#Newton’s law of universal gravitation

[slapstikcomedyentertainment]

Hilarious Histories - July 5

Newton especially struggled with the problem of counterfeit currency...

On July 5, 1687, a man slightly more brilliant than myself, Sir Isaac Newton, published the “Principia Mathematica.” Two hundred fifty years later to the day, Spam was introduced to a grateful world. Coincidence? I think not. The eminent scientist unveiled several wonders for humanity, which in deference to him share his name. These include Newton’s laws of motion, Newton’s law of universal…

[tenth-sentence]

These relationships are encoded in Newton's law, and careful observation of the moon's orbit around the planet therefore allows for the planet's mass to be determined.

"Human Universe" - Professor Brian Cox and Andrew Cohen

[whats-in-a-sentence]

The equation says that the gravitational force between two objects – a planet and a star, say – of masses m1 and m2 can be calculated by multiplying the masses together, dividing by the square of the distance r between them, and multiplying by G, which encodes the strength of the gravitational force itself.

"Human Universe" - Professor Brian Cox and Andrew Cohen

[flowersandspacestuff]

Laws of Physics Series

The Law of Universal Gravitation:

An object attracts another object in direct proportion to their combined mass and inversely related to the square of the distance between them.

[reignpage]

E D E N U M A S T E R L I S T II

Pt 1 Majors Stairs or brooms?

Toji(finished) ❥ Brooklyn Nets: things we really shouldn't do (pt 1) ❥ Charlotte Hornets: plans in motion (pt 2) ❥ Cleveland Cavaliers: full college experience (pt 3) ❥ Dallas Mavericks: nothing but net (pt 4) ❥ Detroit Pistons: reaching for the ball ❥ New York Knicks: jumping through hoops (pt 5) ❥ Miami Heat: setting boundaries (pt 6) ❥ Philadelphia 76ers: shoot and a miss (pt 7) ❥ Indiana Pacers: faking left ❥ Orlando Magic: prove yourself on court (pt 8) ❥ Toronto Raptors: home win Nanami(finished) Guide ❥ Universal Gravitation: attracted to his mass (pt 0) ❥ Conservation of energy: changing forms for you (pt 0) ❥ Conservation of angular momentum: his torque ❥ Newton's first law: without you (pt 0.5) ❥ Newton's third law: steps back and forward (pt 0.5) ❥ Coulomb's first law: unlike charges (pt 1) ❥ Speed of Light: propogate your light (pt 2) ❥ Kirchoff's Law: calculating resistance (pt 3) ❥ Ohm's Law: potential difference (pt 4) ❥ Newton's second law: rate of change (pt 5) ❥ Conservation of momentum: remain at a constant ❥ Law of love: following the stars Sukuna(finished) ❥ Judas: a king with no crown (pt 1) ❥ Brutus: et tu? (pt 2) ❥ Ephialtes: reveal the path to home (pt 3) ❥ Winston Smith: her, not me (pt 4) ❥ Quisling: crumbling defences ❥ Mir Jafar: puppeteer (pt 5) ❥ Hanssen: disasters all around ❥ Jingwei: abandon us (pt 6) ❥ Caesar: all roads (pt 7) ❥ Ames: espionage ❥ Petain: losing it all pt 1 ❥ Petain: losing it all pt 2 ❥ Satan: the end and the beginning

[mysticstronomy]

CAN GRAVITY FORM WAVES??

Blog#456

Saturday, November 23rd, 2024

Welcome back,

Yes, gravity can form waves. Gravitational waves are ripples in spacetime that travel through the universe. If you think of gravity as a force acting at a distance, it is difficult to visualize how gravitational waves could form. However, if you use the more accurate description of gravity that was developed by Einstein in his general theory of relativity, these concepts become more logical.

