Chapter 4: I Am Merely an Enthusiast of Space Exploration

"I am merely an aerospace enthusiast," Lin Ran said indifferently.

"An aerospace enthusiast?" Haynes pondered to himself.

Haynes began to suspect that the man had been sent by China, but that couldn't be right. If he had been sent by China, how could he possibly have derived the J3, J4, and J5 terms? Even Haynes himself didn't know them.

"Since you claim that functionality outweighs precision at this stage, why do you think I am working on deriving the Newtonian gravitational perturbation correction formula?" Haynes felt he was losing control of the conversation and sought to regain the upper hand.

Lin Ran smiled. "Because you want to go to the moon."

If his graduation project hadn't been focused on the Apollo moon landing, and if he hadn't endured the darkness and trials of the void, Lin Ran would never have been able to clearly replicate the fragments of his memory and present them to this man as the cornerstone for establishing his roots in 1960s America.

"Your formula design uses spherical harmonics to decompose the Earth's irregularities, starting from the second term. The second term is the gravitational perturbation caused by the equatorial bulge. The third term accounts for the north-south asymmetry caused by the Earth's slight pear-like shape. The fourth term accounts for higher-order subtle irregularities. The fifth term is the key—it is the very foundation of your calculations."

Lin Ran paused. Haynes’s hand, holding his Americano, began to tremble; he didn't even notice the coffee dripping onto the table. "What is the fifth term?" he asked, his voice shaking.

"The fifth term is the gravitational pull of the sun and the moon. A satellite itself doesn't need to consider these, but if you intend to land on the moon, you must account for the influence of solar and lunar gravity. You must calculate the fifth term."

Haynes stood up and walked over to him, placing both hands on Lin Ran’s shoulders. Leaning in, he looked Lin Ran straight in the eye and asked, "Randolph, who exactly are you?"

Watching the shock on the white engineer's face, Lin Ran felt the thrill of a ghost from another time, tearing through the fabric of established history. If he hadn't known that the two timelines would not interfere with each other, he wouldn't have dared to do this.

Calculating the fifth term in advance wasn't a major issue for the moon landing project as a whole; in terms of overall progress, it wouldn't even speed things up significantly.

"Me? Didn't I tell you I'm just an aerospace enthusiast? Isn't it normal to be able to calculate these things?"

Lin Ran brushed Haynes’s hands off his shoulders. He felt the powerful force in the young man's arms, a strength that contradicted his appearance, which only deepened Haynes’s realization that this young man was extraordinary.

"Pen and paper," Lin Ran said.

Haynes rushed out of the private room, terrified that if he returned, this miraculous young man of Chinese descent would be gone. Panting, he returned with a pen and paper, and even an extra metal basin he had bought along the way.

"Here." Haynes handed the supplies to Lin Ran, feeling a wave of relief upon seeing that he was still there.

"Non-spherical gravitational perturbation of the Earth is not an obscure theory. Newton mentioned in his *Philosophiæ Naturalis Principia Mathematica* that the centrifugal force from the Earth's rotation causes an equatorial bulge, forming an oblate spheroid. Newton estimated the difference between the equatorial and polar radii at 27 kilometers. It wouldn't be strange for your deviation angle to be three degrees, would it? Furthermore, the year before last, Professor Desmond King-Hill detailed the long-term perturbation effects of the J2 term on near-Earth satellite orbits in his paper, *The Effect of the Earth's Oblateness on the Orbit of a Near Satellite*, providing quantitative formulas for the precession of the perigee and the rotation of the orbital plane. It is only natural that I could derive J3, J4, and J5 from the J2 term provided by Professor King-Hill."

As Lin Ran spoke, his hand moved, the metal pen tip dancing across the stationery as he wrote down derivation after derivation. It wasn't until a dozen pages were filled with dense, complex equations that the room finally fell silent.

Haynes took the papers, his mind reeling: "How on earth is any of this 'normal'?"

Although Ebenezer Haynes was not a household name in aerospace history, he was an absolute titan in his field—a man capable of manually calculating corrections for spacecraft orbital inclination due to Earth's oblateness. His margin of error in manual calculations was within five percent, and his methods had become the standard template for such problems within NASA.

"The fourth term here considers the density difference in the crust between the Hawaiian sea surface and the Mariana Trench."

"The J5 term here corresponds to the coupling effect of the Coriolis force and tides."

"I forgot to mention, if you want to further increase precision, the J3 term can actually account for gravitational distortion caused by geological anomalies in the Arctic Circle."

Haynes was mesmerized, and upon hearing the timely interpretations, he felt enlightened.

If this was someone sent by another country, he thought, wouldn't it be better if they sent more? No country would ever send a genius of this caliber just to do grunt work for another.

In his view, the J4 and J5 terms the man had calculated were far more rigorous than his own. The original tolerance for the moon landing's precision error was 100 kilometers; now, with this data, the orbital and landing point error would be reduced to within 20 kilometers.

However, Haynes was still not satisfied. He put the paper down and asked, "Randolph, then why does our theoretical calculation suggest the perigee precession of Explorer 1 should be 1 to 1.5 degrees, when in reality it is 3 degrees?"

Lin Ran tapped his fingers on the black walnut table in the rhythm of the Fibonacci sequence.

"Haynes, you missed a condition. Even in pure theoretical calculations, the perigee precession would not be 1 to 1.5 degrees per orbit. The fact that you got that result means you only considered the pure J2 term. If you account for the fifth term and the coupling effect of atmospheric drag, the theoretical prediction aligns closely with reality."

Lin Ran’s fingers tapped faster and faster on the tabletop. As his words ceased, so did his fingers, ending with thirteen rapid taps in a single second.

Haynes felt as if he could only hear the sound of the tapping and the man’s words; as they fused and entered his ears, they seemed to explode like fireworks.

"No! It's impossible! The coupling effect of atmospheric drag is a phenomenon we only observed after the launch of Explorer 1. The complexity of the interaction between non-spherical perturbation and atmospheric drag was only theoretically validated within NASA this year. We determined that we needed high-precision modeling in orbital mechanics to provide a mathematical foundation for improving subsequent orbital control algorithms. The atmospheric drag coupling effect hasn't been mentioned in any paper. This is NASA's latest achievement in orbital mechanics—no!"

Haynes grabbed the remaining half of his iced Americano and downed it in one gulp. "Randolph, this is absolutely impossible for an aerospace enthusiast to know."