Heinlein, Robert A – Expanded Universe

now I’m going to stop and find out whether I’ve goofed-I’ve had years of practice in

goofing. (Later-seems okay.)

Just two things to remember: 1) This is a 4-piecee trip-boost to midpoint,

flip over and boost to brake; then do the same thing coming home. Treat all four

legs as being equal or 30,000,000 miles, so figure one of them and multiply by four

(Dan, stop frowning; this is an approximation . . . done with a Mickey Mouse watch.)

2) You must keep your units straight. If you start with centimeters, you are

stuck with centimeters; if you start with feet, you are stuck with feet. So we have

1/4 of the trip equals 5280 x 30,000,000 = 1.584 x 1011 feet, or 4.827 x 1012

centimeters.

One last bit: Since it is elapsed time we are after, we will rearrange that

equation (d = 1/2at2) so that you can get the answer in one operation on your

trustybut-outdated pocket calculator. . . or even on a slide rule, as those

four-significant-figures data are mere swank; I’ve used so many approximations and

ignored so many minor variables that I’ll be happy to get answers correct to two

significant figures.

– = t2 This gives us: t = Vd/1/2a

V2a

d is 30,000,000 miles expressed in feet, or 158,400,000,000. Set that into

your pocket calculator. Divide it by one half of one tenth of gee, or 1.61. Push the

square root button. Multiply by 4. You now have the elapsed time of the round trip

expressed in seconds so divide by 3600 and you have it in hours, and divide that by

24 and you have it in days.

At this point you are supposed to be astonished and to start looking for the

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mistake. While you are looking, I’m going to slide out to the refrigerator.

There is no mistake. Work it again, this time in metric. Find a reference

book and check the equation. You will find the answer elsewhere in this book but

don’t look for it yet; we’ll try some other trips you may take by 2000 A.D. if you

speak Japanese or German-or even English if Proxmire and his ilk fail of reelection.

Same trip, worked the same way, but at only one

percent of gee. At that boost I would weigh less than my shoes weigh here in my

study.

Hmmph! Looks as if one answer or the other must be wrong.

Bear with me. This time we’ll work it at a full gee, the acceleration you

experience lying in bed, asleep. (See Einstein’s 1905 paper.)

(Preposterous. All three answers must be wrong.)

Please stick with me a little longer. Let’s run all three problems for a

round trip to Pluto-in 2006 A.D., give or take a year. Why 2006? Because today Pluto

has ducked inside the orbit of Neptune and won’t reach perihelion until 1989-and I

want it to be a bit farther away; I’ve got a rabbit stashed in the hat.

Pluto ducks outside again in 2003 and by 2006 it will be (give or take a few

million miles) 31.6 A.U. from the Sun, figuring an A.U. at 92,900,000 miles or

14,950,000,000,000 centimeters as we’ll work this both ways, MKS and English units.

(All right, all right-i .495 x 1013 centimeters; it gets dull here at this

typewriter.)

Now work it all three ways, a round trip of 63.2 A.U. at a constant boost of

one gravity, one tenth gravity, and one hundredth of a gee-and we’ll dedicate this

to Clyde Tombaugh, the only living man to discover a new planet-through months of

tedious and painstaking examination of many thousands of films.

Some think that Pluto was once a satellite and its small size makes this

possible. But it is not a satellite today. It is both far too big and hundreds of

millions of miles out of position to be an asteroid. It can’t be a comet. So it’s a

planet-or something so exotic as to be still more of a prize.

Its size made it hard to find and thus still more of an achievment. But

Tombaugh continued the search for seventeen weary years and many millions more