Orbital Mechanics for Pony Princesses
The north-eastern side of Canterlot Mountain was a special place for any pony who loved the stars. Being shielded from the city by the rocky promontory and overlooking arid uninhabited land meant that light pollution was virtually non-existent. Upon flying or climbing up to a ledge on the cliff, an adventurous traveller could enjoy an amazing view across the high plateau and rocky desert in the rain shadow of the rock. It was impressive by daylight, but it was during a dark moonless night that the cloudless sky became truly awe inspiring, when you could admire the full glory of the heavens. A glittering dome, broken on one side by the black silhouette of the mountain, with the glowing haze of the Milky Way, the bright spots of the nearby planets and brighter stars, and an uncountable number of fainter specks formed by distant stars, star-clusters, nebulae and galaxies.
Princess Luna and Princess Twilight Sparkle had been lying side by side on a blanket laid on the ground for several hours, staring up at the plethora of luminous dots. They were both familiar with all the visible constellations, and viewed the patterns of Cepheus, Cygnus, Pegasus and others as old friends. The light gathering power of their huge pony eyes let then see far more distant stars than less optically-gifted species. Eventually Twilight felt the need to break the silence.
“Thank you for sharing this with me Luna,” she said softly to the fellow alicorn, and rolled over to gently nuzzle her head.
“You're welcome,” replied the Princess of the Night. “I usually come here alone. But it's also good to come with a friend who appreciates the night sky.”
They had been through a long day of royal business in Canterlot with the other princesses. At the end of which Celestia, with heavy eyes, had lowered the sun and withdrawn to bed. Cadance had departed for the Crystal Empire, mumbling something about marital duties, leaving Twilight and Luna standing together on the castle parapets. Both felt restless, but not in the mood for Canterlot night-life.
At Luna's suggestion, they had flown out of the city and around the summit. On the far side they found a spot, in the shadow of the rock, to camp for the night, and settled down to watch the darkening sky, warmed by a dry wind blowing down the lee slope of the mountain.
“I should raise the moon now,” said Luna. “Although it seems a shame to destroy the darkness and mask the stars. Let's leave it a little longer.” She paused for a moment and then looked at the younger princess with a playful grin. “Would you like to try it?”
“What!” cried Twilight. “Raise the moon! Me?” She had never admitted to either Celestia or Luna just how scared she had felt when she had briefly been responsible for both the sun and moon during Tirek's rampage.
Luna laughed. “Well, maybe the moon is a rather large rock for a beginner. But there's no reason why you shouldn't launch your own micro-satellite. Nothing to it. It's just like skimming stones. Here—” she picked up a small boulder, illuminating its outline with her magical aura, and tossed it over to Twilight, who caught it with her own telekinesis. “Throw that in the sky as hard as you can.”
Unsure where this was leading, Twilight lifted the rock, feeling the shape of the space around it with her mind, and warping it to support the stone. She then formed this into a wave, and let it ripple forwards, carrying the rock, so that it flew far across the mountain landscape before crashing to the ground a few miles away amid other geological debris. Luna laughed again.
“You need to push it a bit higher and faster than that to reach orbit,” she said. “Give it a strong sustained upward thrust for a few minutes, then release.”
She tossed another small chunk of limestone to Twilight, who caught it, and focussed her magic not just to balance gravity, as done in everyday levitation, but to accelerate the rock upwards, several times as fast as it would fall down. She felt it moving faster and faster, high into the night sky. After two or three minutes she released it and sat back down on the ground, looking up. No longer illuminated by her magic, it was hard to see the rock. She stared upwards for many minutes trying to make it out. Was it still moving? Would it fall back down? What had happened to it? Luna waited patiently beside her without comment. Suddenly there was a bright streak of light above their heads, which came and disappeared in less than a second.
“Congratulations Twilight. You just made your first shooting star.”
Twilight's face broke into a smile. “I did that? How?”
