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Two-Body Problem: Assignment 1

By -IceMan-
Created: 18th December 2020 06:44:02 PM

  1. Two-Body Problem
  2. By IceMan
  3.  
  4. Assignment 1: Two-Body Problem
  5.  
  6.  
  7. >Okay, don’t mess this up.
  8. >You just want to ask her to study with you.
  9. >Perfectly platonic.
  10. >Be your normal charming, intelligent self, and don’t mess this up.
  11. >There she is, right in front of you.
  12. >Now go up to her, ask her, and don’t embarrass yourself.
  13. “Hey, Twilight.”
  14. >Her eyes meet yours as she looks up from a thick electrodynamics book.
  15. >“Hey, uh....”
  16. “Anonymous. I’m in Advanced Physics with you, generally sit a row behind you in lecture?”
  17. >“Oh, yeah! Yeah!”
  18. “Look, I think this next problem set might be a bit difficult, so I was wondering if we could maybe combine our brain power and work together on it.”
  19. >Twilight thinks for a moment.
  20. >“I don’t know. I usually find it more efficient to work on them on my own, but if you think it’s going to be difficult.... I don’t know. I really would prefer just to work alone. It’s less distracting.”
  21. “Hey, I’m with you there. I’d really prefer to do it myself too, for the same reason. But the professor gave us seven problems this time. Seven! It’d probably go by much quicker if we pooled our resources. I’m not that chatty when I work, and I know you’re not either, I’ve seen you in lab. So I don’t think distracting each other will be a problem.”
  22. >Again, Twilight considers your proposal.
  23. >“No. I think it’d really be better if I work alone.”
  24. >Now it’s your turn to think.
  25. >Appeal to her scientific nature.
  26. “Have you ever tried working with someone else?”
  27. >“Well, no.”
  28. “Then how can you possibly know for certain that working as team won’t make our efforts more efficient?”
  29. >Gotcha.
  30. >“Alright. Fine. You’ve convinced me. Do we want to meet at my place or yours?”
  31. “Whatever you prefer.”
  32. >“My place it is.”
  33. “Great. I’ve got a meeting with my research advisor until seven thirty, so we could meet at eight?”
  34. >“Sounds good to me.”
  35. “Great. See you then.”
  36. >Twilight furrows her brow for a second.
  37. >“Wait, this isn’t a date is it?”
  38. “What? No! This is perfectly platonic. I give you my word.”
  39. >“Alright then. See you at eight.”
  40.  
  41. >8:00 PM
  42. >You stand in front of a large brown door on the 15th floor of an apartment complex in downtown Manehattan, your backpack slung over your shoulder and digging in slightly with the weight of heavy physics textbooks and papers.
  43. >You firmly rap your knuckles on the hard oak and wait for a reply.
  44. >After a short time, you hear the patter of feet on hardwood comings towards the door, followed by the click of a lock opening.
  45. >“Oh, hi Anon.”
  46. >She has already gotten out of her school uniform, ditching the collared shirt, tie, vest, and tartan skirt for a more comfortable-looking t-shirt and jeans; however, her hair is still up in a neat bun, a pencil holding it together.
  47. >Having been working late, you remain in your uniform.
  48. “Hey, Twilight. Ready to do some physics?”
  49. >“Yeah, sure. Let me just get my stuff from my room, and I’ll meet you in the kitchen.”
  50. >Twilight’s apartment is filled with books.
  51. >It has the feel of an old study or library: hardwood, leather, and large bookshelves filled with dusty tomes.
  52. >A big mirror hangs on the right side of the entry hallway, along with a few photo frames.
  53. >One shows Twilight and what you assume to be her older brother with her parents.
  54. >Another is a photo of her brother and what you presume to be his wife.
  55. >And the third is Twilight alone.
  56. >You head into the kitchen and find a granite island countertop and a small wooden table with chairs set around it, along with some stainless steel and nonstick pans hanging from spokes above the stove.
  57. >Setting your backpack down, you pull out your physics textbook, a few sheets of paper, two pencils, and an eraser.
  58. >Twilight comes back in with her own book, paper, and writing implement, as well as a small set of speakers, and begins filling a kettle.
  59. >“My parents are on vacation in Hawaii, so they shouldn’t be around to bother us. Do you want any tea?” she asks.