General relativity describes gravity as a warping or curvature of space and time. All objects warp spacetime. When other objects travel through this warped spacetime, they end up traveling along curved paths. These curved paths look like they result from a force being exerted on the objects, when in reality they result from spacetime itself being warped. For instance, when you throw a baseball to your friend, it follows a smooth parabolic trajectory under the influence of gravity. Isaac Newton's laws would say that earth's mass is creating a gravitational force which acts on the baseball, gradually pulling the baseball down from straight-line motion.

However, the more accurate description goes like this: The earth warps space and time. The baseball is actually traveling in a straight line relative to spacetime, but since spacetime itself is curved, this straight line becomes a curve when viewed by an external observer. In this way, there is not really any direct force acting on the baseball. It just looks that way because of the spacetime warpage. If all of this sounds too strange to be believed, you should know that Einstein's general relativity has been mainstream science for over a hundred years and has been verified by countless experiments.

In principle, all objects warp spacetime. However, low-mass objects such as houses and trees warp spacetime to such a small extent that it's hard to notice their effects. It takes high-mass objects such as planets, moons, or stars in order for the gravitational effects to be noticeable. The more mass an object has, the more it warps spacetime, and the stronger its gravitational effect on other objects. For instance, a black hole has such a high amount of mass in such a small volume that even light cannot escape. Inside the event horizon of a black hole, spacetime is so strongly warped that all possible paths that light can take eventually lead deeper into the black hole.

Since spacetime warpage is caused by mass, the warpage travels along with the mass. For instance, earth warps the surrounding spacetime into an inward-pinched shape (roughly speaking). As the earth travels around the sun in its year-long orbit, this pattern of spacetime curvature travels along with the earth. An observer that is stationary relative to the sun and is at a point close to earth's path would see the earth get closer and then farther away, closer and then farther away, in one-year cycles.

Therefore, this observer would see earth's pinched spacetime pattern come closer and then farther away, closer and then farther away, in one-year cycles. Because the observer himself sits in spacetime and experiences it, the observer therefore sees his own local spacetime as being pinched, and then not pinched, pinched and then not pinched, in one-year cycles. The observer is therefore experiencing an oscillation of spacetime curvature that is traveling outward from the earth, i.e. a gravitational wave.

This actually happens in the real world. However, in practice, gravitational waves are so incredibly weak that they have no significant effect on daily life. The oscillating spacetime warpage of a passing gravitational wave is far too weak for humans to notice or feel. Only very sensitive, expensive, modern equipment is able to detect gravitational waves. In fact, it took a hundred years after Einstein predicted the existence of gravitational waves for technology to improve enough to be able to detect them.

Originally published on https://www.wtamu.edu

COMING UP!!

(Wednesday, November 27th, 2024)

"HOW NEGATIVE TIME WAS PROVEN??"

[nanamineedstherapy]

Bubble Butt Problems

Nanami X Reader X Gojo

Part 2 of Bubble Butt Problems (Tumblr/Ao3)

Summary: Nanami Kento has a problem—your & your research!

A/N: I stole this idea from @Strangecountrydreamer's unhinged 'ass' comment (pun intended) on the last chapter of this on Ao3. (We all say thank you in unison!) This isn’t just a story; it’s a manifesto for all of us who’ve ever pondered the mysteries of the universe while simultaneously plotting our next reverberating smack! So grab your coins, your measuring tapes, and maybe a towel or two (you’ll see why), and let’s get this madness started!

Chapter 2 - Nanami’s Wagon & the Scientific Method

The fluorescent lights hummed their judgment as Gojo Satoru sipped bubble tea with enough enthusiasm to make the pearls feel seen, his legs swinging like an unbothered toddler.

You, however, were deep in your Villain TedTalk Arc, pacing like a mad scientist on the verge of a breakthrough.

“In my defense,” you began, brandishing a single coin like it was Excalibur, “we’ve shown remarkable restraint. We haven’t bitten him, we haven’t tested its jiggle with a ruler, and we definitely haven’t involved towels. But that—” you pointed dramatically toward Nanami’s glorious backside, framed perfectly as he chopped vegetables, “—deserves answers.”

