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Variable StarsNew Improved Features

Structure of the Universe


stereo[graphic_, view1_, view2_, scale_,
opts___Rule] :=
p1=Show[graphic, opts,
p2=Show[graphic, opts,
Show[GraphicsArray[{p1,p2}], opts,


Structure of Universe at Various Distance Scales

This notebook shows our neighborhood of the universe as seen from various distance scales.

At each scale a different structure appears. At the lowest scale is the Earth followed by the solar system, the nearest stars, the Milky Way galaxy, the Local Group of galaxies, and the Local Super-Cluster of galaxy clusters.

These structures are viewed from the direction of the constellation of Orion. Behind each structure is the constellation of Scorpius. To the top is the direction of the star Polaris, and below is the Southern Cross constellation.

Pairs of 3D images are used so that you can view the structure in full 3D. Converge your eyes to get the 3D effect.

O[] Light Years: Earth

Earth Data



O[] Light Years: Solar System

Solar System Data

r1=180 N[Degree];c1=Cos[r1];s1=Sin[r1];
r2=-23.45 N[Degree];c2=Cos[r2];s2=Sin[r2];

getROT[R1_,R3_,R2_]:= Block[{s1,c1,s2,c2,s3,c3,s3c2,c3c2,a11,a12,a21,a22,a31,a32},
s3c2=s3 c2;c3c2=c3 c2;a11=c3 c1-s3c2 s1;a12=-c3 s1-s3c2 c1;a21=s3 c1+c3c2 s1;a22=-s3 s1+c3c2 c1;a31=s2 s1;a32=s2 c1;


solarSystemGraphic =
Graphics3D[{(Module[{semi, ecc, peri,
asc, tilt, rot, meanDist, dtheta,
theta, c, s, r, i, n = 32},
dtheta = N[(2*Pi)/n];
{semi, ecc, peri, asc, tilt} = #1;
rot = rotate.getROT[peri*N[Degree],
asc*N[Degree], tilt*N[Degree]];
meanDist = semi*(1 - ecc^2)/63240.;
Line[Table[theta = i*dtheta;
c = Cos[theta]; s = Sin[theta];
r = meanDist/(1 + ecc*c);
rot . {r*c, r*s},
{i, 0, n}]]] &) /@

view1, view2, 0.0007];1;

This graphic shows the orbit of the nine planets. The eccentric and tilted orbit is that of Pluto.

O[] Light Years: Nearest Stars

Nearest Stars Data

nearestStars={{"Sun",0,0,0.0,-26.7},{"Proxima.Centaurus",14.50,-62.68,4.2,11.0},{"Alpha.Centaurus",14.67,-60.83,4.3,0.0},{"BarnardsStar",17.97,4.57,6.0,9.5},{"Wolf359",10.93,7.02,7.7,13.5},{"Lalande21185",11.05,35.97,8.2,7.5},{"UV.Cetus",1.65,-17.95,8.4,12.5},{"Sirius",6.75,-16.72,8.6,-1.5},{"Ross154",18.83,-23.83,9.4,10.4},{"Ross248",23.70,44.17,10.4,12.3},{"Epsilon.Eridanus",3.55,-9.47,10.8,3.7},{"Ross128",11.80,0.80,10.9,11.1},{"61 . Cygnus",21.12,38.75,11.1,5.2},{"Epsilon.Indus",22.05,-56.78,11.2,4.7},{"Groombridge34",0.30,44.02,11.2,8.1},{"Luyten789m6",22.65,-15.32,11.2,12.2},{"Procyon",7.65,5.22,11.4,0.4},{"Sigma2398",18.72,59.63,11.6,8.9},{"Lacaille9352",23.10,-35.87,11.7,7.3},{"Tau.Cetus",1.73,-15.93,11.80,3.5}};


nearestStarsGraphic=Graphics3D[Apply[Block[{a=15 #2 N[Degree],d=#3 N[Degree],p,r},p=#4 {Cos[a] Cos[d],Sin[a] Cos[d],Sin[d]};{color[#1],Point[p]}]&,nearestStars,1]];

view1, view2, 11];1;

The graphic shows all the stars within 12 light years of our Sun.

Our Sun is the blue dot in the center of the graphic. Below, and slightly to the right, is the nearest star Proxima Centauri shown as the black dot just next to Alpha Centauri shown in green.

The brightest star in our sky is Sirius, which is shown as the red dot.

Stars in the upper half of the graphic are predominately visible by observers in the northern hemisphere of Earth. Directly above our Sun in the graphic, but 100 light years away, is the star Polaris.

