Calc The Three-Body Problem calcs, part 1

“The Trisolaran Interstellar Fleet. It’s about to begin its expedition.”
“Trisolaran civilization has already achieved the capacity forinterstellar flight?”
“Yes. All those magnificent ships can reach one-tenth the speed of light.”
“That is a great accomplishment, as far as I understand it, but it still seems too slow for interstellar flight.”
“The journey of a thousand miles begins with the first step. The key is finding the right target.”
“What’s the fleet’s destination?”
“A star with planets about four light-years away—the closest star to the Trisolaran system.”
Wang was surprised. “The closest star to us is also about four lightyears away.”
“You?”
“The Earth.”

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INTERROGATOR: One last question, and also the most important: Until now, has Trisolaris sent only radio waves to the Earth?
YE: Almost true.
INTERROGATOR: Almost?
YE: The current Trisolaran civilization is capable of space travel at one-tenth the speed of light. This technology leap occurred a few decades ago in Earth years. Before that point, their maximum speed had hovered around one-thousandth the speed of light. The tiny probes that they sent to the Earth have not even completed one-hundredth of the journey between there and here.
INTERROGATOR: Then I have a question. If the Trisolaran Fleet that had been launched is capable of flight at one-tenth the speed of light, it should take only forty years to reach the solar system. So why do you say that it would take more than four hundred years?
YE: Here’s the thing. The Trisolaran Interstellar Fleet is composed of incredibly massive spaceships. Accelerating them is a slow process. One-tenth the speed of light is only their maximum speed, but they cannot cruise at this speed for long before decelerating as they approach the Earth. Also, the source of propulsion for the Trisolaran ships is matter-antimatter annihilation. In front of each ship is a large magnetic field shaped like a funnel to collect antimatter particles from space. This collection process is slow, and only after a long wait can it gather enough antimatter to allow the ship to accelerate for a brief period. Thus, the fleet’s acceleration occurs in spurts, interspersed by long periods of coasting to collect fuel. This is why the time it takes the Trisolaran Fleet to reach the solar system is ten times longer than the flight time of a small probe.

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“Princeps, given the frequency of the transmission, even the direction of the source cannot be ascertained with great accuracy. The fleet is only capable of cruising at one-hundredth the speed of light. Also, it only has enough power in reserve to perform one deceleration, making it impossible to conduct a wide-area search in that direction. If the distance to the target is unclear, the fleet will ultimately fall into the abyss of space.”

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The young woman raised the bright metal sphere before her with both hands, as though she were getting ready to start a gymnastics routine. Smiling, she said, “Officers, we hold in our hands three nuclear bombs, each with a yield of about one point five kilotons. Not too big,since we like small toys. This is the detonator.”

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The flashlights attached to the soldiers’ guns focused on the young woman holding the nuclear bomb. While she held the destructive power of 1.5 kilotons of TNT in her hands, she smiled brightly, as though enjoying applause and praise on a spotlit stage.

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