  60. “I’m more partial to coffee, but sure. Thank you.”
  61. >She sits at the table across from you, setting her work materials down and plugging her phone into the speakers.
  62. >“You don’t mind if I put on a little music, do you? I’ve always found classical to be very focus-enhancing.”
  63. “No problem.”
  64. >Twilight presses play on her phone, and a piano concerto begins to play from the speakers. (www.youtube.com/watch?v=PduQlZTxuNQ)
  65. >“Alright, let’s get started. Problem set four, number one....”
  66.  
  67. “Okay, problem four dash seven. Find the kinetic and potential energy for a driven damped harmonic oscillator,” you say.
  68. >“Oh, well that’s easy. We know that the equation for x of t for a driven damped harmonic oscillator is A cosine-of-omega-t-plus-delta.”
  69. >Your studymate scribbles something down on her paper.
  70. >“So the kinetic energy is just one-half m x-dot squared, which is one-half m times negative A omega sine-squared of omega t plus delta.”
  71. >Given that you two were the only two members of the Crystal Prep Advanced Physics program, it was simply guaranteed that you two would work together on the homework for the class.
  72. >The program entailed taking a college sophomore-level course at the local university and the production of original research as a final project.
  73. >As the principal said, it was very important to the school’s “reputation.”
  74. “And the potential energy is the integral of force, so one-half k times x of t squared, or one-half k A-squared cosine-squared of omega t plus delta.”
  75. >“Perfect, that’s the last problem.”
  76. “Yeah, jeeze, they consider this college-level work? That was a piece of cake.”
  77. >You staple the pages of the problem set together and place them loosely in your backpack.
  78. >Twilight takes a sip from her mug of tea.
  79. “So, how’s your research going?”
  80. >“Huh?”
  81. “Your research. Is it going well or what?”
  82. >“Oh, yeah. That. I don’t know. I haven’t picked up any of those weird anomalies out by Canterlot High School since the September.”
  83. “Hey, at least you don’t have to deal with trying to get a low-Earth orbit satellite approval through the mess of bureaucracy that is NASA. My advisor is helping me and all, but it’s still enough paperwork that if it were compressed into a small enough space, it would probably just instantly collapse into a blackhole.”
  84. >“Well, at least your cosmic rays will show up once you get your satellite in orbit. I don’t even know what’s going on. Maybe the instruments were just acting funny that day....”
  85. >Twilight furrows her brow.
  86. “Well, if you haven’t figured out some other explanation -”
  87. >“There isn’t one. There’s no source for this much electromagnetic radiation outside of nuclear weapons and particle accelerators. And clearly we’re still alive, and I’m pretty sure CHS doesn’t have its own cyclotron, because we’d have heard about it.”
  88. “Ugh, have you heard about those Friendship Games coming up?”
  89. >Twilight takes another sip of tea; you follow suit.
  90. >“Only a billion times. It’s like the whole school won’t stop talking about how we’re going to wipe the floor with that school. Again. Personally, I want no part in it. Plus, it’s just a big distraction from my research. ‘Hey, Twilight? Where you going? Oh, to the enemy camp? Why don’t you do some spying for us! Har har har.’”
  91. >She lowers her voice and lengthens her vowels for that last part.
  92. >“Morons.”
  93. “Yeah.”
  94. >The two of you take a sip of tea.
  95. >“I really don’t get Crystal Prep sometimes,” Twilight says. “I mean, people are there to learn, right? Why then is there so much emphasis put on our athletics program? Why are there even non-honors programs offered?”
  96. “Because there are plenty of rich assholes who want to send their kids to the most prestigious high school in the county, arguably the most prestigious high school in the state, and aren’t willing to see them get C’s.”
  97. >“Maybe we’re the only two students who actually care about knowledge at that school.”
  98. “Makes you wonder why we’re not closer friends.”
  99. >Twilight blinks.
  100. “Oh, come on, you have to have realized that this is the first time we’ve ever had an interaction beyond passing each other in the hallway. We’ve been top of the pile at Crystal Prep since we got there, we both have this giant interest in science and physics, and yet we’ve barely ever spoken to each other.”
