The Iron Law of Occultism
Inside the observatory.
When Professor Bryce saw Li Mo arrive, he immediately stood and said with a smile, "Look who's here! Isn't this Mr. Li Mo, the mathematical genius Puxiu Academy sees only once in a century, who put an end to a century and a half of ambiguity about limits?"
Li Mo scratched his head. "Good morning, Professor."
Professor Bryce led him to the table and said:
"Mr. Li Mo, congratulations on the tremendous success of your mathematics salon! Here are the orbital data for the two moons that I recorded. I've organized them all as you instructed. Come, take a look!"
Thoroughly embarrassed, Li Mo could only say, "Professor, please don't..."
"Hahahaha!"
Professor Bryce laughed heartily.
The old man had discovered that he could embarrass Li Mo by turning their positions upside down and flattering him to excess, and found it immensely amusing.
He liked to tease Li Mo from time to time.
Once he'd had his fill of laughter, Professor Bryce got down to business. "Come on. I've compiled all the observatory's data on the red and white moons over the ten years from 1851 to 1861. That should keep you busy for a while. Don't thank me."
"Thank you, Professor."
Li Mo sat down at the table.
He had observed the two moons with Anna before.
At the time, there had been too little data to make any meaningful research progress.
But this time was different.
Li Mo interlaced his hands, silently spoke a word, and entered a state of Focus.
The world fell silent.
Time to work.
Observe.
Record.
Calculate.
Summarize.
The Silver Moon's maximum horizontal parallax averaged fifty-seven arcminutes and two arcseconds.
Working backward from that, its average distance from the planet beneath his feet was approximately 384,400 kilometers.
He extracted the Silver Moon's orbital data directly from the ten-year ephemeris:
A sidereal month of 27.32 days.
A synodic month of 29.53 days.
Combining that with changes in apparent diameter yielded an orbital eccentricity of 0.0549.
He then plugged the data into Kepler's third law and Newton's law of universal gravitation to cross-check them.
No problems. Everything was consistent.
Li Mo nodded.
There was essentially no difference between the moons of the two worlds.
Their elliptical orbital precession rates and nodal regression periods were identical as well.
This also fully confirmed the conclusion he had reached earlier when calculating the tides:
The ocean tides at Mendel Port and throughout the kingdom were governed jointly by the gravitational pull of the Silver Moon and the sun.
Then what about the Red Moon?
He turned the ephemeris to the volume containing the Red Moon observation records.
Li Mo frowned as soon as he saw the first set of data.
According to the horizontal parallax records in the ephemeris,
the Red Moon's parallax angle was only about twelve arcminutes.
That put its orbital altitude at approximately 1.8 million kilometers from the planet's surface.
Nearly five times farther away than the Silver Moon.
According to Kepler's third law, for two satellites in the gravitational field of the same central body, the cubes of their orbital semimajor axes were proportional to the squares of their orbital periods.
Since the Red Moon was 4.7 times as far away as the Silver Moon, its orbital period should have been more than ten times as long.
In other words, it should have taken at least 270-odd days to complete one orbit around the planet.
Yet the Red Moon's orbital period as recorded in the ephemeris was a mere thirty-three days!
Completing an orbit with a radius of 1.8 million kilometers in thirty-three days meant that the Red Moon's linear velocity was frighteningly high.
If the planet beneath his feet had only the mass of Earth,
it couldn't possibly hold on to a celestial body moving that fast.
The Red Moon should have long since flown off along a tangent!
Li Mo moved on to check the three-body perturbation terms.
In a normal celestial system, when the Red Moon and the Silver Moon reached the same ecliptic longitude-that is, when the two moons were in conjunction-their mutual gravitational pull would inevitably cause slight deflections in each other's orbits, a phenomenon known in astronomy as periodic perturbation.
Li Mo picked out the Silver Moon's coordinates before and after twenty-three conjunctions of the red and white moons from the ten-year ephemeris. He wrote out a Fourier series expansion, attempting to isolate the amplitude of the gravitational perturbation the Red Moon caused in the Silver Moon.
He filled three whole pages of scratch paper.
When the last residual term had been eliminated, the perturbation coefficient at the bottom of the scratch paper was:
Zero.