Gojo slurped his drink, nodding solemnly. “A true show of self-control. Honestly, I think you’re doing God’s work.”

You pointed at him, energized. “Exactly. And yet! Kento Nanami parades around with that absolute dump truck, no regard for the moisture he’s causing in his wake. It’s criminal!”

Gojo gasped. “You’re so right. That man owes reparations to anyone wearing gray sweatpants within a ten-mile radius.”

“Exactly!” you exclaimed, tossing the coin between your fingers. “We’ve got a duty to humanity, Gojo. If NASA won’t investigate the gravitational anomaly that is Nanami Kento’s ass, we will.”

“Say less.” Gojo’s grin was practically feral. “You wanna toss coins? I’ll raid my piggy bank.”

“Physics, Gojo. It’s all about trajectory. With a perfect angle, that ass could probably bounce a quarter across the Pacific.”

“Meter minimum,” Gojo agreed solemnly.

Nanami, meanwhile, was oblivious of your scientific aspirations—or so you thought. His chopping rhythm faltered as the low hum of your voices reached his ears. But he kept his focus on the carrots, his aura screaming, leave me out of this.

“This,” you whispered, flipping a coin between your fingers, “is for Isaac Newton.”

Clink.

The coin sailed through the air, a shining testament to your audacity.

Boeing.

It hit its mark and rebounded.

High.

Embarrassingly high.

Like, Olympic pole-vault-level high.

You and Gojo stared, slack-jawed.

You staggered back, hand to your forehead. “We’ve just unlocked a new law of physics. Nanami’s ass is a literal phenomenon.”

Gojo gasped like a reality TV star witnessing street food. “Did you see that arc? Bro, I think it broke the sound barrier.”

“His ass is so phat he didn’t even feel it.” You marveled, eyes wide.

But before you could start drafting your Nobel acceptance speech, a shadow loomed over you, and a low, deadly voice interrupted.

You froze. Gojo froze.

Then turned, slow as molasses, to find Nanami standing there. Not blinking. Not speaking. Just staring. The knife in his hand gleamed ominously under the kitchen lights, but it was the deadpan death stare that really sold the vibe.

Gojo waved weakly. “Hey, Nanamin. We were just discussing the—uh—elastic properties of your posterior.”

Nanami blinked. “My what?”

You coughed into your fist, attempting to hide your laughter. “Your ass, Kento. Your glorious, gravity-defying ass.”

“Your wagon,” Gojo added helpfully, before clapping his hands. “Certified dump truck. Beep beep!”

A muscle in his jaw twitched. “You two threw a coin. At my—”

“For science!” you interrupted, because if you were going down, you were going down swinging.

Gojo jumped in. “And it bounced! Like, at least 1.2 meters. Honestly, you should be flattered.”

For a moment, Nanami said nothing. Then, to your absolute horror, a faint flush crept up his neck. “You’re joking,” he said, though his tone betrayed a hint of doubt.

“Oh, I never joke about science,” you replied, straight-faced.

“Or butts,” Gojo added helpfully.

Nanami’s eyes narrowed, and his grip on the knife tightened. “You two,” he said slowly, “are immature.”

Gojo grinned, unfazed. “You’re just mad because you know we’re right. Honestly, Nanamin, you should be flattered. People would kill for an ass like yours.”

And that’s when it happened. A twitch. Barely noticeable, but it was there. Nanami’s silence was deafening. Slowly, he set the knife down and rolled up his sleeves like he was about to baptize you both in regret.

Gojo froze mid-celebratory high-five. “Oh no.”

“Oh yes,” Nanami replied, voice low and terrifying, cracked his knuckles, and started toward you.

“Run,” you grabbed Gojo’s arm and bolted.

“Wait—what about the experiment?!” Gojo yelled, already halfway out the door.

“Run first, science later!”

