Chapter 5: I am just an aerospace enthusiast

"I am just an aerospace enthusiast," Lin Ran said lightly.

"An aerospace enthusiast?" Haines pondered inwardly.

Haines began to suspect that the other party was sent by Cultural Huaguo, but that shouldn't be right; if sent by Cultural Huaguo, how could he write out all the J3, J4, and J5 terms.

You have to know that even he himself didn't know J4 and J5.

"Since you say that function is greater than precision now, why do you think I want to deduce the Newton gravitational perturbation correction formula?" Haines felt that the initiative of the conversation was being lost, and he wanted to regain his ground.

Lin Ran laughed: "Because you want to go to the moon."

If his graduation project hadn't been the Apollo moon landing, and if he hadn't gone through the torture and tempering of darkness in the void, Lin Ran really wouldn't have been able to clearly reproduce the fragments in his memory and bring them to the other party, becoming the key to his rooting in America in the 60s.

"Your formula design is to decompose the Earth's deformity through spherical harmonic functions, starting from the second term.

The second term is the gravitational perturbation caused by the equatorial bulge.

The third term is the north-south asymmetry caused by the Earth being slightly pear-shaped.

The fourth term is the subtle unevenness of higher order.

The fifth term is the key, and it is the root of your calculation."

Lin Ran paused, and Haines's hand holding the American coffee was shaking. Coffee dripped onto the table, but he didn't notice it at all. He said with a trembling voice: "What is the fifth term?"

"The fifth term is the gravitational pull of the sun and the moon. The satellite itself doesn't need to consider these at all, but if you want to land on the moon, you must estimate the impact of the sun and moon's gravity.

You must calculate the fifth term."

Haines got up and walked to his side, put his hands on Lin Ran's shoulders, leaned in, and looked directly at Lin Ran:

"Randolph, who on earth are you!"

Looking at the horrified expression of the white engineer in front of him, Lin Ran had the thrill of being a ghost from time and space, tearing apart established history.

If he didn't know that the two time-spaces would not interfere with each other, Lin Ran really wouldn't dare to do this.

However, calculating the fifth term in advance was not a big deal for the entire moon landing project, and it couldn't even speed up the progress much from the perspective of overall progress.

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

Lin Ran pushed away Haines's hand on his shoulder, feeling the powerful thrust from the young white man's arm that was seriously inconsistent with his appearance, which made Haines deepen his understanding of the extraordinary nature of the young man in front of him.

"Pen and paper," Lin Ran said.

Haines hurriedly rushed out of the private room, fearing that he wouldn't see this magical Asian young man when he came back.

He brought back pen and paper panting, and he even bought a metal basin.

"Here," Haines handed the pen and paper to Lin Ran, and seeing that Lin Ran was still there, he breathed a sigh of relief.

"Earth's non-spherical gravitational perturbation is not a profound theory.

Newton mentioned in his *Philosophical Principles of Natural Philosophy* that the centrifugal force caused by the Earth's rotation would cause the equator to bulge, thereby forming an oblate spheroid. Newton could estimate that the difference between the equatorial and polar radii was 27 kilometers. I don't think it's strange that your deviation angle is 3 degrees, right?

In addition, Professor Desmond King-Hele detailed the long-term perturbation impact of the J2 term on the orbit of near-Earth satellites in his paper *The Effect of the Earth's Oblateness on the Orbit of a Near Satellite* the year before last, and gave a quantitative formula for the precession of the perigee and the rotation of the orbital plane.

It's normal for me to deduce J3, J4, and J5 from the J2 term given by Professor King-Hele, right?"

Lin Ran was talking while controlling the metal pen tip to write constantly on the letterhead. It wasn't until a full ten or more sheets of paper were filled with dense derivation formulas that the whole room fell into silence.

Haines took the derivation formula, and his heart was thinking: "Where on earth is this normal?"

Although Ebenezer Haines was unknown in the history of aerospace, he was also an out-and-out top big shot, a ruthless person who could manually calculate the correction value of the orbital inclination of a spacecraft due to the Earth's oblateness.

The error rate of his manual calculation was even within 5%, and his calculation steps even became the standard template for manual calculations of similar problems within NASA.

"The fourth term here considers the crustal density difference formed by the Hawaiian sea surface and the Mariana Trench."

"The J5 term here corresponds to the Coriolis force-tide coupling effect."

"Forgot to tell you, if you want to further pursue precision, the J3 term can actually take into account the gravitational distortion caused by geological anomalies in the Arctic Circle."

Haines was fascinated, and after hearing the timely interpretation, he felt a sense of enlightenment.

If this could be someone sent by another country, wouldn't it be better to send more? Haines thought so.

No matter which country it was, it was impossible to send such a top-tier genius to work for you.

In his view, the J4 and J5 terms calculated by the other party were much more rigorous than what he calculated himself. The original tolerance for the moon landing precision error was 100 kilometers, but now this orbit and landing point error would be shortened to within 20 kilometers.

However, Haines was still not satisfied. After putting down the paper, he asked:

"Randolph, so why is our theoretical calculation that the perigee precession of Explorer 1 should be 1 to 1.5 degrees, but in fact it is 3 degrees?"

Lin Ran tapped on the black walnut dining table with his finger according to the frequency of the Fibonacci sequence:

"Haines, you missed a condition. Even if it is a pure theoretical calculation, the perigee precession will not be 1 to 1.5 degrees per lap. Getting this result means your calculation only considered the pure J2 term.

And if you consider the fifth term, as well as the coupling effect of atmospheric drag, the theoretical calculation will not be much different from the actual situation."

Lin Ran's fingertips tapped on the desktop faster and faster. As the words stopped, his fingers also stopped with the words. Finally, he tapped 13 times in just one second.

Haines felt that he could only hear the tapping of the other party's fingers and the other party's words. After the two combined and drilled into his ears, they exploded instantly like fireworks.

"No! 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 demonstrated within NASA this year, and it was determined to provide a mathematical basis for the improvement of subsequent orbital control algorithms through high-precision modeling of orbital mechanics.

The atmospheric drag coupling effect is not mentioned in any paper.

This is NASA's latest achievement in orbital mechanics, no!"

Haines fiercely picked up the remaining half of the iced Americano on the table and drank it in one gulp. "Randolph, this is absolutely not something an aerospace enthusiast could know." ===== CHAPTER 6 =====