In other words, no matter how close the Red Moon came to the Silver Moon, the Silver Moon's orbit showed not the slightest deflection.
The enormous Red Moon hanging high in the night sky did not exist as far as the gravitational field was concerned. Mathematically, its gravitational mass was exactly zero.
"No mass, and it doesn't obey Kepler's laws..."
Li Mo extracted all the data on the Red Moon's changes in declination and apparent magnitude over the ten years.
He plotted and connected the points on graph paper, then performed a spectral analysis.
As the line extended segment by segment, he discovered a mathematical pattern.
The Red Moon's orbital inclination was not fixed; its trajectory oscillated in a periodic sine wave.
If he combined its rate of change in declination and the other data in his calculations,
he found that they were all locked to one constant fundamental frequency and its integer-multiple harmonics.
Over ten years,
it had completed 110 orbital cycles.
Yet that frequency had not changed at all.
In plain language,
the Red Moon... was rather like a massive oscillator fixed in an orbit on the celestial sphere, continuously broadcasting a signal according to a precise mathematical cycle.
Li Mo exited his state of Focus and let out a long breath.
Just then, a noise came from beside him.
Li Mo turned and saw that the sound was coming from an artifact in front of Professor Bryce.
The professor looked miserable and kept sighing.
Li Mo got up and went over. "Professor, what's wrong?"
Professor Bryce sighed. "This is the Star-Track Resonance Time Calibration Instrument, a Mystical Artifact. I accidentally activated the thing just now. Why is it so sensitive?"
While studying in Wellington, Li Mo had learned an iron law:
Once an artifact's ritual began, it was like spilled water that could not be gathered up.
People only knew how to awaken it; no one had ever known how to shut it down safely halfway through.
If anyone dared smash it by brute force halfway through, the uncontrolled energy would explode on the spot... That would be terrible.
Li Mo asked, "How long will it keep making that noise?"
The professor said, pained, "Forty-eight hours... The worst part is, it'll burn through a whole ounce of the Star Silver Powder loaded into it beforehand! That's an ounce of Star Silver Powder, all wasted for nothing!"
The more Professor Bryce spoke, the more his heart ached. He even walked twice around the table.
At that moment, however, Li Mo recalled the experiment he had conducted at home.
Wrapping the firestone in linseed oil.
When the silver threads extending from the firestone's surface had come into contact with that medium, their connection to the outside world had weakened.
Li Mo's interest was instantly piqued.
He said with great interest, "Professor, let me study it."
Professor Bryce asked, "What are you going to study?"
Li Mo said, "I want to see if I can stop the ritual..."
Professor Bryce said, "Huh?"
Without further ado, Li Mo took a deep breath and entered a state of Focus.
Dozens of silver threads immediately appeared above the Star-Track Resonance Time Calibration Instrument.
Li Mo narrowed his eyes slightly and carefully observed the state of the threads.
A larger Mystical Artifact was indeed more satisfying to observe than a firestone.
Soon,
he really did notice something different.
The threads on the artifact were trembling.
After observing them for a while, he could tell:
The threads were shaking in a regular pattern.
He silently counted the cycles and intervals...
Li Mo suddenly froze.
Then,
he strode over to the table and snatched up the scratch paper.
Professor Bryce asked blankly, "What's wrong?"
Li Mo answered absentmindedly, then carried the scratch paper back to the display stand, checking the numbers on the paper against the rhythm at which the silver threads absorbed energy...
After repeated checks,
Li Mo gradually tightened his grip on the scratch paper.
That was right.
The trembling of the threads and the Red Moon's natural harmonic frequency he had just calculated-
they almost perfectly matched!
He had long been pondering a question:
Where exactly did the silver threads lead? And where were they drawing their energy from?
He had naturally made some guesses, but those had only been guesses in the end.
Now, through science and mathematics, he had actually connected the two!
He seemed to have... found the first key to entering the black box of occultism...
He continued thinking.
Since the essence of the threads' energy absorption was resonance at the same frequency,
what if he used that frequency to introduce an opposing half-wave phase and disrupt the conditions for resonance?
Li Mo's eyes lit up, and he grew excited all over!
He spoke rapidly:
"Professor! Help me find a vernier caliper, a brass probe, and a bottle of linseed oil! Quick!"