“You threw the rock up in the air. It reached a maximum height, probably about a thousand kilometres, then fell back to earth accelerating under gravity. It entered the atmosphere moving at several kilometres per second, and burnt up just before it hit the ground.”
“Wow!”
“That's what happens when you let it move through the air too fast. Now, to get a stable orbit, you need to get it into the thermosphere, moving parallel to the surface. Launch it at a shallow angle.”
On her third attempt, Twilight pushed her projectile forwards and upwards at a slight angle. She felt the rock accelerate, impeded by air resistance and pulled downwards by gravity. But once it was above most of the atmosphere she could feel it fly free. She bent its path around until parallel to the surface, and only stopped pushing once it was at the horizon. She then let out a breath and stared forwards tracking the rapidly dimming speck of light.
“I think you overshot that one a bit,” said Luna. “Too fast. It look like it's on a hyperbola and will escape forever. Or it may establish a highly eccentric orbit and come back eventually. Unless it hits the moon.”
“Sorry,” said Twilight.
“It's no problem—the moon is hit by many meteorites every day. The trick is to get the speed just right. Too slow, and it falls back to the ground. Too fast, and it gets into a hyperbolic or highly elliptical orbit.
“I'm not sure I can do this,” said Twilight, feeling discouraged.
“Let's try it together.”
Luna picked up two rocks—larger than the previous one—and tossed one of them to Twilight.
“I'll give them a polish, to make them nice and shiny.” She levitated a cloud of sand around the rocks, blasting them until the surface was as smooth and reflective as a mirror. “Celestia's probably parked the sun not far below the horizon, so they will be well-lit once up high. Now let's go!”
Together the two princesses launched their rocks into the air. Twilight mimicked Luna's motions to set the angle and speed such they moved in unison. They both accelerated upwards, and at an angle, bending around into a horizontal path. Then, when Luna judged the speed was right, they released their rocks and watched them move forwards and down beneath the horizon. Two bright stars—the light from Celestia's sun reflected by the mirrored surface.
“I think we did it,” said Luna. “Mission accomplished.”
“Yes!” said Twilight grinning and hopping up in the air on all four hooves. “What will happen to them now?”
“They will orbit around the earth, and come back overhead in one or two hours.”
“How do you know?”
“We set them moving at a fixed speed. As they move, their path will be bent by gravity, so they follow a circle all around the planet. You're good at algebra—I bet you can work out the orbital period.”
They lay back down on the blanket. Twilight took out a notebook and, by the light of her horn, scribbled calculations with a pencil. Meanwhile Luna passed the time idly braiding her friend's tail—separating out the indigo, pink and purple hairs, plaiting them together, and weaving in a little of her own magic sparkle.
Once Twilight had completed the calculations. She then took a pocket watch out of her saddlebag and set it on the ground. She turned to Luna with the glowing face of a school filly who had completed an assignment.
“They should reappear an hour before dawn.”
They settled down to wait, lying on their backs, staring back up at the sky.
“Tell me how you raise the moon,” asked Twilight.
“In much the same way—just on a larger scale. The moon is just a huge rock orbiting the earth with a period of just over twenty-seven days. We see it rise and fall as our planet spins on its axis.”
“So why do you need to move it at all? If the orbit is stable, can't you leave it alone?”
“If only... Unfortunately those Canterlot bureaucrats have other ideas.” Luna rolled her eyes.
“What?” Twilight stared at her with a curious look.
“For some silly reason—I never understood why—it's just what the officials tell me—the ponies of Equestria think the moon should rise every evening, just after sunset. By its natural cycle, moonrise would be an hour or so later each day, sometimes when the sun is still in the sky. But instead I have to sync it to the solar rhythm, or else I get complaints. And to make things even more complicated they don't understand the proper order of the lunar phases. Usually they want a full moon, to keep the streets well-lit. But then on some special occasions they want a crescent, because they think it looks artistic. At the last Summer Sun Celebration, they wanted me to lower a full moon below the horizon, just as Celestia would raise the sun at almost the same azimuth. That took quite a bit of behind-the-scenes magic by my sister and I, and some large mirrors, but we did it.”
