Castor said, ‘Dad, if you’re afraid of that skew orbit, I’ll pilot. I know—’
‘Silence!’ When he got it he went on as if to himself, ‘It says right here in the book to give orders, not explanations, and never to let them be argued. So help me, I’m going to run a taut ship if I have to put my own mother in irons.’ He raised his voice. ‘All hands! Prepare for maneuvering. Departure for Mars, gravity-well procedure.’
Edith Stone said softly to Hazel, ‘The baby is all right. Mother. I’m sure.’ Then she turned to her sons. ‘Castor, Pollux — come here, dears.’
‘But Dad said —’
‘I know. Come here first.’ She kissed each of them and said, ‘Now man your stations.’
Meade appeared at the hatch, towing Lowell behind her like a toy balloon. He seemed cheerful and his face was cheerfully smeared with chocolate. ‘What’s all the racket about?’ she demanded. ‘You not only woke us; you must be disturbing people three ships behind.’
VII — IN THE GRAVITY WELL
A gravity-well maneuver involves what appears to be a contradiction in the law of conservation of energy. A ship leaving the Moon or a space station for some distant planet can go faster on less fuel by dropping first toward Earth, then performing her principal acceleration while as close to Earth as possible. To be sure, a ship gains kinetic energy (speed) in falling towards Earth, but one would expect that she would lose exactly the same amount of kinetic energy as she coasted away from Earth.
The trick lies in the fact that the reactive mass or ‘fuel’ is itself mass and as such has potential energy of position when the ship leaves the Moon. The reactive mass used in accelerating near Earth (that is to say, at the bottom of the gravity well) has lost its energy of position by falling down the gravity well. That energy has to go somewhere, and so it does — into the ship, as kinetic energy. The ship ends up going faster for the same force and duration of thrust than she possibly could by departing directly from the Moon or from a space station. The mathematics of this is somewhat baffling — but it works.
Captain Stone put both the boys in the power room for this maneuver and placed Hazel as second pilot. Castor’s feelings were hurt but he did not argue, as the last discussion of ship’s discipline was still echoing. The pilot has his hands full in this maneuver, leaving it up to the co-pilot to guard the auto-pilot, to be ready to fire manually if need he, and to watch for brennschluss. It is the pilot’s duty to juggle his ship on her gyros and flywheel with his eyes glued to a measuring telescope, a ‘coelostat,’ to be utterly sure to the extreme limit of the accuracy of his instruments that his ship is aimed exactly right when the jet fires.
In the passage from Earth to Mars a mistake in angle of one minute of arc, one sixtieth of a degree, will amount to — at the far end — about fifteen thousand miles. Such mistakes must be paid for in reactive mass by maneuvering to correct, or, if the mistake is large enough, it will he paid for tragically and inexorably with the lives of captain and crew while the ship plunges endlessly on into the empty depths of space.
Roger Stone had a high opinion of the abilities of his twins, but’ on this touchy occasion, he wanted the co-pilot backing him up to have the steadiness of age and experience. With Hazel riding the other. couch he could give his whole mind to his delicate task.
To establish a frame of reference against which to aim his ship he had three stars, Spica, Deneb, and Fomalhaut, lined up in his scope, their images brought together by prisms. Mars was still out of sight beyond the bulging breast of Earth, nor would it have helped to aim for Mars; the road to Mars is a long curve, not a straight line. One of the images seemed to drift a trifle away from the others; sweating, he unclutched his gyros and nudged the ship by flywheel. The errant image crept back into position. ‘Doppler?’ he demanded.