Once We Lived in Nanjing

"Newton?" The voice on the other end was puzzled, "What is Newton?"

"Newton was a person from the UK, a great physicist," Bai Yang explained, "The equation F=G·(m₁m₂/r²) that your teacher wrote on the draft paper is the law of universal gravitation. Here, F represents gravitational force, G is the gravitational constant, the two m's are the masses of celestial bodies, and r is the distance. It means that the force of gravity between two celestial bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, OVER."

"Oh..."

The girl nodded with a half-understanding.

It doesn't matter if she doesn't understand what the monk chants as long as she keeps ringing the bell; nodding is enough.

"I deduce that your teacher was studying the relationship between the Black Moon and Earth, which is why these numbers and formulas were written on the draft paper," Bai Yang said, "It's just that you didn't understand it at the time, OVER."

"I still don't understand it now."

"It doesn't matter if you don't understand, I do!" Bai Yang was very confident.

Bai Yang's confidence was well-grounded as he was a high school senior soon to face the college entrance examination.

At this moment, he was at the stage in his life where his knowledge was the broadest, his thinking skills the strongest, knowledgeable about astronomy and geography, and well-informed on history and politics.

"Let's sort out these data, Miss. Do you believe that with just the 1200 kilometers data, I could deduce the entire shape of the Black Moon?" Bai Yang claimed, "OVER."

The girl paused for a moment, "Really?"

"Really." Bai Yang nodded, "Miss, let's first look at the 1200 kilometers. Your teacher wrote this number on the 'Journey to the West' draft, we assume it to be the diameter of the Black Moon, right?"

Ban Xia nodded.

On this page of the 'Journey to the West' draft, there were two numbers and two circles, the numbers being 1200 and 3476, labeled beside the circles. Ban Xia and Bai Yang reached a consensus in interpreting the draft, considering these circles as the White Moon and the Black Moon, with 3476 being the diameter of the White Moon, and thus 1200 should be the diameter of the Black Moon.

"In your eyes, are the Black Moon and White Moon the same size?" Bai Yang continued to ask, "Is that so, Miss? OVER."

"Yes, they look to be the same size," Ban Xia nodded.

"Then I can figure out how far the Black Moon is from you..."

Bai Yang opened the calculator, and hurriedly began jotting down figures on a piece of paper.

He had never been this diligent in his whole life; doing math and physics during a power outage, his mom said if he usually studied with such enthusiasm, he wouldn't need to kowtow all the way from Zijin Mountain to Xuanwu Lake to get into Nanjing University.

"The Moon's radius is 1737 kilometers."

"The distance from the Earth to the Moon is 380,000 kilometers."

"The tangent should be 0.0045718..."

Half a minute later, Bai Yang had the answer.

"Miss, the Black Moon is approximately 131,239 kilometers away from you, OVER."

Ban Xia was astounded.

"How did you come to know that?"

"Radian measure, Miss, it's a simple calculation. The White Moon and the Black Moon appear the same size to you, so when you look at them, their angular diameters are the same," Bai Yang explained, "The White Moon is 380,000 kilometers from you with a diameter of 3476 kilometers, hence the Black Moon with a diameter of 1200 kilometers, using trigonometric functions, should be about 130,000 kilometers away from you, OVER."

"That's amazing."

Even though Ban Xia didn't understand, she thought it was amazing.

"Let's continue with the calculations. Now that we know the distance between the Black Moon and the Earth's surface, we can calculate the Black Moon's orbital period, the period it takes to revolve around Earth," Bai Yang said rather proudly, the admiration from a beautiful girl was much more satisfying than praise from a bald physics teacher. He began listing formulas on the draft paper, and with momentum worked on the calculation, "Including the Earth's radius, r should be 137,610 kilometers, G is the gravitational constant, we take 6.67×10^(-11) Nm²/kg... With the formula T=√(4π²r³/GM), therefore T should be..."

Bai Yang held the microphone in his hand, calculating and murmuring as he went along, in the dead silence of the late-night room, with only the girl twenty years his junior listening attentively.

Digits and formulae flowed from the tip of the boy's pen, forming little streams on the white paper.