“I didn't know it was so complicated.” Twilight thought back to the celebration. At the time she had been so focussed on her own role, that she hadn't noticed the apparently unphysical stage lighting.
“It's not easy being a princess.”
Twilight nodded.
“There's a particularly annoying retired civil servant in Trottingham,” continued Luna. “Who has nothing better to do with his time than write letters to me every time moonrise is late. I bet he's drafting one at this moment. But tonight I don't care.”
They were both wide awake, and knew there was no chance of getting any sleep on this night. They were content to spend the time watching the stars. Eventually the awaited time arrived.
“Any minute now...”
Two bright stars rose above the rock behind them and moved quickly, in unison, tracing an arc across the sky. After a minute or so they had crossed half the sky and fell into the shadow of the planet, no longer illuminated, and disappeared from sight.
Twilight continued staring at the sky with a big grin. “What will happen to them now?”
“They will keep on orbiting. As they are at a low altitude, they will likely drift into the atmosphere and burn up in a few weeks or so.”
Twilight threw her hooves around Luna's neck in an impromptu hug, which her teacher returned with a happy smile.
Meanwhile, on the other side of the mountain, Princess Celestia, having got out of bed, washed her face, and brushed her mane, walked out onto her balcony, ready to raise the sun and start the new day. She looked out at the dark pre-dawn sky, saw the two new stars moving together, and smiled softly to herself, having guessed the pair of ponies who were responsible.
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That was both informative and cute.
Cute. I liked that bit about braiding the tail. That was a really nice touch.
img4.wikia.nocookie.net/__cb20121223051816/mlp/images/thumb/1/10/Applejack_Shooting_Stars_S3E08.png/640px-Applejack_Shooting_Stars_S3E08.png
I'm slightly worried they weren't worried about accidentally braining somebody if Twi didn't managed to give the rocks enough speed.
Also, nice reason at why Luna and Celestia have to move the celetial bodies manually.
Freaking Bureaucrats
Alternate ending:
Twilight continued staring at the sky with a big grin. “What will happen to them now?”
Luna shrugged. “They will keep on orbiting. That high, there is no drag from air resistance to return the rocks to Equestria.”
"That was cool!" Twilight said. "Let's launch more!"
* * *
A thousand years later
The first Equestrian space mission had just cleared the atmosphere. Over the radio, Apollo Pioneer could hear the ecstatic cheering from Mission Control.
The radio crackled to life with Princess Twilight Sparkle's voice. "Congratulations, my little ponies! This is truly a momentous time in Equestrian history."
"Thank you, Princess," Apollo said — then his attention was drawn by a glint of light off to the right side of the window that he could have sworn he hadn't seen a moment ago. He squinted. "Hey, is that a piece of —"
* * *
And that's why there are no ponies in space.
*Grins* Very cool, you always do such excellent intelligent and educational fics.
They have actual magic, and still had to use mirrors.
And I agree with AppleTank: Freaking Bureaucrats.
If Cheerilee's any indication, ponies teach orbital mechanics in elementary school. Probably a matter of some practical interest given the princesses.
I really like the reason for Luna having to tweak the moon's orbit. The only thing worse than a bureaucrat who knows nothing about what he's administrating is that same bureaucrat thinking he's an artist.
In all, some wonderful Twiluna friendshipping with a tasty dash of science. Thank you for it.
I just imagined Luna playing Kerbal Space Program. And it was totally awesome.
4789058
When Luna was young she didn't understand how orbit worked. This frustrated her because was unable to control the moon as well as her sister could control the sun. Eventually she snapped and turned into Nightmare Moon.
During the first century of her banishment, strange, plant-like creatures crashed into her moon and stabbed it with a flag. Still filled with rage, she trekked for miles so that she could destroy the defilers, but was overcome with compassion when she saw the euphoria on the little alien's face. It identified itself as Jebediah of the Kerbal race (though it took some time to decipher its nonsensical language).
