"All right children," she joked, as Dan sailed past the big screen, "behave yourselves."
"Of course." he replied, crashing into the far wall. "Sorry if we woke you."
"Well you did, but it's high time I got up."
"Oh," commented Garvin as he prepared for a mid-air somersault, "there's a message from NASA, marked Captain Present, medium priority." If it had been marked Eyes Only, her crewmates would be excluded; but Captain Present simply meant she had to listen to the message along with the others.
"Ok, it doesn't sound terribly urgent. Let's get some breakfast and we'll watch it in the kitchen."
Nancy pulled out a melon, the last piece of fresh fruit on board, and cut it into slices for herself and Dan, catching the drops in a paper towel before they floated away. Garvin, who preferred a more substantial breakfast, placed a frozen egg sausage biscuit in the microwave, set the time, and pressed power, while Dan activated the message on the small screen. They recognized Julie at once, the capcom from the first shift. She was smiling, as always, but her expression was tempered with concern.
"Hi Nancy. This is mission control. If Dan and Garvin aren't with you, you might want to go get them. We're kind of confused here on the ground, and we need everybody's input on this one." She paused for a moment, then resumed. "As you know, the probe has been glowing red hot, which makes it easy to track. This is waste heat, as the engines slow its descent into our solar system. Anyways, the probe has been cooling for the past 3 hours, and it seems to be in a coast phase. As far as we can tell, the engines are off. But here's the strange part. It looks like it's going to miss Earth altogether." Julie disappeared as the screen presented an animation of the solar system. However, her voice continued to narrate. "The red dot is the probe. Assuming it remains in a coast phase, it will fall towards the sun and swing by Jupiter." The dot traveled along an arc, passing through the orbits of Neptune, Uranus, and Saturn, and slipping behind Jupiter. "The gravity assist will change its trajectory, but there's more than Jupiter involved. The probe will come within a few hundred miles of Ganymede, Jupiter's largest moon. This bends the path of the probe by another fraction of a degree. This couldn't happen by accident; it has to be part of their flight plan." The animation zoomed in on Jupiter and its moons as the probe passed across the leading edge of Ganymede. The path looked like a refracted beam of light. The red dot left the Jovian system on its new heading towards the inner planets. "Now watch, the probe is going to miss Earth by several million miles." As if in confirmation, the dot crossed the orbit of Earth several degrees ahead of the oversized blue circle.
"Not even close." remarked Garvin.
"And there's no turning back.", Julie continued from behind her animation. "The orbit is still hyperbolic. The probe will sail past our sun and head out to the next star. It hasn't slowed down enough to become part of our solar system. Now I'll grant you, the engines could restart at any time, but when it comes to orbital mechanics, the best time to change your trajectory is yesterday. Why would they delay? Every hour makes it harder to change course. Unless we're missing something, we don't see how they can rendezvous with Earth and complete their mission. We are wondering if there is a technical malfunction on board. The engines may have stopped prematurely. I hope we're wrong, because it will be another 15,000 years before the Arcots can try again."
Julie's image returned to the screen. "That's all we've got for now. It will be 13 hours before you get this message, and another 13 hours before we get your response, but we're interested in your thoughts. You should be close enough to scan the probe; let us know what you find out. We'll send updates as appropriate. This is Houston, signing off."
The screen went blank. "Comments?" asked the Captain.
"I don't believe it is a malfunction." replied Dan. "The Arcots possess technology that we can't even imagine, and they get every detail right, across 6,000 light years, then make a mistake at the last minute? I don't think so. Besides, Julie said it best; the close approach to Ganymede can't be an accident. It's part of their flight plan. This is the trajectory they want." He took a bite of melon, wiped his mouth, then continued. "Perhaps NASA miscalculated. A few miles closer to Ganymede, or farther away, and the path could be quite different. I'm sure the Arcots' computers are better than ours."
"That's a good thought," granted Garvin, "but I really doubt it. NASA has been calculating orbital mechanics with pinpoint accuracy since the dawn of technology, and the laws of physics haven't changed. I have every confidence in the folks on the ground. The path you saw on the screen is the path the probe will take."
"Unless one of our cherished assumptions is wrong." Nancy was always able to think outside the box; that's why she was in command.
"Which assumption?" asked Garvin. He wasn't being disrespectful, but he couldn't imagine which law of physics she was willing to break.
"I don't know." Nancy tossed her rine into the disposal unit.
"I suppose they wanted the Jupiter assist, then they'll change course as they pass the orbit of Mars." Dan tossed his rine away.
"I suppose." Nancy mused. "It will take a lot of power to change course at that point, but I guess it's within their capabilities." She floated out of the kitchen and into the lounge, with her crewmates close behind. "Garvin, I need some down time, time to mull this over in my subconscious. Put on one of those old movies that you like - something I can watch and ignore at the same time - like maybe one of those John Wayne westerns."
Garvin called up The Shootist, and Nancy found a comfortable position near the ceiling. In zero gravity you could watch the movie from above. The 3 dimensional perspective wasn't quite right, but the human brain can usually fill in the details. She let the movie wash over her as she thought about the probe, on its way to Earth, or not, as the case may be. What was she missing?
Halfway through the film Nancy slipped out, unbeknownst to her companions, to watch the animation again. The red path bent in obedience to Jupiter's gravity, with an extra kick from Ganymede. "It has to be right, but it can't be right. Our understanding of orbital mechanics is 15,000 years old, but it is incomplete. What is different about this probe?" She turned off the animation and went back to the lounge, and immersed herself in the 19th century. A gun, and a steady hand, and a good understanding of other human beings. That always put John Wayne ahead of the game. "Pretty good flick." Nancy mumbled aloud as Mr. Books breathed his last breath.
