A View from the Back of the Envelope top

The relative size of
Earth, Jupiter, Sun
1 : 10 : 100
Megameters in your hands
A ball's volume and area are 1/2 of its box's
Length Area Volume
Developing "deep" understanding

Clarifying size, and practice with spheres...

diameter vs Earth
Earth 107 × 1.27 m 1 x
Jupiter 108 × 1.43 m 10 x(closer to 11)
Sun 109 × 1.39 m 100 x(closer to 110)

length, area, volume
m1 m2 m3
If length (m) goes 1 : 101 : 102 (ie 1 : 10 : 100)
then area (m2) goes 1 : 102 : 104 (12 : 102 : 1002)
and volume (m3) goes 1 : 103 : 106 (13 : 103 : 1003).

diameter vs Earth
Earth 107 × 1.27 m 1 x100
Jupiter 108 × 1.43 m 10 x101 (closer to 11)
Sun 109 × 1.39 m 100 x102 (closer to 110)

surface area vs Earth
Earth 1015 × 0.510 m2 1 x100
Jupiter 1017 × 0.641 m2 100 x102 (closer to 130)
Sun 1019 × 0.609 m2 10,000 x104 (closer to 12,000)

volume vs Earth
Earth 1021 × 1.1 m3 1 x100
Jupiter 1025 × 1.52 m3 1,000 x103 (closer to 1,400)
Sun 1027 × 1.41 m3 1,000,000 x106 (closer to 1,300,000)

diameter area volume
Earth 107 × 1.27 m 1015 × 0.510 m2 1021 × 1.1 m3
Jupiter 108 × 1.43 m 1017 × 0.641 m2 1024 × 1.52 m3
Sun 109 × 1.39 m 1019 × 0.609 m2 1027 × 1.41 m3
1 : 101 : 102
m		 1 : 102 : 104
m2		 1 : 103 : 106
m3

mass
The densities (kg/m3) are somewhat similar, so mass follows volume.

density volume mass
Earth 103 × 5.5 kg/m3 (5.5 g/cm3) 1021 × 1.1 m3 1025 × 0.60 kg 100
Jupiter 103 × 1.3 kg/m3 (1.3 g/cm3) 1024 × 1.52 m3 1027 × 1.9 kg 103
Sun 103 × 1.4 kg/m3 (1.4 g/cm3) 1027 × 1.41 m3 1030 × 2.0 kg 106

Say the Earth is a 107 m cube.

Then its area is 107 × 107 × 6 (sides) m2.
And its volume is 107 × 107 × 107 m3.

length
m1		 area
m2		 volume
m3
Cube
107m
1014 × 6m2
1021m3
Earth
107 × 1.3m
1014 × 5.1m2
1021 × 1.1m3

Surface area of the Earth?

1015 × 0.6m2
 a 107 m cube
1015 × 0.3m2
 a 107 m sphere, roughed as 1/2 of the cube
1015 × 0.432m2
 107 × 1.2 m sphere ("six ee six" radius), using 1/2 of cube
1015 × 0.510m2
 107 × 1.27 m sphere, using 4 pi r2
1015 × 0.510m2
 Earth's area [Cow p235]
The surface area of Earth is about 1015 m2.

Perhaps a number to remember

Earth radius - "Six ee Six meters" (6 × 106 m, aka 6E6, -6%, ±<1% )

Earth diameter - "Two times Six ee Six meters" (1.2 × 107 m, aka 12E6, -6%, ±<1% )
107 (-×0.22, ±<1%)

107 × 1.276 | 1.272 m±<1%from equatorial | polar radius [Cow]
107 × 1.3 m+2%, ±<1%
107 × 1.2 m-6%, ±<1%2 × 6E6, "twelve ee six meters"
107 × 1.4 m+10%, ±<1%7E7
107 m-22%, ±<1%

Remembering the size of Earth, and the 1 : 10 : 100 size relation, you then know the size of Jupiter and the Sun, too. And area and volume. And rough mass if you remember a rough density.

Earth's surface as a 20 x 25 Megameter rectangle

Some links

Doing Geometry with Jupiter
Doing Geometry with Saturn
The Sun and Earth Size Comparison
A Solar System Scale Model Meta Page

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu> 

Doables:
 Too much is only implicit.
 Needs a few worked examples.
   Like earth landmark (6E6 m) to earth area to solar area,
   perhaps then power release, transmission to earth.
 Perhaps return a few of the landmarks?
 Mention invariance of diameter vs radius.
 Mention sun size vs earth-moon.
 Give sources for numbers.
 Earth-only blocks perhaps belong elsewhere.
 Now always saying 1:10:100.  Should explicitly point out this means S = 10 x J.
 Add link to Scaling the universe to your desktop's Megameters in your hands.


History:
 2003-Feb-03  Fixed 1 link.
 2000-Oct-10  Spelling correction "equitorial" - thanks to a reader.
              Added link to `Megameters in your hands'.
 1999.Dec.14  Added `20x25 Mm' link.
 1998.May.21  Added `Doing Geometry with Jupiter/Saturn' links.
 1997.Aug.10  First draft.  Removed landmarks.
 1997.Aug.06  First pass.