Their mission was to move their apogee from where it was now—just a few kilometers higher than the altitude of the perigee—all the way out to the altitude of Cleft, some 378,000 kilometers more distant. It was a reversal of the maneuvers that Markus, Dinah, Jiro, and Vyacheslav had executed in order to bring Ymir into orbital sync with Izzy. The way to achieve it was to burn the engines for brief intervals as Endurance made her regular swings through perigee.
The first of those burns happened about thirty minutes after she was christened, and yielded a delta vee of four meters per second. The acceleration was so mild that most of the crew could not even sense it. For the combined thrust of eighty-one arklet engines was nearly powerless against the bulk of Endurance, with her roughly equal masses of iron and ice. Nonetheless it was enough to boost her apogee, which occurred some forty-six minutes later, by 14.18 kilometers. And forty-six minutes after that, another burn during another scrape with the atmosphere gained them another four meters per second that, at the ensuing apogee, added 14.21 kilometers on top of that. The result of Endurance’s first day of operations was a boost in apogee altitude of more than one hundred kilometers, enough to get them clear of the expanded atmosphere except during the few minutes each orbit when they swung through perigee.
After that, however, they had to suspend operations, since they’d used up all the propellant stored in the Shipyard’s ice-buried tanks. They needed to give the reactor and the splitters some time to catch up. Even a nuclear power plant could split water only so fast.
Not long after, the operation was shut down for a week by problems in feeding clean water to the system. For another month it could only operate at about a quarter of its planned capacity. But over time they worked the bugs out and began to burn the engines more and more at each perigee, gradually extending Endurance’s reach toward Cleft.
If they could keep it up, that reach would get less gradual over time. The first delta vee had gained them 14.18 kilometers. The second, equivalent delta vee had reaped 14.21 kilometers—an improvement of about thirty meters. These gains were tiny in comparison to the distances of outer space, but from a mathematical standpoint the trend was extremely significant. It meant that the higher they went—the more elongated the orbit became—the more leverage they could obtain from each one of those tiny delta vees. That difference of thirty meters would grow and grow until it spanned many kilometers, and each of those improvements would feed back into the equations and amplify the next result a little bit more. It was an exponential sort of phenomenon, and this time humanity was on the right side of it.
This didn’t even take into account another piece of good mathematical news, which was that Endurance grew a little bit lighter with each one of those burns. She had less mass with which to resist the force of the thrusters, and so it gradually became possible to produce more than a piddling four meters per second of delta vee on each turn around the planet.
So everything was going to get better, if they could stay alive and keep Endurance working. But these gains accrued painfully slowly at the beginning.
IT ENDED UP TAKING THREE YEARS.
They had planned for one. It took longer because things kept breaking and needed to be fixed. The tools and supplies needed to fix them weren’t always available. Sometimes they had to be improvised. Elaborate workarounds had to be devised through the force of human ingenuity, hard work, and, when all else failed, the risking and the sacrifice of lives.