Argument of Periapsis

by Anjou

Rating: everyone
Tags: Princess Celestia, Slice of Life, Princess Luna, My Little Pony: Friendship is Magic
Length: 2110

Celestia has a long list of things she is good at. However, neither math nor science are on that list. Unfortunately the sun only obeys math and science. It’s time for her to turn to Luna for help.

As keepers of celestial bodies, the two royal sisters must have thorough knowledge of orbital mechanics. Celestia has studied many things, but unfortunately those things don’t include math and physics. This makes managing an object that obeys only the laws of math and physics rather difficult.

Celestia is struggling with her astrodynamics assignment, when Luna comes in. She finds that she has trouble with more than just her assignment.

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Published 2014-11-24 05:40:03 UTC
Last updated 2014-11-24 05:40:03 UTC

1: Sister! The True Anomaly is Most Anomalous!

There was a lonely horseshoe drawn on the parchment. The black ink had been set into the fine surface many hours ago. Celestia stared at her writing intently, trying to decipher whatever secrets it held. Her mother once said that the horseshoe held greater meaning, but it was entirely lost to Celestia. She vaguely remembered seeing it in one lecture or another a few days back. Unfortunately, every detail involving a circle or an angle simply faded away. She tentatively wrote an equals sign beside the horseshoe to give it some company.

At a loss for how to proceed, Celestia instead reflected upon recent events. The last unicorn to touch the sun and the moon had passed away some time ago, and his funeral was just this past week. It was a small, solemn affair; the final yawn of an ancient order that shall never again awaken.

She and her sister had taken on the task of moving the sun and the moon, respectively, several years prior. Just a century ago, a single pony moving the sun would have been unfathomable. Anyone claiming such nonsense would have been exiled for insanity. And in just another century or two, it would become unthinkable that ponies once had to sacrifice their lives for such a task.

She wondered how many individuals were lost to the endeavor. There was so much potential wasted on the motion of the heavens. Those ponies could have lead full lives; they could have been doctors, or teachers, or even bakers—

Celestia’s stomach growled. While she was not the best at keeping track of time, her stomach always knew it to the exact second. And her stomach told her that it was precisely noon, or more descriptively, ‘cake time’. Celestia stood to follow the sublime scent drifting up the stairs. But before she could reach the doors, her ears caught a cacophony of metal on marble that only her sister could produce.

“Tia! Tia! The crossing of the meridian is late!” Luna shouted while charging in. She collided directly with Celestia’s chest, but somehow managed to maintain the volume of her voice despite being embedded in fur.
“Tis late! You must rectify this issue! Posthaste!”

Celestia held a blank expression as Luna slowly backed away. She blinked. And then she blinked again. Luna spoke up once she realized none of her words made it through to her sister.

“Tis noon!” she declared, with a shimmer of indignation in her eyes.

Celestia’s stomach growled in emphatic agreement.
“Why yes, it appears to be so.”

“The sun has not yet crossed the meridian!”

“It… appears to not have?” Celestia tilted her head out of confusion.

“It should have! The sun must reach zenith at noon! It must cross the meridian! ‘Tis an hour slow!”

“Oh, yes. The sun should be at its peak. We can remedy that immediately.”
Celestia smiled a knowing smile. She had been practicing that particular expression recently, and using it in exact opposition to her current emotions would be a perfect test.
“Come, dear sister, we may fix this together. And afterwards, we may partake in cake.”

Suddenly, Celestia found her sister’s scrunched face very close to her own. Luna’s brow was deeply furrowed in examination, and Celestia worried that her bluff had failed. The silence held for some moments, but the smaller alicorn finally backed down.

“Hmm… the cake does sound most appealing.” Luna closed her eyes and inhaled deeply.
“It smells most appealing too. We must act quickly, and then we shall save Equestria from delectable, delicious horrors.”

The two sisters stepped out onto the balcony and looked up at the sky. The sun was not yet at its peak, and by now it should have been some distance beyond it. Celestia could feel the cold sting of the winter air. She quickly reached out to move the sun, hoping to return to the warm indoors as soon as possible. It was merely a matter of shifting it over to its proper posit—

“What are you doing? STOP!” Luna shouted as she tackled her sister. The two fell to the floor in a flailing mess of limbs.

“Ow! Was that truly necessary?” Celestia asked, wincing. She struggled to untangle one wing while Luna’s weight pinned the other.

“I was saving Equestria! You were about to doom us all!”

“No I was not. I was moving the sun.”

“And that would have destroyed Equestria! Surely, you cannot believe that to be good idea!”
Luna was the first off the ground, as gravity had favored her in the fall. And so, Celestia had to look up at her as she spoke.

“I see nothing wrong with simply moving the sun.”

“Nothing wrong? We cannot simply move the sun and the moon as we please.”
Luna stopped shouting, but was instead staring at her sister fiercely.
“Had you simply moved the sun, you most certainly would have changed the argument of periapsis. We cannot condense half a year of precession into a moment.”

“… Pardon?”

“The anomaly lies in the true anomaly. We must address that with minimal long term disturbance to the other orbital elements.”

“An anomaly should exist in the true anomaly, correct?” Celestia tested her knowing smile once more.

Luna hesitated for a moment as she was overcome by laughter.
“Oh, you always make the most excellent jests!”

“Cease laughing, ‘tis not a jest! How do we fix this?”

“Simple. We slow down the sun.”

It was then Celestia’s turn to laugh. She bowed her head and began giggling. Luna stomped on the ground in response, and Celestia could feel the impact transfer through the entire balcony.