Nanami didn’t run. He didn’t need to. His calm, measured footsteps were somehow worse.

He chased you with all the unrelenting energy of a dad fed up with your nonsense. You darted behind the couch, Gojo scrambled into the bathroom, and Nanami stalked through the apartment like Jason Voorhees in a business-casual ensemble.

You and Gojo ducked into the living room, panting. “Vents,” Gojo said. “We’ll hide in the vents.”

Moments later, you were crammed together in the claustrophobic space, both of you shaking with suppressed laughter.

“Do you think he’ll kill us?” you whispered.

Gojo grinned. “If he does, I’m haunting his perfect ass forever.”

You could hear Nanami muttering to himself below.

“Next time,” Gojo whispered, “we should try nickels. Bigger surface area.”

But before you could agree, a massive spider scuttled across your arm.

“SPIDER!” Gojo shrieked, scrambling out of the vent like his life depended on it.

You weren’t far behind. “Ken! Help!”

The vent became a clown car of chaos as you and Gojo screamed your way out, landing in a heap on the living room floor.

Nanami, who was already there, stared down at you both. “Why are you like this?”

“SPIDER!” You wailed, pointing.

For a moment, Nanami looked like he might leave you both to your fate.

But with a sigh so heavy it could crush galaxies, Nanami dispatched the spider with the broom, then turned back to you.

“If I hear the word ‘wagon,’ ‘elastic properties,’ or ‘buttcheeks’ again,” he said, voice flat, “I’m filing a restraining order.”

Gojo, ever the menace, threw an arm around your shoulders. “C’mon, Nanamin. Don’t be like that. You know you’re a national treasure.”

Nanami walked away, muttering something about therapy bills.

A/N: Let me know your creative ideas for our next ass-ault attempt below! What should our next scientific endeavor focused on Nanami be? The Great Sweatpants Investigation: Measuring the gravitational pull of Nanami’s assets in various fabrics. Nanami’s Ass Appreciation Day: A detailed study on the effects of his glorious backside on the emotional well-being of those around him.

All Works Masterlist

[bonzos-number-1-fan]

TMAGP 19 Thoughts: Bad Scientist

Another really strong episode, and one with a lot to get into. Probably the densest episode yet in terms of historical context, lore content, and mystery clues. So a lot to get into and no point in any more preamble.

Spoilers for episode 19 below the cut.

Sam and Celia's chat is somewhat interesting. She's now looking into alchemy. It looks like she's looking into the exact stuff Sam was, because she's also looking into the Magnus Institute now. Darrien 2 did a world hop and the Magnus Institute scooped him up so that lead makes sense to follow. Although it's curious that she hadn't done that yet. She's continuing to push Sam to keep up that research too. Celia is pretty much always trying to pull people's strings like that. It being such a consistent character trait does bring into question how sincere any of her actions really are with the rest of the office.

Before I get into the incident proper, this is going to be a bit of a weird one. There is a lot of historical context and alchemic terminology in this one. As such I'll be quoting the show more than usual to explain and explaining who people are, what they're doing, why it's relevant, etc. Like I said, it's very dense. There are also a couple of points of interesting grammar to mention as well which would be missed without the transcripts.

The incident's format is a letter from Robert Hook to Robert Boyle who are both Fellows of the Royal Society. Which is a lot of context off the bat. So, Robert Hook was a 17th century polymath who's most well know these days for his work in microscopy with a microscope of his own design, and for his work in helping rebuild London after the Great Fire (which we'll get to). He also did a lot of work on gravity and planetary rotations which ended up being quite foundational to Newton's law of universal gravitation. He wasn't, however, an alchemist. Boyle on the other hand very much was. Widely regarded as the first modern chemist and he's most famous for The Sceptical Chymist, a work that would be hard to overstate the importance of for the field. Hook, Boyle, and Newton all overlapped a lot in a lot of ways outside of these things too, especially in fields like optics and colour theory.

