Chapter 4: I’m Just An Aerospace Enthusiast
“I’m just an aerospace enthusiast.” Lin Ran said faintly.
“Aerospace enthusiast?” Haines thought to himself.
Haines began to suspect that the other was sent by China, but that shouldn’t be the case; if China sent him, how could he possibly write out all the J3, J4, and J5 terms.
You know, he himself didn’t even know J4 and J5.
“Since you say that function now matters more than precision, then why do you think I derived the gravitational perturbation correction formula?” Haines felt the initiative in the conversation slipping away, and he wanted to regain the upper hand.
Lin Ran smiled and said: “Because you want to go to the Moon.”
If it weren’t for choosing the Apollo Moon Landing for his graduation design, and if it weren’t for the torment and trials in the darkness of the void, Lin Ran really couldn’t have clearly replicated the fragments from his memory and brought them in front of the other, becoming the key to his rooting in America of the 1960s.
“Your formula design decomposes Earth’s irregularity using spherical harmonics, starting from the second term.
The second term is the gravitational perturbation from the equatorial bulge.
The third term is the north-south asymmetry caused by Earth being slightly pear-shaped.
The fourth term is higher-order subtle undulations.
The fifth term is the key, the root of your calculations.”
Lin Ran paused in his words, Haines’s hand holding the American-style coffee was shaking, the coffee dripping on the table without him noticing at all, his voice trembling as he said: “What is the fifth term?”
“The fifth term is the traction from the Sun and Moon; the satellite itself doesn’t need to consider these at all, but if you want to go to the Moon, you must estimate the influence from the Sun and Moon’s gravity.
You must calculate the fifth term.”
Haines stood up and walked to his side, placing both hands on Lin Ran’s shoulders, leaning in close and staring straight at Lin Ran as he asked:
“Randolph, who exactly are you!”
Looking at the horrified expression on the white person engineer’s face before him, Lin Ran felt a thrill like he was a ghost from spacetime tearing apart established history.
If he didn’t know that the two spacetimes wouldn’t interfere with each other, Lin Ran really wouldn’t dare to do this.
However, calculating the fifth term ahead of time wasn’t a big deal for the entire moon landing project; even from the perspective of overall progress, it wouldn’t speed things up by much.
“Me? Didn’t I tell you I’m just an aerospace enthusiast? Isn’t it normal to calculate these?”
Lin Ran used his hand to brush away Haines’s hands on his shoulders, feeling the powerful thrust transmitted from the young man’s arm in front of him, which seriously didn’t match his appearance; this deepened Haines’s recognition once again that the young man before him was no ordinary person.
“Pen and paper.” Lin Ran said.
Haines hurriedly rushed out of the room, afraid that when he returned, he wouldn’t see this miraculous young man of Chinese descent.
Panting, he brought pen and paper, and even bought an extra metal washbasin.
“Here.” Haines handed the pen and paper to Lin Ran, seeing that Lin Ran was still there, and breathed a sigh of relief inwardly.
“Non-spherical gravitational perturbation isn’t some profound theory.
Newton mentioned in his Mathematical Principles of Natural Philosophy that Earth’s rotation causes centrifugal force leading to equatorial bulge, forming an oblate spheroid; Newton could estimate the gap between equatorial and polar radii at 27 kilometers. I guess your deviation angle of 3 degrees isn’t strange, right?
Additionally, two years ago, Professor Desmond King-Hele detailed in his paper ‘The Effect of the Earth’s Oblateness on the Orbit of a Near Satellite’ the long-term perturbation effects of the J2 term on near-Earth satellite orbits, providing quantitative formulas for perigee precession and orbital plane rotation.
It’s also normal for me to derive J3, J4, and J5 from the J2 term given by Professor King-Hele.”
Lin Ran was talking with his mouth while controlling the metal pen tip to continuously write on the letter paper with his hand, until a full ten or so sheets were densely filled with derivation formulas, and only then did the entire room fall silent.
Haines took the derivation formula, thinking inwardly: “Where exactly is this normal?”
Although Ebenezer Haines is unknown in aerospace history, he is undoubtedly a top-tier expert, a ruthless person who can manually calculate the orbital inclination correction value for spaceship orbits due to Earth’s oblateness.
His manual calculation error rate is even within 5%, and his calculation steps became the standard template for similar problems internally at NASA.
“The fourth term here considers the crustal density difference formed by the Hawaii sea surface and the Mariana Trench.”
“The J5 term here corresponds to the Coriolis force-tide coupling effect.”
“I forgot to tell you, if you want to pursue further precision, the J3 term can actually include the gravitational distortion caused by geological anomalies in the Arctic Circle.”
Haines was entranced as he read, and upon hearing the timely interpretation, he felt a sense of enlightenment.
If this were someone sent from another country, wouldn’t it be good to send more over quickly? Haines thought to himself.
No country would send such a top-tier genius to work for you.
In his view, the J4 and J5 terms calculated by the other were far more meticulous than his own; originally, the precision error tolerance for moon landing was 100 kilometers, but now the orbit and landing point error would shorten to within 20 kilometers.
However, Haines was still not satisfied; he put down the paper and asked:
“Randolph, so why is it that in our theoretical calculations, Explorer 1’s perigee precession should be 1 to 1.5 degrees, but in reality it’s 3 degrees?”
Lin Ran tapped his fingers on the black walnut wood dining table according to the frequency of the Fibonacci sequence:
“Haines, you missed a condition; even in pure theoretical calculation, the perigee precession wouldn’t be 1 to 1.5 degrees per orbit. That it is this result means your calculations only considered the pure J2 term.
But if you consider the fifth term, as well as the atmospheric drag coupling effect, the theoretical calculation matches reality with little error.”
Lin Ran’s fingertips tapped faster and faster on the tabletop, stopping along with his words; for the last tap, he struck 13 times in a short second.
Haines felt that now he could only hear the tapping of the other’s fingers and the other’s words; once these two combined and drilled into his ears, they exploded like fireworks.
“No! Impossible!
The atmospheric drag coupling effect was a phenomenon we only observed after Explorer 1’s launch.
The complexity of non-spherical perturbation interacting with atmospheric drag was only theoretically demonstrated internally at NASA this year, confirming the need for high-precision orbital mechanics modeling to provide a mathematical foundation for improvements in subsequent orbit control algorithms.
The atmospheric drag coupling effect isn’t mentioned in any paper.
This is NASA’s latest achievement in orbital mechanics, no!”
Haines suddenly grabbed the half-remaining iced American-style coffee on the table and downed it in one gulp. “Randolph, this absolutely cannot be something an aerospace enthusiast would know.”