  101. >“Well, we don’t exactly have time for friendships, do we? We’ve got work and research and all the other things that come with being genius teenagers. And that’s way more important than friendships. Preparing for the future. Discovering new knowledge.”
  102. “Crystal Prep definitely isn’t helping with that. They send us over to some other place when we get too smart for them. Or lock us in unused closets and make us do work there.”
  103. >“Speaking of which, are you applying to the Everton Institute?”
  104. “Yeah, probably. Are you?”
  105. >“Yeah. At least there our research might be appreciated.”
  106. “Yeah, hopefully.”
  107. >You think back for a second.
  108. “Hey, wouldn’t being friends be a form of discovering new knowledge? Especially if you’ve never really had them before?”
  109. >“Well, I don’t know....”
  110. “Look, I think I’m just as bad at this friendship thing as you. So I’m sorry if I seem a bit forward. I was worried about that earlier as well. I mean, I was... I was bullied a lot as a kid, for being ‘the smart one.’ So I didn’t have many friends. Never really figured out the whole ‘friendship’ thing.”
  111. >You take a sip of tea.
  112. >Dammit, man, you’re making a frigging embarrassment of yourself.
  113. >Stop it.
  114. >Shut up.
  115. >Say your goodbyes, get your keys, and drive home.
  116. “I’m sorry, maybe that was a bit much.”
  117. >“No, no! It’s fine. Don’t worry about it. I mean, well, for me it was just that I study all the time. And when I’m not studying, I’m organizing my time for how I’m going to work and do more studying. There’s just no time in my life for friends. It’d just be a big distraction.”
  118. “Well, I wasn’t too much of a distraction tonight. How long does it usually take you to do a problem set?”
  119. >“I don’t know, an hour and a half?”
  120. “Well, it’s now -”
  121. >You both check the clock.
  122. “Nine o’clock. And that was a long problem set too.”
  123. >“Then I guess your hypothesis that working together would increase efficiency was correct.”
  124. “But that’s the thing. We did our work together. As classmates, as acquaintances, as friends, as whatever. You can make time in your studies for friends.”
  125. >“I... I guess I can.”
  126. >You look at the clock again.
  127. “So, now what? I told my parents I wouldn’t be home until ten. I mean, I could go now, we’re done and all....”
  128. >“No! You don’t need to - I mean, we could just hang out, I guess? Isn’t that what normal teenagers do on a Friday night?”
  129. “Wait, it’s Friday?”
  130. >Twilight nods.
  131. “Damn, weeks go by faster than I think they do these days.”
  132. >“Time moves at a constant rate of one second per second, Anonymous.”
  133. “Unless we’re experiencing relativistic effects.”
  134. >“I think we’d notice if the Earth’s gravity suddenly increased or a black hole appeared or something.”
  135. >You chuckle.
  136. “But, seriously, what do you want to do?”
  137. >Twilight thinks for a moment.
  138. >“We could watch a movie,” she says.
  139. “Sounds good to me. Whatcha got?”
  140. >“I’ll go look. Probably mostly my brother’s stuff that he’s left here, but we might have something good.”
  141. “Do you have any popcorn?”
  142. >“I don’t know, maybe? Look in the pantry.”
  143. >You find a box on the third shelf up, take out two bags, and put them in the microwave.
  144. >“Alright, it looks like it’s either one of about a dozen romcoms, The Godfather, or Star Wars,” you hear from the other room.
  145. “Which Star Wars?” you reply.
  146. >“Uh, Episode Five. That’s it.”
  147. “Guess that’s it then.”
  148. >“Cool, I’ll put it in.”
  149. >The microwave dings.
  150. >You pour the two bags into a bowl, grab the kettle, tea, and mugs and put them on a tea tray, and bring it all into the living room.
  151. >Should be enough popcorn for two people over the course of one movie.
  152. >You sit down on the couch next to Twilight, though not too close, and set the popcorn bowl and tea tray on the coffee table.
  153. >“Ready?” Twilight asks.
  154. >You take a handful of popcorn and stuff it in your mouth.
  155. “Gah.”
  156. >She dims the lights and presses play.
  157. >The brass fanfare blares from the surround sound.
  158. >A lone Imperial Star Destroyer launches a tiny black probe towards a desolate ice planet.
  159. >The Imperials discover the Rebel base on Hoth, and send their massive AT-AT walkers to destroy it.