With his means of transportation destroyed in the crash, his 'rocket' as he called it, Jeb had no way to leave the moon. With little else to do, the two spent centuries discussing the cosmos (and visiting interesting rock formations). Jeb told her of the numberless worlds he had visited. From the violet seas of Eve to the choking emerald clouds of Jool to the minty freshness of Minmus, she was filled with wonder. But, like all good things, it could not last.
A day came when the two were journeying to the north of the moon in search of an elusive magic boulder that they had seen fly high overhead on occasion. While normally careful in their travels, the two had become lax over the centuries, and so it is no surprise that calamity claimed them. As they drew near their destination Jeb, ever fearless, stepped upon a crack. Now this was no mere crack in the substrate. No, this crack, perfect in its straightness, represented a fissure in the nature of space itself. From this crack came a mighty tentacle, visible only the the princess' magical sight, that in an instant struck the kerbal. In a heartbeat he was accelerated to several times the speed of light, spacetime itself warping to accommodate the Kraken's fury.
With her only friend in her prison taken from her, Luna's fury overwhelmed her and she reverted to Nightmare Moon. She swore to destroy her first true friend's assailant. Steeling her resolve, she stepped upon the crack to summon the beast. For decades the two fought, and at last the kraken was struck down by her mighty power. As she gazed upon her foe's broken form sorrow invaded her heart in memory of her lost Kerbal friend. Unable the deal with the heartache, she launched the corpse into the stars, hoping that someday Jeb's kind would come across the body. In years the corpse would be captured by the planet Jool before coming to its final resting place on the rocky surface of Bop.
Thanks for all your kind comments
4786188
Pony space flight will have to wait until they can teleport direct to high earth orbit
4786169 4788959
It's amazing the number of failures of logic which can be explained by meddling bureaucrats
4789058
I first taught myself orbital mechanics playing on Frontier Elite - that was some years ago.
Relax and think about the Crystal Empire.*
Seriously, this is another masterpiece.
* The Crystal Empire is really a citystate. I hypothesize that its current name come from when King Sombra used his mindcontrolmagic for conquering the city and proclaiming himself king. He probably changed the name to Crystal Empire and started conuring its neighbors, which did not go unnoticed by the Diarchy of Equestria.
Within a century of battling King Sombra and his mental magic, Princess Luna gave into jealousy and became the Mare-In-The-Moon NightMareMoon. I doubt that this is a coincidence.
When Princess Mi Amore Cadenza and Royal Consort Prince Shining Armor finish their marital duties, they should change the name from Crystal Empire to CrystalHeartPrincessipality or the like. I am certain that their subjects want to forget about the reign of King Sombra and do not want to keep using the name for their city he chose.
It is very hard to launch things. I do not know about Equus, but on Tellus, one must get objects 200 kilometers above the surface and moving at 8 kilometers per second for achieving orbit. For launching 40 tons of cargo (1 DescentStage, 1 AscentStage, 1 CommandModule, 1 ServiceModule, and 3 Asronauts) to Luna (our moon —— not the Princess) required 3,000 tons of fuel.
This story even touches on the physics of vision:
With their large eyes, ponies have larger pupils which increases both lightgathering for lowlight vision and visual acuity. Their larger eyes can fit more cones and rods on their retinas, thus also increasing visual acuity. I always imagined the ponies as pentachromates with cones for Near Ultra Violet, Blue, Green, Red, and Near InfraRed.
As always, ponies plus physics equals wonderful.
Double limestone all the way across the sky~
This question doesn't seem to make much sense as you already mentioned that Twilight has done that herself, so she must at least kinda know.
4786053 I know right, the tail braiding was sooo adorable.
4793423
Like any clever student, Twilight isn't afraid to ask the teacher silly questions
And now explain how the moon's gravitation isn't destroying the ecosystem of the planet and how Luna can move 73.490.000.000.000.000.000 tons.
