside:
filename="lkm.ucl" entry="basic" transfer=cuberoot repeat=yes
p_colorby="magnitude"
outside:
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=8 index=0 color=16777215 index=50 color=14532495
index=100 color=11829312 index=150 color=8405008 index=200
color=0
index=250 color=8405008 index=300 color=11829312 index=350
color=14532495
layer:
method=multipass caption="comet 2" opacity=33 visible=yes
alpha=no
mapping:
center=0/0 magn=1 angle=0
formula:
filename="lkm.ufm" entry="gravity3-comet" maxiter=628 percheck=off
p_zc0=-2/-0.1 p_vc0=1/0 p_z10=1/0 p_z20=-0.5/0.866025403784438647
p_z30=-0.5/-0.866025403784438647 p_v10=0/1
p_v20=-0.866025403784438647/-0.5 p_v30=0.866025403784438647/-0.5
p_mass1=3.466 p_mass2=3.466 p_mass3=3.466 p_timestep=0.01
p_ztype="comet position" p_bailout=1000
inside:
filename="lkm.ucl" entry="basic" transfer=cuberoot repeat=yes
p_colorby="magnitude"
outside:
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=8 index=0 color=16777215 index=50 color=9428415
index=100 color=4240512 index=150 color=1081408 index=200
color=0
index=250 color=1081408 index=300 color=4240512 index=350
color=9428415
layer:
method=multipass caption="comet 1" visible=yes alpha=no
mapping:
center=0/0 magn=1 angle=0
formula:
filename="lkm.ufm" entry="gravity3-comet" maxiter=628 percheck=off
p_zc0=-2/0 p_vc0=1/0 p_z10=1/0 p_z20=-0.5/0.866025403784438647
p_z30=-0.5/-0.866025403784438647 p_v10=0/1
p_v20=-0.866025403784438647/-0.5 p_v30=0.866025403784438647/-0.5
p_mass1=3.466 p_mass2=3.466 p_mass3=3.466 p_timestep=0.01
p_ztype="comet position" p_bailout=1000
inside:
filename="lkm.ucl" entry="basic" transfer=cuberoot repeat=yes
p_colorby="magnitude"
outside:
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=8 index=0 color=16777215 index=50 color=12554205
index=100 color=8405172 index=150 color=4198528 index=200
color=0
index=250 color=4198528 index=300 color=8405172 index=350
color=12554205
layer:
method=multipass caption="stars" opacity=25 visible=yes
alpha=no
mapping:
center=0/0 magn=1 angle=0
formula:
filename="lkm.ufm" entry="gravity3-comet" maxiter=628 percheck=off
p_zc0=-2/0 p_vc0=1/0 p_z10=1/0 p_z20=-0.5/0.866025403784438647
p_z30=-0.5/-0.866025403784438647 p_v10=0/1
p_v20=-0.866025403784438647/-0.5 p_v30=0.866025403784438647/-0.5
p_mass1=3.466 p_mass2=3.466 p_mass3=3.466 p_timestep=0.01
p_ztype="all stars" p_bailout=1000
inside:
filename="lkm.ucl" entry="basic" transfer=cuberoot repeat=yes
p_colorby="magnitude"
outside:
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=4 index=0 color=16777215 index=100 color=8421504
index=200 color=0 index=300 color=8421504
}