There are an unlimited number of distances between rather wide parameters for an Earth - Mars Earth 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 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 - pieces 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 trusty but - 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.

This gives us: t = Vd/1/2a

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 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 - 1.495 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 achievement. But Tombaugh continued the search for seventeen weary years and many millions more films. If there is an Earth - size planet out there, it is at least three times as distant as Pluto, and a gas giant would have to be six times as far. Negative data win no prizes but they are the bedrock of science.

Until James W. Christy on 22 June 1978 discovered Pluto's satellite, Charon, it was possible for us romantics to entertain the happy thought that Pluto was loaded with valuable heavy metals; the best estimate of its density made this plausible. But the mass of a planet with a satellite can be calculated quite easily and accurately, and from that, its density.

The new figure was much too low, only half again as heavy as water. Methane snow? Perhaps.

So once again a lovely theory is demolished by an awkward fact.

Nevertheless Pluto remains a most mysterious and most intriguing heavenly body. A planet the size and mass of Mars might not be too much use to us out there ... but think of it as a fuel dump. Many stories and many nonfictional projections speak of using the gas giants and/or the rings of Saturn as sources of fuel. But if Pluto is methane ice or water ice or frozen hydrogen or all three, as a source of fuel - conventional, or fusion, or even reaction mass - Pluto has one supremely important advantage over the gas giants: Pluto is not at the bottom of a horridly deep gravity well.

Finished calculating? Good. Please turn to page 368 and see why I wanted our trip to Pluto to be a distance of 31.6 A.U. - plus other goodies, perhaps.

11. 1950 Your personal telephone will be small enough to carry in your handbag. Your house telephone will record messages, answer simple inquiries, and transmit vision.

1965 No new comment.

1980 This prediction is trivial and timid. Most of it has already come true and the telephone system will hand you the rest on a custom basis if you'll pay for it. In the year 2000, with modern telephones tied into home computers (as common then as flush toilets are today) you'll be able to have 3 - dimensional holovision along with stereo speech. Arthur C. Clarke says that this will do away with most personal contact in business. I agree with all of Mr. Clarke's arguments and disagree with his conclusion; with us monkey folk there is no substitute for personal contact; we enjoy it and it fills a spiritual need.