They were all also Fellows of the Royal Society at this stage too. Which to give it its full name is The Royal Society of London for Improving Natural Knowledge. It's general goal is to promote science, offer support to scientists, and helping shape policy. It was only founded in 1660 and so hasn't been around for a very long time at the time of this incident. The Royal Society is also what's being referred to with the numerous mentions of "Good Science". In short, it's about using science for the public good and to aid in further the endeavours of other scientists to that end. So the Royal Society is probably not up to anything nefarious here. Despite the fact that Newton ends up becoming its president later in life.

Another big thing mentioned here and repeated throughout is the "Protocol". Capital P in the transcripts. So, yes, they said the thing. It's not the first time it's come up but both times it's come up it has been standalone. I don't know if I mentioned it in last time but I have a feeling that the "Magnus Protocol" isn't really a thing. There is just the Protocol and it was used against the Magnus Institute. For its full title to be the "Magnus Protocol" it'd likely have to be named after Albertus Magnus, who is a noted alchemist himself, but I think it's more likely that the Magnus Institute is named after him than the Protocol itself. The most interesting detail we get about it though is that whatever the Protocol is it was enacted against London to burn out a plague. Which would mean in this setting the Great Fire of London was deliberately set to combat the Great Plague of London.

So now we're at Newton himself. The gravity guy. But also the laws of motion guy, the calculus guy, the optics guy, and a lot of other guys guy. Of note here is that Newton was a very noted alchemist and theologian. Both fields were large parts of his full body of works. I think Newton is well known enough that I don't need to get into that though. Besides it's not the first time I've talked about him. As a quick reminder of that though Newton was Warden and Master of the Royal Mint. At the time he served in those roles the Royal Mint had moved out of the Tower of London to Royal Mint Court. Which is where the OIAR is currently located.

Okay for our first quote we have this:

It was only through the Protocol that we were spared from that Dread emission and I fear that such an act is once again required

The capitalisation there is how it appears in the transcript. Protocol we've talked about but "Dread emission" is very interesting. The capital implies that it's the name of something. Which I would wager is either one of, or the whole of, forces Lena mentioned that need to be kept in check.

Then we get to Newton's work proper with this:

he had finally perfected the work of Wilhelm Homberg to produce what he termed the Arbor Philosophorum Perfecta.

Which is very interesting for a number of reasons. Arbor Philosophorum, the Philosopher's Tree, or Diana's tree is a real thing. It's a dendritic amalgam of silver and mercury. Basically meaning it's a metal who's crystalline structure grows to resemble a tree. Wilhelm Homberg is German natural philosopher that wrote a fairly simple recipe for this process and while it's not known if Newton ever attempted it we do know he had a recipe for this. Although it's actually George Starkey's recipe which is a gold mercury amalgam instead. What's more important is that Diana's tree was thought to be a precursor to the philosopher's stone itself. So Newton has basically perfected something of similar nature to it. With some fairly fucked up results, as we'll see.

Out next quote is Latin:

de ligno autem scientiae boni et mali ne comedas in quocumque enim die comederis ex eo morte morieris

Which is Genesis 2:17, and in English (NET) it reads:

but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will surely die.

Because, as noted, Newton was a theologian too. People probably think of him as a rational scientist atheist type but back then there wasn't as much conflict between the two. He was a devout, if not exactly orthodox, Christian.

Christian or not he's playing God a little. We get to see what the fruit of his labours are and it's not looking like good science at all.

such a creature must by all natural law lack that essential and ephemeral anima that is required for such awful knowledge I tell you here Robert, it saw me and it knew me.

So this is an interesting thing to say. Anima in this context isn't the Jungian syzygy but something more akin to "spirit". The anima has a lot of overlap with the tria prima. Which I've spoken about a fair bit before but is an alchemical concept that sulfur, mercury, and salt embody three fundamental principals, but also defined human personality. Mercury is spirit and is related to concepts like morality, imagination, but most importantly for us higher reasoning. A lot of emphasis is placed on the dog's knowledge and Diana's tree, the catalyst for this transformation, is a silver mercury amalgam. So it looks like Newton found a way impart spirit onto something.