The only problem is there isn't enough of it. Looking forward to more.
I love the way you mixed in magic with the science, well done on that by the way - it also seem to check out
And for the rest of you there is a reason they haven't shown any other planets in the equestrian sky (they exploded them by screwing with solar mechanics (or in Kerbal space program - hyper edit))
Story full of awws
i loved it
A nice little story.
The easiest way to turn me away from a story:
Mistakes in the description. You typed "and" twice in a row.
I'll read it anyway, but that's probably my biggest pet peeve.
4806000
Oops - thanks for pointing that out
It's a nice little story - combining friendship and physics with a dash of astronomy and respect for the night. Plus complaining about nobles, which always scores points with me.
Nice work!
4790292 I wonder... How much fun it would be if the royal sisters got so tired of the nobles shit that they ended up going fuckyouimdone, letting the orbits return to their natural state.
and sending every noble that complains to the moon after asking a simple question...
Do you like... Bananas?
Finally, some believable headcanon on the sun/moon issue in Equestria. ^_^
Cute story, too! Makes we want to start up Kerbal Space Program.
Exerting an exact amount of force to achieve orbit on a single 500-600 second burn is pretty tricky. Also, wouldn't the rocks have to be about the size of a small house to be easily spotted from the ground?
4808510
Tricky - yes - even to super-talented pony princesses, with the power to manipulate the speed of flying objects to considerable precision. But Luna has had hundreds of years of practice. Small satellites would not be visible to us humans, but to observers with eyes the size of teacups, they should be easily spotted, especially if polished to have a mirror-like surface.
I wonder what would happen if one night Luna just said, "F
it. Let the moon do what it wants." Eventually the bureaucratic outcry would die down, right? 
4786188
2,001 words.
Heh.
4827047
Your laws of physics pale before the indomitable solidity of bureaucracy!
4793999
Luna: "Do you even lift, bro?" *flexes horn*
5410508
Finally someone noticed
4791879
That's a really good point. I think I'd postulate that Pegasi almost have to have this kind of vision for perfect weather control.
Unicorns would likely have eyesight with extremely high resolution and depth of field for superb accuracy in manipulating objects and spell targeting.
Earth ponies would have to be able to see very different things, probably limiting their sight to near-infrared to green to make room for all the other receptors.
Now as an Alicorn... uh, wow. You'll need that larger cranium for image processing alone. Twilight probably didn't dare to open her eyes for the first week after transformation :)
Ah, ponies and science. The possibilities for theorizing are limitless.
5580387
Without red-sensitive cones, MacIntoshes and Granny Smiths look identical. Since Apple Jack and Apple Bloom can tell their brother and Grand Mother apart, they probably have red-sensitive cones.
Seriously, we Old-World Monkeys probably reevolved the red-sensitive cones so that we can tell whether fruit is ripe or not. Here is the evolutionary history of our color vision:
Our fishy ancestors had multiple cone-types 500 million years ago.
All tetrapods seem to be descended from a tetrachromate about 400 million years ago.
During the mesozoic, our nocturnal ancestors lost all but 2 cone-types.
About 40 million years ago, a gene-duplication made 2 copies of a photosensitive pigment in Old-world Monkeys, with 1 copy evolving into our red-sensitive pigment, and the other copy evolving into our green-sensitive pigment.
We monkeys are trichromates, but our equines are only dichromates. Most of our scaly, feather, and wet-skinned friends are tetrachromates, but some of our feathered friends, such as pigeons are pentachromates.
I imagine the ponies as having pentachromatic vision and linearly polarized lenses like any of the dinosaurs have (sea-birds have linearly polarized lenses for reducing glare from light reflecting from the water and pigeons are pentachromates).
Cute
Now just bounce beams of magic light off your super-shiny orbiting rocks, and you've got long-distance communication. Heck, combine some rubies and such the right way and even a non-unicorn could bounce light beams off it to send long-distance messages... Don't forget your safety filter goggles when playing around with that stuff though, of course.
Awesome story!