perspective; look back thirty-five years to 1930-the American Rocket Society had not
yet been founded. Another curve, similar to the one herewith in shape but derived
entirely from speed of transportation, extrapolates to show faster-than-light travel
by year 2000. I guess I’m chicken, for I am not predicting FTL ships by then, if
ever. But the prediction still stands without hedging.
1980 My money is still on the table at twenty years
and counting. Senator Proxmire can’t live forever. In the last 101/2 years men have
been to the Moon several times; much of the Solar system has been most thoroughly
explored within the limits of “black box” technology and more will be visited before
this year is out.
Ah, but not explored by men-and the distances are so great. Surely they are.
. . by free-fall orbits, which is all that we have been using. But there are
numerous proposals (and not all ours!) for constant-boost ships, proposals that
require R&D on present art only-no breakthroughs.
Reach for your pocket calculator and figure how long it would take to make a
trip to Mars and back if your ship could boost at one-tenth gee. We will omit some
trivia by making it from parking orbit to parking orbit, use straight-line
trajectories, and ignore the Sun’s field-we’ll be going uphill to Mars, downhill to
Earth; what we lose on the roundabouts we win on the shys.
These casual assumptions would cause Dan Alderson, ballistician at Jet
Propulsion Laboratory, to faint. But after he comes out of his faint he would agree
that our answers would be of correct close order of magnitude-and all I’m trying to
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prove is that even a slight constant boost makes an enormous difference in touring
the Solar System. (Late in the 21st century we’ll offer the Economy Tour: Ten
Planets in Ten Days.)
There are an unlimited number of distances between rather wide parameters
for an Earth-MarsEarth trip but we will select one that is nearly minimum (it’s
cheating to wait in orbit at Mars for about a year in order take the shortest trip
each way.. . and unthinkable to wait years for the closest approach). We’ll do this
Space Patrol style: There’s Mars, here we are at L-5; let’s scoot over, swing around
Mars, and come straight home. Just for drill.
Conditions: Earth-surface gravity (one “gee”) is an acceleration of 32.2
feet per second squared, or 980.7 centimeters per second squared. Mars is in or near
op
position (Mars is rising as Sun is setting). We will assume that the round trip is
120,000,000 miles. If we were willing to wait for closest approach we could trim
that to less than 70,000,000 miles .. . but we might have to wait as long as 17
years. So we’ll take a common or garden variety opposition-one every 26 months-for
which the distance to Mars is about 50- to 60,000,000 miles and never over 64
million.
(With Mars in conjunction on the far side of the Sun, we could take the
scenic route of over 500 million miles-how much over depends on how easily you
sunburn. I suggest a minimum of 700 million miles.)
You now have all necessary data to figure the time it takes to travel
Earth-Mars-Earth in a constant-boost ship-any constant-boost ship-when Mars is at
opposition. (If you insist on the scenic route, you can’t treat the trajectory
approximations as straight lines and you can’t treat space as flat but a bit uphill.
You’ll need Alderson or his equal and a big computer, not a pocket calculator; the
equations are very hairy and sometimes shoot back.)
But us two space cadets are doing this by eyeballing it, using Tennessee
windage, an aerospace almanac, a Mickey Mouse watch, and an SR-50 Pop discarded
years ago.
We need just one equation: Velocity equals acceleration times elapsed time:
v = at
This tells us that our average speed is 1/2at-and from that we know that the
distance achieved is the average speed times the elapsed time: d = 1/2at2
If you don’t believe me, check any physics text, encyclopedia, or nineteen
other sorts of reference books-and I did that derivation without cracking a book but