O[] Light Years: Milky Way Galaxy

Milky Way Data

rA = 10000; rB = 50000 - rA;
r1 = 12.857*15*N[Degree];
c1 = Cos[r1]; s1 = Sin[r1];
r2 = (90 - 27.13)*N[Degree];
c2 = Cos[r2]; s2 = Sin[r2];
rotate =
{{c1,-s1,0}, {s1,c1,0}, {0,0,1}} .
{{c2,0, s2}, {0, 1, 0}, {-s2,0,c2}};
n = 16; da = N[Pi/n];

spiral = Table[
a = i*da;
r11 = rA/2 + (rB*a)/N[3*Pi];
r12 = rA/2 + (rB*(a + da))/N[3*Pi];
r21 = rA + (rB*a)/N[3*Pi];
r22 = rA + (rB*(a + da))/N[3*Pi];
x1 = rotate . {Cos[a], Sin[a], 0};
x2 = rotate . {Cos[a+da],Sin[a+da],0};
p = {r11*x1, r21*x1, r22*x2, r12*x2};
{Polygon[p], Polygon[-p]},
{i, 0, 3*n}];

sphere=Polygon[Table[a=i da;rA rotate.{Cos[a],Sin[a],0},{i,0,2 n}]];

a=5.76 15 N[Degree];d=28.94 N[Degree];
sun=Point[30000 {Cos[a] Cos[d],Sin[a] Cos[d],Sin[d]}];


view1, view2, 50000];1;

Our Sun resides in the MilkyWay Galaxy.

The Milky Way is a spiral galaxy, 100 thousand light years in diameter, with a 20 thousand light years diameter sphere at the center. Its arms are 2 thousand light years wide.

Our Sun is 30 thousand light years from the center, and is on an outer arm of the galaxy. It is shown as the blue dot in the above graphic.

The parts of the Milky Way that are in the upper half of the graphic are predominately visible by observers in the northern hemisphere of Earth. The center is the Milky Way galaxy, being below the level of the Sun in the graphic, is therefore best visible from the southern hemisphere.

There are around 100 globular clusters in halo around the center of the Milky Way.

O[] Light Years: Local Group of Galaxies

Local Group Data



localGroupGraphic =
Block[{a = 15*#2*N[Degree],
d = #3*N[Degree], p, r},
p = 10^3*#4*{Cos[a]*Cos[d],
Sin[a]*Cos[d], Sin[d]};
r = 10^3*Max[#5/2., 10];
{color[#1], Cuboid[p - r, p + r]}] & ,
localGroup, 1]]; 1;

view1, view2, 2500*10^3]; 1;

Relative sizes are correctly shown to scale in the graphic.

Our Milky Way galaxy is a member of the so-called Local Group of galaxies. This cluster of galaxies is several million light years across, and contains about 30 galaxies.

Our own galaxy, the Milky Way, is the blue object in the middle of the graphic above. It is 100 thousand light years across, and is the second largest galaxy in the Local Group.

To the upper left and shown in green is the larger Andromeda Galaxy, which is the farthest object visible to the naked eye (2.2 million light years away). Further still is the smaller and fainter Triangulum Galaxy shown in red on the upper left.

The three largest galaxies (Andromeda, Milky Way and Triangulum) are all spirals.

Surrounding our Milky Way are seven dwarf elliptical galaxies: Draco, Carina, Sculptor, Fornax, UrsaMinor, LeoI and LeoII. But closer still are the Large and Small Magellanic Clouds. The Large Magellanic Cloud is a spiral galaxy, and the Small Magellanic Cloud is an irregular galaxy.

Surrounding Andromeda are five dwarf elliptical galaxies: NGC185, NGC147, AndromedaI, AndromedaII and AndromedaIII. But the closest galaxies to Andromeda are M32 and M110. M32 is an elliptical galaxy, and M110 is a spiral galaxy.

Slightly to the left and at the back of the view, is the irregular galaxy NGC6822; and to the left below Andromeda, is the irregular galaxy IC1613.

Beyond the Local Group there is mostly empty space, devoid of galaxies for at least 10 million light years. But eventually there are other clusters of galaxies.

Galaxies in the upper half of the graphic are predominately visible by observers in the northern hemisphere of Earth. Andromeda is visible only to northern hemisphere observers.

O[] Light Years: Local Super-Cluster

Super-Cluster Data



galaxyClustersGraphic =
Block[{a = 15*#2*N[Degree],
d = #3*N[Degree], p, r},
p = 10^6*#4*{Cos[a]*Cos[d],
Sin[a]*Cos[d], Sin[d]};
r = 10^6*Max[#5/2., 5]*4;
{color[#1], Cuboid[p - r, p + r]}] & ,
galaxyClusters, 1]];

view1, view2, 1000*10^6];1;

Objects are shown quadruple their true relative scale in the graphic.

Our Local Group of galaxies is the small blue object in the center of the graphic. Just next to it is the Virgo Galaxy Cluster shown in green. Beyond that is the Coma Galaxy Cluster in red, and the Pisces Galaxy Cluster in yellow. The large Centaurus Galaxy Cluster is shown in purple.

The galaxy clusters shown above form part of the local super-cluster of galaxies. The local supe- cluster is approximately a plane ranging from the upper-right to lower-left of the graphic.

Variable StarsNew Improved Features