MMM Classics Year 10: MMM #s 91-100 - Moon Society
MMM Classics Year 10: MMM #s 91-100 - Moon Society
MMM Classics Year 10: MMM #s 91-100 - Moon Society
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Pluto—Charon Cable Car<br />
by Robert Dinkel and Francis Graham<br />
Pluto and its moon, Charon, are both tidally locked<br />
bodies, with one face of Charon facing Pluto, as our own <strong>Moon</strong><br />
does to Earth. But in addition Pluto has one face to Charon. So<br />
neither Pluto nor Charon rise and set in each others' skies.<br />
A straight line could be connected between any two<br />
points on the mutually facing hemispheres, and it is tempting to<br />
think a cable could be strung as well between the two points.<br />
Such a scheme has been proposed for a cable car connecting a<br />
point on Earth's surface with a geosynchronous space station<br />
22,000 miles above the Earth. The problem is, with such a<br />
scheme, the weight of the cable would snap itself after progressing<br />
to a height on the order of ten miles, even if the cable were<br />
made of continuously cast steel. It doesn't matter if the cable is<br />
made thick; [ed. note by Mark R. Kaehny - actually tapering<br />
the cable is generally proposed] the increased thickness adds to<br />
the weight. When the weight per unit area equals the tensile<br />
strength the cable snaps.<br />
Is Pluto's case different? On June 15, Francis Graham<br />
and Robert Dinkel set out to solve this problem. Off the shelf<br />
steel is available which has a tensile strength of 311 kpsi so we<br />
assume that with some reasonable engineering advance and<br />
special order it could be pushed to 400 kpsi.<br />
These rough dimensions of Pluto and Charon are assumed:<br />
Separation 17,500 km [<strong>10</strong>,850 mi.]<br />
Period 6.39 days<br />
Mass of Pluto 0.0018 x Earth [0.146 x <strong>Moon</strong>]<br />
Mass of Charon 0.00018 x Earth [0.015 x <strong>Moon</strong>]<br />
Pluto Radius 1500 km [1463 mi. Diameter]<br />
Charon Radius 650 km [807 mi. Diameter]<br />
Mass of Earth 6 x <strong>10</strong>24 kg.<br />
First, we calculated the libration point L1 by setting<br />
the gravitational accelerations of Pluto and Charon equal to<br />
each other. Solving the resulting quadratic gives 13,295 km<br />
from Pluto's center as the point L1. That will be our upper limit<br />
for the weight integral. The lower limit is Pluto's radius.<br />
The element of weight per unit area is<br />
dw/A = -pdrGMPLr -2<br />
where p is the density of the steel (~6 x <strong>10</strong>3 kg/m3.<br />
Integrating over the entire length of the cable from Pluto to L1<br />
Ú w/A = | -pdrGMPLr -2 = 2.55 x <strong>10</strong>9 Nt.m-2.<br />
The required tensile strength is thus 370 kpsi. 400<br />
kpsi, our futuristic steel, can go to 2.75 x <strong>10</strong>^9 Nt.m-2, easily<br />
enough. If a cable can be thus strung from the libration point to<br />
Pluto surface, it certainly can be strung from the libration point<br />
to Charon's surface.<br />
Thus we conclude that a future cable car between<br />
Charon and Pluto can be built, and safe, flightless transport for<br />
a Pluto base made. Such a cable car might be valuable at Pluto<br />
because of the vastly decreased solar power available for energetic<br />
transport by photovoltaically synthesized chemical fuels,<br />
and may be worth the use of the iron, (perhaps) a rare<br />
substance on Pluto. A Pluto base might be valuable for solar<br />
system science of all kinds, a new reference for stellar parallax<br />
measurements, and a host of other fundamental science<br />
experiments.<br />
References:<br />
Zeilik, M., The Evolving Universe, 4th ed. Harper & Row, NY:<br />
1985 (Pluto data).<br />
Rothbart, H.A., ed., Mechanical Design and Systems<br />
Handbook McGraw-Hill, NY: 1964. (Steel Data). RD & FG<br />
<strong>Moon</strong> Miners’ Manifesto <strong>Classics</strong> - <strong>Year</strong> <strong>10</strong> - Republished January 2006 - Page 73