Bai Yang had lived for eighteen years and studied physics for five, now for the first time, the dragon-slaying skills that could reach the heavens to capture the moon and dive the oceans to snatch turtles came into practical use.

It was only when he really put them into use, that Bai Yang realized he had mastered such a powerful tool—the laws governing the universe's mechanics, the underlying code of the cosmos online. Every high school student once constructed the grand edifice of classical physics in their minds, yet few ever truly utilized it, allowing it to erode and collapse with time.

"16 days!"

"Miss, the orbit period of the Black Moon is 16 days; it orbits Earth once every sixteen days, OVER."

"Incredible! It's magical, BG4MXH, how did you do that?"

Ban Xia couldn't believe it; she felt that BG4MXH was performing magic.

He had never seen the Black Moon, so how could he know how long it took for the Black Moon to make an orbit?

"I didn't do it alone; behind me stands Newton, Kepler, and all the physicists throughout human history." Bai Yang said, "Also my physics teacher, who taught me all the top wisdom contained in the most brilliant minds in history."

"Then your physics teacher is amazing!"

"On behalf of our physics teacher, thank you, Miss. Your teacher must have calculated all these things back then too," Bai Yang said. "Let's continue with our deductions. We now know that the Black Moon is 130,000 kilometers away from us, but I can't understand why it orbits at a distance of 130,000 kilometers from Earth?"

Ban Xia was dumbfounded; she didn't understand the significance of the question.

Why orbit at a distance of 130,000 kilometers from Earth?

The Black Moon is free to stay there if it wishes, right?

How could she possibly know why?

"Miss, Big Eye came from the Black Moon, right? So why doesn't the Black Moon come closer, to make it easier for Big Eye to descend?" Bai Yang raised a question that Ban Xia had never considered. "130,000 kilometers, eh, that's not a close distance. It takes a long time even to fly. Why doesn't it come a bit closer? OVER."

"Um… maybe there is some special reason?"

The girl pondered.

"There's always a reason behind any phenomenon." Bai Yang said, "Miss, let's hypothesize this: the reason it can't get closer is that it can't get any closer. The reason it stays in an orbit 130,000 kilometers away is that it can only stay at an orbit at a distance of 130,000 kilometers, OVER."

"Why?" Ban Xia asked, "Why can it only stay there?"

"Because a force is restricting it," Bai Yang answered. "A force that no one can resist is restraining it, OVER."

"What force?"

"Gravitation, Miss, it's universal gravitation." Bai Yang said, "The only force in the universe that cannot be united or controlled, it restrains the Black Moon. If Black Moon gets too close, it will be torn apart by Earth's massive gravitational pull. 130,000 kilometers is within its safe range, it cannot cross this red line; anyone who crosses the threshold shall be utterly shattered... This red line is called the Roche limit, OVER."

"Assuming that 130,000 kilometers is the Roche Limit between Earth and the Black Moon, we can derive the density of the Black Moon… Let me find the formula for the Roche Limit! There's a Roche limit for fluids and a rigid body Roche limit..." Bai Yang frantically opened his smartphone to search on Baidu and pulled out a blank sheet of draft paper, "I've found it! Let me calculate, the formula is d=2.423R(ρ₁/ρ₂)^(1/3), and the average density of Earth is 5507.85kg/m³... so under the fluid Roche limit, the average density of the Black Moon is 7.83kg/m³, and under the rigid body Roche limit, it's 1.09kg/m³."

"Miss, the average density of the Black Moon is between 1.09kg/m³ and 7.83kg/m³."

Ban Xia was a bit flabbergasted, not understanding what these numbers meant.

What is the concept of this density?

The density of the air we breathe in daily life is 1.3kg/m³. The density of nitrogen is 1.26kg/m³, the density of oxygen is 1.46kg/m³, and the denser gas, radon, is 9.73kg/m³, which means the maximum density of the Black Moon is even less than that of radon.

"What does this mean?" Ban Xia asked.

"It means that either the Black Moon is a gaseous satellite, actually a mass of gas," Bai Yang paused, "or it has a huge cavity inside, it's hollow."