Heinlein, Robert A – Have Space Suit will Travel

Which reminded me that I had not worked out how long it would take to get home on a one-gee boost, if it turned out that I could not arrange automatic piloting at eight gees. I was stymied on getting out of the cell, I hadn’t even nibbled at what I would do if I did get out (correction: when I got out), but I could work ballistics.

I didn’t need books. I’ve met people, even in this day and age, who can’t tell a star from a planet and who think of astronomical distances simply as “big.” They remind me of those primitives who have just four numbers: one, two, three, and “many.” But any tenderfoot Scout knows the basic facts and a fellow bitten by the space bug (such as myself) usually knows a number of figures.

“Mother very thoughtfully made a jelly sandwich under no protest.” Could you forget that after saying it a few times? Okay, lay it out so:

Mother MERCURY $.39

Very VENUS $.72

Thoughtfully TERRA $1.00

Made MARS $1.50

A ASTEROIDS (assorted prices, unimportant)

Jelly JUPITER $5.20

Sandwich SATURN $9.50

Under URANUS $19.00

No NEPTUNE $30.00

Protest PLUTO $39.50

The “prices” are distances from the Sun in astronomical units. An A.U. is the mean distance of Earth from Sun, 93,000,000 miles. It is easier to remember one figure that everybody knows and some little figures than it is to remember figures in millions and billions. I use dollar signs because a figure has more flavor if I think of it as money-which Dad considers deplorable. Some way you must remember them, or you don’t know your own neighborhood.

Now we come to a joker. The list says that Pluto’s distance is thirty-nine and a half times Earth’s distance. But Pluto and Mercury have very eccentric orbits and Pluto’s is a dilly; its distance varies almost two billion miles, more than the distance from the Sun to Uranus. Pluto creeps to the orbit of Neptune and a hair inside, then swings way out and stays there a couple of centuries-it makes only four round trips in a thousand years.

But I had seen that article about how Pluto was coming into its “summer.” So I knew it was close to the orbit of Neptune now, and would be for the rest of my life-my life expectancy in Centerville; I didn’t look like a preferred risk here. That gave an easy figure-30 astronomical units.

Acceleration problems are simple s=1/2 at2; distance equals half the acceleration times the square of elapsed time. If astrogation were that simple any sophomore could pilot a rocket ship-the complications come from gravitational fields and the fact that everything moves fourteen directions at once. But I could disregard gravitational fields and planetary motions; at the speeds a wormface ship makes neither factor matters until you are very close. I wanted a rough answer.

I missed my slipstick. Dad says that anyone who can’t use a slide rule is a cultural illiterate and should not be allowed to vote. Mine is a beauty- a K&E 20″ Log-log Duplex Decitrig. Dad surprised me with it after I mastered a ten-inch polyphase. We ate potato soup that week-but Dad says you should always budget luxuries first. I knew where it was. Home on my desk.

No matter. I had figures, formula, pencil and paper.

First a check problem. Fats had said “Pluto,” “five days,” and “eight gravities.”

It’s a two-piece problem; accelerate for half time (and half distance); do a skew-flip and decelerate the other half time (and distance). You can’t use the whole distance in the equation, as “time” appears as a square-it’s a parabolic. Was Pluto in opposition? Or quadrature? Or conjunction? Nobody looks at Pluto-so why remember where it is on the ecliptic? Oh, well, the average distance was 30 A.U.s-that would give a close-enough answer. Half that distance, in feet, is: 1/2 x 30 x 93,000,000 x 5280. Eight gravities is: 8 x 32.2 ft./sec./sec.-speed increases by 258 feet per second every second up to skew-flip and decreases just as fast thereafter.

So- 1/2 x 30 x 93,000,000 x 5280 = 1/2 x 8 x 32.2 x t2 -and you wind up with the time for half the trip, in seconds. Double that for full trip. Divide by 3600 to get hours; divide by 24 and you have days. On a slide rule such a problem takes forty seconds, most of it to get your decimal point correct. It’s as easy as computing sales tax.