Technology invades the modern world

Chapter 4 I'm Just a Space Enthusiast
"I'm just a space enthusiast." Lin Ran said lightly.

"A space enthusiast?" Haynes thought to himself.

Haynes began to suspect that the other party was sent by China. But that shouldn't be the case. If someone was sent by China, how could he possibly write out all the J3, J4 and J5 items?

You have to know about J4 and J5, he himself doesn’t know.

"Since you said that function is more important than accuracy now, then why do you think I should derive Newton's gravitational perturbation correction formula?" Haynes felt that he was losing the initiative in the conversation, and he wanted to get back at it.

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

If his graduation project had not been about the Apollo moon landing, and if he had not experienced the torture and trials of darkness in the void, Lin Ran really would not have been able to clearly reproduce the fragments of his memory and bring them to the other party, which would have become the key to his taking root in America in the 60s.

"Your formula is designed to decompose the Earth's deformity through spherical harmonics, starting with the second term.

The second is the gravitational disturbance caused by the equatorial bulge.

The third is the north-south asymmetry caused by the Earth's slightly pear-shaped shape.

The fourth item is higher-order subtle bumps and depressions.

The fifth item is the key and the basis of your calculation."

Lin Ran paused. Haynes's hand was shaking as he held the Americano. He didn't even notice it dripping onto the table. His voice trembled as he asked, "What's the fifth item?"

"The fifth factor is the pull of the sun and moon. Satellites don't need to consider this at all, but if you want to land on the moon, you must estimate the effects of the sun and moon's gravity.

The fifth term must be calculated."

Haynes stood up and walked to his side, put his hands on Lin Ran's shoulders, and after getting closer, he looked directly at Lin Ran and asked:

"Randolph, who the hell are you?"

Looking at the horrified expression of the white engineer in front of him, Lin Ran felt as if he were a ghost from time and space, tearing up the established history.

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

However, calculating the fifth item in advance is not a big deal for the entire moon landing project. Even from the perspective of overall progress, it will not speed up the progress much.

"Me? Didn't I tell you I'm just a space enthusiast? Isn't it normal for me to come up with these calculations?"

Lin Ran used his hand to push away the hand that Haynes had placed on his shoulder, feeling the powerful push from the young man's arm that was seriously inconsistent with his appearance. This made Haynes realize even more deeply that the young man in front of him was unusual.

"Pen and paper." Lin Ran said.

Haynes rushed out of the private room, fearing that he would not be able to see this amazing young Chinese man when he returned.

He brought pen and paper breathlessly, and even bought an extra metal washbasin.

"Yes." Haynes handed the pen and paper to Lin Ran. Seeing that Lin Ran was still there, he felt relieved.

"The gravitational perturbations of the Earth's non-spherical shape are not some profound theory.

Newton mentioned in his Mathematical Principles of Natural Philosophy that the centrifugal force caused by Earth's rotation causes the equator to bulge, forming an oblate spheroid. Newton was able to estimate the difference between the equatorial and polar radii to be 27 kilometers. I guess your deviation of 3 degrees is not surprising. Furthermore, two years ago, Professor Desmond Kinghill, in his paper "The Effect of the Earth's Oblateness on the Orbit of a Near Satellite," detailed the long-term perturbation effect of the J2 term on the orbits of near-Earth satellites and provided quantitative formulas for perigee precession and orbital plane rotation.

It's not surprising that I can deduce J2, J3, and J4 from Professor Kinghill's J5 term.

Lin Ran was talking while controlling the metal pen tip in his hand to write on the letter paper. Only after more than ten pages were filled with derivation formulas did the whole room fall into silence.

Haynes took over the derivation and thought to himself, "What's so normal about this?"

Although Ebenezer Haynes is not well-known in the history of aerospace, he is an absolute top expert who can manually calculate the correction value of the Earth's oblateness for the inclination angle of the spacecraft's orbit.

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

"The fourth term considered here is the difference in crustal density between the Hawaiian Sea and the Mariana Trench."

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

"I forgot to mention that if we want to pursue even greater precision, the J3 term can actually take into account the gravitational distortion caused by geological anomalies in the Arctic Circle."

Haynes was fascinated by the book, and after hearing the timely interpretation, he felt like he had been enlightened.

If these people could be sent by other countries, wouldn't it be better to send more of them quickly? Haynes thought.

No matter which country it is, it is impossible to send such top talents to work for you.

In his opinion, the J4 and J5 items calculated by the other party were much more meticulous than his own calculations. The original accuracy error tolerance for the moon landing was 100 kilometers, but now the orbit and landing point error will be shortened to within 20 kilometers.

But Haines was not satisfied. He put the paper down and asked:
"Randolph, so why is it that our theoretical calculations say Explorer 1's perigee precession should be 1.5 to 3 degrees, but it's actually degrees?"

Lin Ran tapped his fingers on the black walnut dining table in the order of the Fibonacci sequence:

"Haines, you missed a condition. Even if it's a purely theoretical calculation, the precession of perigee wouldn't be 1 to 1.5 degrees per revolution. This result shows that your calculation only considered the pure J2 term.

If the fifth factor and the coupling effect of atmospheric drag are taken into account, the theoretical calculations are not much different from the actual situation."

Lin Ran's fingertips tapped on the table faster and faster. When he stopped talking, his fingers stopped with him. The last time, he tapped 13 times in just one second.

Haynes felt that he could only hear the other person's finger tapping and the other person's words. The combination of the two entered his ears and 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 perturbations and atmospheric drag was only theoretically demonstrated within NASA this year. It was determined that high-precision modeling of orbital mechanics would provide a mathematical basis for the subsequent improvement of orbital control algorithms.

The atmospheric drag coupling effect is not mentioned in any of the papers.

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

Haynes suddenly picked up the half-empty iced Americano on the table and drank it all in one gulp. "Randolph, this is absolutely impossible for a space enthusiast to know."

(End of this chapter)