There is also this:

I propose that we enact the Protocol but limit it only to his laboratory, destroying his research and correspondence

Fun fact: the dog Newton is experimenting on is likely Diamond. Diamond has a lot of stories about him. The most important one is that he burned about 20 years worth of Newton's manuscripts.

And that's that. Quite a lot to break down as I said. But we're not quite done.

Sam talks to Alice about the computers listening to them. Which isn't the first time he's had that thought but it's nice to see him bringing it up. Alice is very Alice about it but Sam is at least trying to figure things out.

Lena and Gwen have a Lena and Gwen conversation about Lena sending Gwen to her probable doom. But Starkwall is mention again. Nothing too interesting to say on it though.

We finally get more of Colin. It's been too long. He obviously know's Freddy is listening in at this stage but what I want to focus on is the last two sentences here:

No, what I need is to not be seen. He sees too much already. Doing mummy and daddy Stasi proud, I’m sure. Not that anyone cares as long as it all balances, right? Not too much mercury or the world ends, not too much sulfur or we all go mad…

So as I was just talking about the tria prima, here it is again. Sulfur is the soul which is emotions and desires. Which lines up fairly well with how Colin describes what too much of it would do. But this whole thing seems to tie into Lena's talk about balancing forces. Which makes a great deal of sense as the alchemical symbols for the tria prima, along with the philosopher's stone, all appear in the OIAR's logo. How Newton ties into that remains to be seen but there is a very large link there. The mention of the Stasi is also sort of interesting here. For those that don't know the Stasi are the East German secret police. Germany has come up a few times before with Freddy having German source code, Klaus being a German, and most relevant to this in the ARG the largest body of text was a usenet group about people leaving East Germany. Which then ties back into Colin as one of its member hacked the OIAR, and also seemed to be helping out jmj.

Okay, all done. Now it's time for more of the same but nerdier and unhinged.

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Incident/CAT#R#DPHW Master Sheet and Terminology Sheet

DPHW Theory: 1137 is very reasonable. Just a Weird thing that was very weird and had a little bit of mental manipulation to it which looks to be Helplessness' purview. It's also more weight on my idea that 1 is the floor with 0 being the ceiling and counting as 10. There was nothing in the supernatural element of this one that had any strong resonance with Death or Pain as concepts or themes. If 0 was the floor I'd expect to see it for this one.

CAT# Theory: CAT13 is a great a CAT#. It's exactly the sort of thing I was talking about in the essay on why it's not Person/Place/Object. The supernatural "person" here is either Newton performing the magic, or the dog that's the subject of the magic. The object is the crystal that induces the transformation. Which is a virtually identical setup to the tattoo incidents but those aren't CAT13. They're CAT3, CAT23, and CAT1. It's continuing that trend of data that you can explain in isolation but becomes incongruous when taken as a whole.

Anyone that's read most of these rambles will have heard me mention the notion of CAT# being related to the tria prima. It's something I talked about when the first couple of eps came out. Colin mentioning sulfur and mercury is a fairly overt reference to it, and Diana's tree is a silver mercury amalgam. In relation to CAT# it's always been something that felt right. What tria prima describes and how CAT# works would go hand in hand for this sort of thing. Now, I'd be a hypocrite if I clung to the idea just because it felt good. So I quickly discarded it because episodes didn't line up will with it pretty early on but it might warrant a fresh look. I might have been right but with too little data to see the pattern.

The way Colin talks about it also ties in with another idea I've floated that CAT# is about the domains of either three entities, a triple deity, three purviews multiple entities share, or that each combination is an entity that's a portion of a whole. Lena's comment about the OIAR balancing forces would obviously tie into that notion too.

