Heinlein, Robert A – Expanded Universe

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

Page 140

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