Gregory had drawn a half ellipse, which touched Earth’s orbit at one extreme, and reached out to kiss Mars’s orbit at the other. “Here we have a minimum-energy transfer orbit. It is called a Hohmann ellipse. Any other trajectory requires a greater expenditure of energy than this… To return to Earth, we must follow a similar half ellipse.” He moved Mars around perhaps two-thirds of its orbital path, and drew another kissing ellipse, this one out of Mars and inward toward the Earth. “The flight home takes just as long as the flight out, around 260 days. And in addition, we must wait all this time at Mars, until Earth and Mars have moved into the right configuration for us to return: for no fewer than 480 days. And so our mission time is a remarkable 977 days: more than two and a half years. Our longest spaceflight to date has been around two weeks; we surely can’t contemplate a mission of such magnitude.”

“And yet, Rockwell is studying just such a mission profile, for NASA,” Dana said. “Chemical technology only. And at Marshall they are looking at nuclear options.” Nuclear rockets, more powerful, could put ships into shallower, more direct ellipses. “The Marshall study is showing journey times of no more than 450 days, total…”

“More big rockets! Huh!”

Dana grinned. “Still not elegant enough for you, Dad? But where’s the room for elegance in all this? It seems we’re kind of constrained by the laws of celestial mechanics. It’s either Hohmann, or brute force.”

“Exactly. So the elegant thing to do is wait: wait until we’ve developed a smart engine, like an ion drive, which can really cut down the transit times. But that won’t come in my lifetime, and maybe not yours.”

“Hmm.” Dana took the chalk from his father and drew more concentric circles. “Of course, you didn’t show the full picture here. There are other planets in the system: Venus inside Earth, Jupiter beyond Mars. And the others.”

Gregory scowled. “What difference does that make?”

“I don’t know.” Dana dropped the fragment of chalk back into his father’s pocket. “You’re the specialist.”

“No, no, this is not my field.”

“Maybe there is some way to use the other planets, to get to Mars. There are NASA studies going on of a Grand Tour: using the gravity field of Jupiter and the other giant planets to accelerate a probe out to Neptune…”

“So what are you suggesting? That we fly to Mars via Jupiter? That’s ridiculous. Jupiter is three times as far from the sun as Mars is.”

This tone — hectoring, impatient — was all too familiar to Dana. He held his hands up, irritated. “I’m not suggesting anything, Dad. I’m just chewing the fat. The hell with it.”

But Gregory continued to stare at the board, his eyes invisible behind the layer of chalk dust on his glasses. Some remark of Dana’s had sent him off, like a Jules Verne impulse, on some new speculative trajectory of his own; Jim Dana might as well not have been there.

The hell with it, he thought. I have my own life now, my own concerns. I don’t have time for this anymore.

Maybe I never did.

Dana withdrew from the workshop, brushing the dust off his jacket, leaving his father to his thoughts.

He spent the rest of the afternoon with his mother. They sat on the swing seat back of the house, drinking homemade lemonade and talking in the warmth of the sun. In the distance, seagulls cried.

Gregory Dana carefully sketched interplanetary trajectories.

…At age fifteen, in the year 1944, Gregory Dana was no rocket engineer. In fact he was no more than garbage, just one of the thirty thousand French, Russians, Czechs, and Poles who toiled inside a carved-out mountain in Thuringia.

Everything was slow — even dressing was slow — and Dana was already hungry by the start of his work at 5 A.M. And yet he would receive nothing until his soup, at two in the afternoon.

And then would come the rush into the smoking mouth of the tunnel into the mountain, with the SS guards lashing out with their sticks and fists at the heads and shoulders of the worker herd which passed them. The tunnel was like hell itself, with prisoners made white with dust and laden with rubble, cement bags, girders, and boxes, and the corpses of the night being dragged by their feet from the sleep galleries.

Gregory Dana was prized by the supervisors for the capacity of his small hands for skilled work. So he was assigned to lighter, more complex tasks. Gradually he picked up something of the nature of the great machines on which he toiled and learned of the visions of the Reich’s military planners.

It was well-known among the workers within the Mittelwerk that Hitler had ordered the production of no less than twelve thousand of von Braun’s A-2 rockets — or rather, what the Germans called their V-2: V for Vergeltungswaffe, revenge weapon.

There was a plan to construct an immense dome at the Pas de Calais — sixty thousand tons of concrete — from which rockets would be fired off at England in batches of fourteen at once. And then there were the further schemes: of hurling rockets from submarine craft, of greater rockets which might bombard targets thousands of miles distant, and — the greatest dream of all! — of a huge station orbiting five thousand miles above the Earth and bearing a huge mirror capable of reflecting sunlight, so that cities would flash to smoke and oceans might boil.

Such visions!

…But the V-2 was the daily, extraordinary reality. That great, finned bullet-shape — no less than forty-seven feet long — was capable of carrying a warhead of more than two thousand pounds across two hundred miles! Its four tons of metal contained no less than twenty-two thousand components!

Dana came to love the V-2. It was magnificent, a machine from another world, from a bright future — and the true dream inherent in its lines, the dream of its designers, was obvious to Dana.

Even as it slowly killed him.

One morning, so early that the stars still shone and frost coated the ground, he saw the engineers from the research facility at Peenemьnde — Wernher von Braun, Hans Udet, Walter Riedel, and the rest, smartly uniformed young men, some not much older than Dana — looking up at the stars, and pointing, and talking softly.

Dana had glanced up, to see where they were looking. There was a star, bright, glowing steadily, with the faintest glimmer of red, like a ruby.

The “star” was, of course, the planet Mars, burning brightly.

Of course: that was the dream which motivated and sustained those young, clever Germans: that one day the disk of Mars would be lit up with cities built by men — men carried there by some unimaginable descendant of the V-2.

At fifteen, Gregory Dana had been able to understand how those young men from Peenemьnde were blinded by the dazzling beauty of their V-2 and what it represented. It was not simple callousness: yes, he could understand the duality of it, and he would comfort himself with plans for after the war. Perhaps, he would dream, he himself would pursue a career in building still greater rocket machines, and even father a son who would be the first to travel beyond the air to Mars or Venus.

How he envied the young engineers from Peenemьnde, who walked about the Mittelwerk in their smart uniforms; they seemed to find it an easy thing to brush past the stacks of corpses piled up for daily collection, the people gaunt as skeletons toiling around the great metal spaceships! The duality of it crushed Dana. Was such squalor and agony the inevitable price to be paid for the dream of spaceflight?

He tried to imagine how it would have been had he been born to become one of those smart young Germans in their SS uniforms.

When he immersed himself in such dreams, something of his own daily pain would fall from him.

But then the morning would come again.

In his workshop, in the sunny June of 1970, Gregory Dana labored at his blackboard, immersed in memories, and the resolving dream of spaceflight.