R# Theory: Rank BC is about what I expected on this one. It's not something you'd think happened but it's at least backed up by a historical account of someone well known. So more weight behind it than a letter about a mass hysteria event, but still in the realms of "yeah, nah".

Header talk: Transformation (canine) -/- growth (Crystalline) is bonkers. Transformation (Canine) you would think is a Transformation that is somehow canine in nature. Transformation (Eyes) isn't just your eyes. So, if this is correctly filed, dogs have their own subsection that encompasses all of transformations that occur to dogs. Any transformation, regardless of what it does, so long as it transforms a dog would be Transformation (Canine)? Growth is fine. It grew root-like things/Diana's tree is grown. So it makes sense. Although I'm not sure it's the most compelling crosslink when it was doing the whole "know the nature of you" thing. Crystalline on the other hand is madness. Sure, Diana's tree is a crystal but it's formatted like the subsection of a crosslink. Or a sub-crosslink, I suppose. Which hasn't been implied to be possible thus far and if it is possible why don't they all include it? Surely this helps with the problem in specificity that was mentioned in the very first episode? This one feels the most like a misfile so far. No format again either.

[eclipsellium]

Sirius A and B taken on 13th December 2005 by Hubble Space Telescope

Sirius A is well known for being the brightest star in the night sky and a part of the constellation Canis Major. However, its binary partner, Sirius B was only discovered in 1862.

Ever since the creation of Newton’s law of universal gravitation, star mechanics became not only descriptive, but also predictive. Sirius A’s path across the night sky was unexpected. It wasn’t a straight line, but rather oscillated across its path. This caused many scientists to suspect that Sirius A had a binary partner.

Sirius B was first observed by Alvan Clark, who was testing a new telescope at the time. This was later on confirmed by other telescopes.

Sirius B is a white dwarf, while Sirius A is a main sequence star, meaning it is much larger and much brighter. 1000x brighter than Sirius B, in fact.

In the photo, Sirius A is in the center (although there are some effects due to the instruments) and Sirius B can be seen in the lower left.

[xyymath]

Real-Life Uses of Calculus

Calculus isn’t just an abstract, ivory tower concept relegated to textbooks—it’s a powerful tool woven deeply into the fabric of our daily lives, from the precision of medical dosage to the unpredictability of the stock market.

1. Medicine: Optimizing Drug Dosage

Calculus plays a key role in pharmacokinetics, the branch of science that deals with the absorption, distribution, metabolism, and excretion of drugs in the body. When doctors prescribe medication, they need to ensure that drug levels remain within therapeutic bounds, not too high to cause toxicity and not too low to be ineffective. This is where differential equations, a core part of calculus, come into play. The rate of change of drug concentration over time is modeled with calculus to determine optimal dosage and scheduling for sustained, effective drug levels.

Take antibiotics, for example: they must be administered at specific intervals to maintain an effective concentration in the bloodstream while preventing bacterial resistance. Calculus allows for the continuous monitoring of drug levels and the adjustment of dosages based on individual metabolism rates, ensuring maximum therapeutic benefit.

2. Physics and Engineering: Motion and Forces

In classical mechanics, calculus is used to describe motion. Newton's laws of motion and universal gravitation are based on derivatives and integrals, the foundational elements of calculus. The change in velocity (acceleration) is the derivative of position with respect to time, while the area under the velocity-time graph gives us the distance traveled.

For instance, when designing cars, engineers use calculus to model the forces acting on the vehicle, such as friction, air resistance, and engine power. Calculus helps optimize everything from fuel efficiency to safety features, ensuring that a car can handle various conditions without exceeding performance thresholds.

3. Economics and Finance: Predicting Stock Market Trends

In economics, calculus is used to understand and predict market behavior. The concept of marginal analysis—examining the effects of small changes in variables—relies heavily on calculus. For example, marginal cost is the derivative of total cost with respect to quantity, and marginal revenue is the derivative of total revenue with respect to the quantity of goods sold.