"Thought you'd like it."
They had a quiet lunch together, then Nancy went to her bedroom and turned off all the lights. Her window glittered with thousands of stars, more than you could ever see on Earth. They seemed fixed for all time. She pulled out two handweights and began a light exercise regimen, keeping her eyes focused on the stars. Her body recoiled slightly as she pushed the weights away, then returned as she pulled the weights back to her chest. "Equal and opposite reaction." she declared, to nobody in particular. "Thank you Isaac, for unlocking the secrets of the universe. They seem so obvious now, in retrospect." Suddenly she released the weights, pushed herself across the room, opened her bedroom door, and called for her crewmates.
"Garvin. Dan. I think I have the answer. Meet me on the bridge."
Nancy sat in the captain's chair, flanked by Garvin and Dan. GPS transmitters, scattered about the solar system, established their position and velocity to a resolution of a few feet. "I'm getting an update on the probe's position and velocity and feeding it into the ship's computers." Nancy explained as the radar dish slewed into position. She sent a radar pulse towards the probe, which continued to betray its position with waste heat. The object was nearly spherical, scattering most of the electromagnetic energy into space, but there was a detectable echo nonetheless, and the probe's position and velocity soon appeared on the screen. "Garvin, do you know how to run the orbital mechanics program?"
"Sure."
"Good, cause I don't. Project the probes path all the way to Earth, using the new position and velocity. And try to use the same colors and graphics as NASA, so we know what we're looking at."
"No problem. They used the default colors, so I can just let it run." A red dot appeared on the screen, tracking the probe's path. It flew towards the sun, sailed past Jupiter and Ganymede, and missed Earth, just as it had done earlier that morning.
"Looks the same." remarked Dan.
"Yes, I expected that. But what is the underlying assumption?" Nancy paused for a moment, then answered her own question. "This simulation assumes the probe has a trivial mass relative to the planets and moons. The planet pulls on the probe; the probe does not pull on the planet. That's always been the case with our space craft, and meteors, and comets. But this probe is heavy - it pulls back. It's path is not bent as much as an asteroid or a space ship."
Garvin performed some analog math in his head. "But Nans, even a mountain is trivial compared to Jupiter and Ganymede. Large asteroids, larger than a mountain, are plotted using this software, and the predictions are spot on."
"Yes," countered Nancy, "but what if it's bigger than a mountain? What if they lied? Give the probe a higher mass and run the simulation again."
Garvin was skeptical, but he did as directed. "I'll assign it the mass of a continent." He set the original path in light pink and ran the simulation again. As the red dot passed through the Jovian system it followed the pink curve perfectly, i.e. within a pixel, but somewhere between Jupiter and Mars the two paths diverged. The red dot still missed Earth by a wide margin, but it was a tad closer.
"Right direction," Dan concluded, "but you need more mass."
Garvin ran the simulation again and again, adding more mass with each iteration. Finally they saw the red dot glide neatly into the vicinity of the Earth, in a resonant orbit with the moon. "That's it!" shouted Nancy. "What's the mass?"
"About 5.1 times 10 to the 22nd kilograms." replied Garvin. "That's almost as massive as our own moon!" For a moment the three sat in stunned silence. The Arcots were capable of packing the mass of the moon into a relatively small space, and sending it across the galaxy to a specific destination with perfect accuracy. This was indeed a race to be respected, and feared.
Nancy was the first to speak. "We need to tell Mission Control right away. Garvin, can you relay our findings, and transmit your animation as an attachment?"
"Of course." He keyed his mike and recorded a voice message for NASA, explaining the change in trajectory brought about by the excess mass. "It also solves the evaporation paradox." he added. "A black hole of this size could indeed survive the journey." When he was finished, Nancy took over. "If I may bring some psychology to bear, I am once again concerned by the Arcots' inaccuracy and/or deception. They told us their black hole had the mass of a mountain, and Dan assures me the translation is correct. A mountain is hardly comparable to the moon. I don't know why they would mislead us regarding the mass of their probe, but this is just one more inconsistency that's going to keep me awake at night." She closed the mike and looked towards her crewmates. They shook their heads, indicating there was nothing more to add. She keyed her mike again. "Garvin is attaching the revised parameters for the probe's position, velocity, and mass, along with his latest orbital animation. You can check our results, but you're using the same computers and the same software, so I'm sure it will come out the same. Well that's all for now. This is Explorer 29 signing off." She closed her mike, pressed transmit, and leaned back in her chair. "The mass of the moon." she said out loud.
Garvin was busy running calculations and simulations on his console. "You know, if we had approached the probe assuming it was just another large asteroid, ... well, ... I mean, ... we would have been sucked in by its gravity, and I don't think our engines could pull us out in time." A red dot and a yellow dot collided and merged on the screen. "You may have saved our lives. You may have saved the mission."
Nancy took two steps away from Garvin's compliment. "I'm sure the GPS units would have alerted us when the ship was pulled off course. I think we would have detected the probe's gravitational field in time to refine our approach."
"Perhaps." said Garvin, but he didn't believe it. They didn't program the ship's computers to watch for minor deviations in trajectory, so naturally, nobody was watching. By the time someone noticed, it might be too late. The subject was never brought up again, but Garvin was sure they would have crashed into the side of the probe, if it weren't for Nancy's persistent curiosity and keen intellect. Somehow Nancy could see the big picture. She didn't get lost in the details the way Garvin sometimes did. That's why she was in command. He was proud to serve at her side, proud to be a member of this crew, and proud to represent Earth at first contact.