  160. >The Rebels are forced to retreat, their fleet fleeing to unknown parts of space.
  161. >Luke Skywalker, having received a vision from the dead Jedi master Obi-Wan Kenobi, heads to Dagobah to train with Yoda.
  162. >Han Solo, Leia Organa, Chewbacca, and C-3PO miss the last transport and are forced to flee into the asteroid field around Hoth in the Millenium Falcon.
  163. >It was around the time where the Falcon lands inside the giant space slug to repair the hyperdrive that you noticed Twilight had shifted a bit closer to you.
  164. >She reaches forward to grab her mug of tea and accidentally brushes against you.
  165. >“Sorry,” she whispers.
  166. >Leia and Han are arguing over something.
  167. >You feel a soft weight pressing against your left shoulder.
  168. >Looking over, you find Twilight’s head rest upon it.
  169. >She immediately sits up, ramrod straight.
  170. >“Sorry, sorry,” she whispers, “I didn’t -”
  171. “I didn’t say you couldn’t.”
  172. >The weight is replaced.
  173. >You wrap your left arm around her, squeezing her close.
  174. >Twilight sighs.
  175. >“This is... unscientific, irrational, we barely know each other....”
  176. “Shh... let the hormones do their job.”
  177. >You carefully push the pencil holding Twilight’s hair up out, letting it fall down in a light avalanche of thin violet strands.
  178. >Curling a thick lock around a finger, you feel the soft, airy texture and lightly play with it.
  179. >Twilight shifts a little bit in your arms, her head now against your chest and lavender eyes staring directly into yours.
  180. >Your arm falls across her stomach, and she runs a neatly-manicured hand along it.
  181. >You delicately grab hold of it, interlacing your fingers with hers.
  182. >Twilight pulls you into an embrace.
  183. >“You’re quite warm,” she says.
  184. “Uh, well, I manage to keep my internal temperature at a constant thirty-seven degrees Celsius.”
  185. >Twilight giggles.
  186. >“Always have to be scientists, huh?”
  187. “Why should we ever stop?”
  188. >“So we can do irrational things like this.”
  189. >“I love you,” Leia says to Han Solo, about to be frozen in carbonite.
  190. >“I know,” he replies.
  191. >You pull Twilight in tight.
  192. >Luke learns the terrible truth about his father.
  193. >The Rebels regroup on the edge of the galaxy, and the movie ends with a triple blast of trumpets.
  194. “Hey, you wouldn’t happen to have the time, would you?”
  195. >You both look over to the clock on the DVD player.
  196. “Eleven o’clock! Guess what Einstein said about time, relativity, and pretty girls is right.”
  197. >Then something hits you.
  198. “Wait, shit, I need to get home! Mom and Dad will be pissed.”
  199. >You get up and dig around in your pockets for your keys.
  200. >“Why don’t you just text them you were invited to stay here for the night?” Twilight suggests.
  201. “Twilight, you and I both know that sounds suspicious.”
  202. >“Just say that you got caught up working on a problem set and it took you longer than you thought it would. It’s a Friday night, I don’t think they’ll mind.”
  203. >You consider the proposal, then pull out your find and send the message.
  204. “There. Done. Crisis averted.”
  205. >You sigh.
  206. “You know, I was a bit worried that you would take the whole ‘Can we study together?’ thing the wrong way, but I never would have expected -”
  207. >“You should have asked me sooner.”
  208. “If I had known you felt the same way -”
  209. >Twilight kisses you on the cheek.
  210. “I - I wanted to keep things platonic for now, see how you felt about me, but I guess -”
  211. >“I would have loved to study with you at any time.”
  212. “I - I - I just -”
  213. >“Jeeze, you’re so nervous. You can handle advanced calculus, I think you can handle a girlfriend.”
  214. “You’re... you’re right.”
  215. >“Now, should we watch another movie, or what?”
  216. “Guess it’s going to have to be The Godfather.”
  217. >“I’ll have my brother bring over a few more sci-fi flicks the next time he’s around. But yeah.”
  218. “Pop it in.”  
  219. >Twilight puts the movie in, then sits down next you and leans her head on your shoulder.
  220. >Relationships and studies.
  221. >Maybe it isn’t some kind of two-body problem?
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