“I would NOT joke about so serious a topic!”
Luna’s eyes were sparkling with false rage. She was always a great actor. Celestia could not control herself and fell into another fit of mirth.

“ENOUGH! Do not mock me, sister! Do you not remember any of mother’s lessons?” Luna shouted, with an edge in her voice.

Celestia stiffened at those words. She looked at her sister closely. It was, in fact, true anger in her eyes.
“I d—”

“I am certain I could use the moon to keep the sun from rising, and you would not know how to stop me!” Luna shouted venomously.

“Surely, you would nev—”

Just then, Luna levitated her sister’s parchment and quill over. It was still emblazoned with little more than the horseshoe. She began writing furiously.
“In order to speed up the orbit of the sun, we must shorten its period! To do that we must reduce the semi-major axis, which is dependent on orbital energy!”

Celestia looked on in horror as the culmination of her entire morning’s work was defiled by foreign markings.

“If we reduce the velocity of the sun, we reduce the energy by its square! We reduce semi-major axis by the inverse, and period by the cube of the square root!”

Celestia was not struggling to comprehend what Luna had said, but only for a lack of trying. She was not even attempting to understand it. Moisture began to gather in Celestia’s eyes, but there seemed to be no end to her sister’s tirade.

“When the mean anomalies align, we must accelerate the sun back into its original trajectory! Only through that may we correct the orbit of the sun!”

“My homework…” Celestia was barely able to speak through the tears she had been fighting back.

Luna’s anger faded immediately at the pitiable sound of her sister’s voice. She approached slowly.
“Homework? The assignment on orbital mechanics? But ‘tis due on the morrow!”

Celestia’s eyes widened in panic.
“You must be mistaken! ‘Twas due the day after the new moon!”

“Tia, today saw the new moon.”

A bout of nausea threw Celestia onto her side. She curled up on the floor of the balcony. The entire world seemed to close in on her.
“No, no no no, no, I don’t know… how can I… I won’t…”

The frigid air was penetrating through Celestia’s fur. The moisture on her face stung as it helped the cold pierce even farther. She felt small, and worse, she felt alone.

But then Celestia felt her sister’s embrace. Luna draped a wing over her back. It was too small to offer much shelter, but Celestia leaned into it for all the comfort that she could find. She leaned into her sister, and began crying.

“M-mother wanted… she said…” Celestia managed to choke out between sobs.

“Shh… I miss mother too. But she believes in us,” Luna said quietly.
“She would not have left us otherwise.”

Celestia laid still, as the sun’s unaltered trajectory brought it past its zenith. She was struggling to steady her voice, but finally found the ability to speak again.

“I c-cannot properly manage the sun. I cannot even finish a simple assignment!”
Celestia felt as if she were about to fall back into tears, though she managed to continue.
“I am to begin holding court by the new year, and I will certainly make a fool of myself there. I would never be able to rule over the country as mother wished!”

“No.”

Luna removed her wing from Celestia’s back and stood up. The cold air left in its place was almost painful.

The chill was nothing in comparison to the pain of the silence that smothered Celestia. She was about to let out a sob for the sake of noise, but her sister finally continued.

“No, you are wrong. You will succeed at all of those, I guarantee it.”

Celestia lifted her head to look at her sister. Her vision was still unfocused and bleary, but she could track Luna pacing back and forth.

“I know you will succeed, because I will help you move the sun. I will help you with the assignment, and when you are in court I will sit there next to you. When you are on the throne, I will be by your side and we shall rule together.”

Suddenly, Celestia found herself wrapped in her sister’s wings. She returned the embrace and the two of them sheltered each other from the cold air.

“I will do all this because I know you would do the same for me.”

Luna nuzzled Celestia gently. Celestia nuzzled her back as tears soaked into her fur. She couldn’t tell whom they came from, but she didn’t quite care. The quietude now was far more pleasant; tranquil rather than stifling. The two sat motionless as the sun continued along its path.

It was Celestia’s stomach that broke the silence.
Before she could apologize, her sister giggled and blinded her with a flash of cyan light. Celestia’s vision returned slowly, but her nose immediately recognized the banquet hall.

“Quickly Tia, the cake grows cold!” Luna said while nudging her sister toward a seat. “We can work on your astrodynamics later.”

Celestia was blinking to rid herself of the spots that obscured her vision. What she saw of the cake seemed as delicious as it smelled, but she was hesitant to begin eating.

“What of the sun? ‘Tis still an hour slow,” she asked as her mouth watered.

Luna paused while a spoon, dangerously full of cake, levitated directly in front of her mouth. Momentum separated some cake from the spoon and carried it onto her nose. It hung there for a moment, as if unaffected by gravity. Luna caught it with a deft twist right before it began to slide, and she pondered as she chewed.

“Hmm… ‘tis only an hour. The cake is a higher priority.” Luna shrugged.
“I can delay moonrise, which would give us more time to work on your assignment. We can change all the palace clocks before sunrise.”

“And none shall be the wiser.”
Celestia giggled at Luna’s appearance. A small bit of vanilla frosting was left behind, and it stood out against her sister’s blue fur. She looked down at her own cake, but she found that her stomach was still closed.

“What is wrong, dear sister?” Luna asked with concern.

“Y-you said that you could keep the sun from rising…”

Luna put her spoon down and stared at her plate. Her shoulders slumped and she let out a sigh. Celestia was almost ready to drop her line of inquiry, but Luna replied first.

“I spoke in anger and regret it. I would never do such a thing.”
Luna took another bite of cake, and Celestia finally responded in kind.
“As long as I am well of body and of mind, I shall never keep the sun from rising."

“Promise?”

“I promise."