Astronomical Scale Models

In these scale models, we go from one scale to the next in factors of 10E3 = 1000. To envision the magnitude of this step, take 1 millimeter and then look at it as part of 1 meter. The meter is 10E3 times larger. Or go from 1 meter to 1 kilometer.  The scales below go through 4 such steps, beginning with the terrestrial scale of a regional map, 1:10 million  (1cm = 100 km).

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True Values and Distances (approximate) : c   =   3x10E8 m/s   =   300 Mm/s ; 1 AU  =  149.5979 Gm; 1 Year  =  365.2422 d  =  31.557 x 10E6 s  (tropic); 1LY =  63241.077 AU  =  9.467 Pm   ~  10E13 km;  1 Parsec   =  206264.8062 AU  =   30.856776 Pm  ~ 3.262 LY;  ØEarth  =  12.75  Mm;   ØSun  =  1,4 Gm;  D Earth - Moon  =  385 Mm,  Earth - Sun  =  1AU;  Sun - Mars   ~  1.5 AU  ~   230 Gm;   Sun - Jupiter   ~   5  AU  ~  778 Gm;  Sun - Saturn   ~  10 AU  ~  1.4 Tm;  Sun - Neptune  ~  30  AU  ~  4.5 Tm.

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Terrestrial Scale:  Reduction  10E7   -->   scaled  c'  =    30 m/s;   ØEarth  ~ 1.26 m,   L.A. to Boston  ~  430 mm,    D Earth - Moon  =  38.5m,    Ø Sun  =  140m   1 AU    ~   15 km  ~  500 Ls,    Sun - Jupiter   =   78 km,  Sun - Neptune  =  450 km   =  15 kLs, 1 LY -> 1Gm.

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Planetary Scale:   Reduction  10E10     [1 m -->  100 pm  =  1 Å (!)];    c''   =  30 mm/s;   Ø Earth  ~  1.3 mm,  Earth - Moon   ~  38.5 mm,  Ø Sun   ~ 140 mm;  1 AU  ---->  15 m.,  D Sun - Jupiter   ~  78m,   Sun - Neptune  ~  450 m, 1 LY ->  1 Mm   [Wash. DC - Chicago, Ill],   D to next star   >  4Mm  (DC  to SF, Cal)

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Stellar Scale:      Reduction  10E13  --->     c'''  =  30 μm/s  ~  1 km/year;    ØEarth  ~   1.3 μm,   ØSun   ~  140 μm,  D Earth to Sun (1 AU)  ~  15 mm ;   D Sun - Jupiter  78 mm, D Sun - Neptune  450 mm,  1Ly  ~  1km,   D  to Sirius ~   8 km;  D to M13  ~  22 Mm;   Ø Galaxy  ~ 100 Mm (1/3 to moon);  D  to Magellanic cloud  ~ 160 Mm,  D to  M31  ~  2 Gm.

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Galactic Scale:   Reduction  10E16  --->   c'''' = 1 m/year;   ØEarth  ~  1.3 nm (5 Cs atoms);  1 AU  ~  15 μm,  1 LY = 1 m,  D  Sun - Neptune  ~  450 μm.  D to Sirius  ~  8m; D to M13  ~  22 km,   Ø Galaxy  ~  100 km  [Wash, DC - Hagerstown, MD],    D to M31  ~  2 Mm  [Wash - Dallas];  to Virgo Cluster  ~  45 Mm !

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Cosmic Scale:     Reduction  10E19  --->   Model  c  =  1 mm/year;  Ø Sun  ~  150 pm (~ Lithium ion),   1AU    ~  15 nm,   1 LY -> 1 mm,  1 MLY -> 1km,  Ø Galaxy  ~  100 m,  D to Sirius  ~  8mm,  to M13  ~ 22 m,  to M31  ~   2.2 km,  to Virgo Cluster  ~  45 km,  to Coma Cluster   ~  400 km,  1 GLY -> 1 Mm  (Wash - Chicago).  The distance  to the very remotest,  somehow  “detectable” objects is   ~  4 GLY  -- > 4 Mm.  In this scale, the today “observable” part of the Universe covers about the size of North America.

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Abbreviations:  AU  Astronomical Unit,  D  Distance,  Ø Diameter,  LY  Lightyear,  s  second;   k, M, G, T, P are the Decimal Prefixes of the International System for the decimal exponents of  3, 6, 9, 12, and 15  (e.g., 10E6 m  = 1Mm);   m, μ, n, p, f, are for the corresponding exponents of  -3,  -6, -9, -12, and -15;   M13 is the globular cluster in Hercules,  M31 is the great galaxy in Andromeda.

Gernot M. R. Winkler,        02/22/2009