Supramundane Earth: design considerations
- From: Phillip Thorne <thorne@xxxxxxxxxxxxx>
- Date: Wed, 07 Sep 2005 22:13:29 -0400
Paul Birch introduced the concept of "supramundane planets" in an
article in _Analog_ around 1992. (If I've got my cites right.) You
take a planet with an inconvenient surface gravity (such as Jupiter)
and build a shell around it at an altitude such that the acceleration
of gravity *is* convenient. The shell is supported against streams of
masses moving at greater than orbital velocity.
Now, let's apply this idea to *Earth*. (Anyone aware of precedent for
this particular variant?)
Why? So if technology fails on the shell, you can still evacuate to
the natural surface, which has natural geologic cycles to renew
surface features. (In contrast to the failed flup pumps and spill
mountains of Niven's Ringworld.) The easiest way to evacuate is along
basal stalks (the lower portions of orbital towers), which requires
the shell to be fixed relative to Earth's surface. You'll want to
*avoid* this if you want to avoid permanently shadowing portions of
Earth's surface. (The supramundane shell can have penetrations.)
So, what's a convenient altitude?
******************************************************************
The acceleration of gravity g_h at a particular altitude h above a
planet of radius R and mass M:
(1) g_h = G M / (R + h)^2
The ratio of g_h to surface gravity g0 at h=0:
(2) g_h / g0 = R^2 / (R + h)^2
(3) h = [some quadratic rearrangement I'm not up to right now]
If h=0, (R^2)/(R+0)^2 = 1/1, so g_h=1 gee.
If h=R, (R^2)/(R+R)^2 = R^2/4R^2, so g_h=1/4 gee.
For g_h=1/3 gee, [intuitive pattern-detection leap here]
(sqrt(3)*R)^2, h = (sqrt(3)-1)*R ~ 0.73*R
******************************************************************
For Martian gravity of ~1/3 gee, you want an altitude of 0.73
Earth-radii, or about 4,300 km. (Geosynch is at 33,000 km, and has a
local gravity of ~1/56 gee.) Since surface area of a sphere goes as
the square of the radius, and R2 = sqrt(3) * R, then supramundane_area
= 3 floor_area.
[Insert calculation about umbra and penumbra cast by objects at that
altitude.]
If you skip the beanstalks, you can build multiple concentric shells,
each independently rotating (not necessarily "in orbit") and with
numerous penetrations, for a final effect like a spherical orrery --
or one of those (insanely complex) Chinese carved ivory latticework
balls. Every level still has "day" and "night", but broken up into
complex intervals more akin to frequent eclipses or passing heavy
clouds. Agricultural efficiency will be accordingly affected.
(To compensate, orbiting or statite mirrors beyond the shells could
gather several Earth-surface-worth's of sunlight, reflecting it
through unvarying penetrations at the poles and/or a system of
light-pipes.)
[Insert calculations about the scale-height of the atmosphere.]
Challenge for the reader: design an atmosphere such that air-barges
can travel between the various levels and the "floor". A transparent
outer roof is permissible.
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