In the stock market, calculus is utilized in quantitative finance to model stock prices using stochastic differential equations. Techniques like Black-Scholes for options pricing rely on calculus to determine the fair price of financial derivatives by analyzing how small fluctuations in stock prices impact their expected value. The concept of risk management—how much risk is worth taking for a given return—also uses derivatives to evaluate the rate of change of potential outcomes over time.

4. Environmental Science: Climate Modeling

Climate change models are inherently tied to calculus. Calculus is used to model the flow of energy through the Earth's atmosphere, oceans, and land, and how this energy affects global temperatures. The change in temperature over time is governed by differential equations, accounting for factors like greenhouse gas emissions, solar radiation, and ocean currents. As a result, climate scientists use calculus to predict future climate scenarios under various emission levels, helping inform policy decisions on global warming and sustainability.

5. Computer Science and Machine Learning: Optimization Algorithms

In machine learning, algorithms are designed to optimize a given function—whether it's minimizing the error in predictions or maximizing efficiency in a task. These algorithms often rely on derivatives to find the minimum or maximum of a function. For example, gradient descent, a popular optimization algorithm, uses the derivative of a function to iteratively adjust parameters and reach the optimal solution.

In computer graphics, calculus is essential for creating smooth curves and realistic animations. The mathematical process of curvature, which is the rate of change of direction along a curve, is vital for rendering images in 3D modeling and augmented reality.

6. Astronomy and Space Exploration: Orbital Mechanics

In space travel, calculus is crucial in calculating orbits, trajectories, and spaceship velocity. The path a spacecraft takes through space is influenced by gravitational forces, which can be modeled using calculus. For example, NASA’s mission to Mars relied on calculus to calculate the optimal launch window by accounting for the positions and motions of both Earth and Mars, ensuring the spacecraft would reach its destination efficiently.

[sigmaleph]

everyone rightly considers 'Newton invented gravity' as an obvious joke. we all know things fell down before Newton, and his law of universal gravitation told us some about why and how it happens but didn't cause it to become true.

so why are people so willing to make the minimally-different statement that "we wouldn't have [modern convenience that runs on electricity] without Faraday"? he didn't invent electromagnetic induction any more than Newton invented gravity. do people think he's literally the only person in the past nearly-two-centuries who could've figured out his eponymous law? almost certainly not, and yet. surprisingly common sentiment.

[derinthescarletpescatarian]

Trick or Treat! 👻

You get Newton's law of universal gravitation

[dont-f-with-moogles]

Terra Darling 💚 your fake fic ideas are all amazing!!!

🐑 So I couldn't help sending a set of tags for SNK 😉

Can't wait to read the summary!!! (no pressure though! Take your time 😘)

Press My Buzzer, Baby

Rating: Teen and Up Fandom: Attack on Titan Characters: Levi Ackerman / Hange Zoe; one-sided Levi Ackerman / Erwin Smith; one-sided Zeke Jaeger / Hange Zoe Additional tags: #janitor!levi returns  #levihan  #eruri  #zekehan  #AU college/university  #academic rivals to lovers  #meet ugly  #love rectangle  #Hange Zoe is Mess  #Levi Ackerman is a tease  #Erwin Smith is whipped  #science pick-up lines  #teasing  #banter  #tension  #affectionate insults  #accidental flirt  #romantic face punching  #awkward sexual situations  #inappropriate erections  #Levi Ackerman wears glasses 

Summary: “Speaking of Newton’s law of universal gravitation…” Hange purred, leaning their elbow upon the podium, “...if I’m attracted to you then you must be equally attracted to me.”

It’s the annual Inter-departmental Physics Bowl Final. Shingeki Technology College’s team of four are set to face the intimidatingly gifted Zeke Jaeger from Liberio University. Hange is nervous to meet their ex-crush head on, but fortunately Zeke’s brashness has rubbed his colleagues up the wrong way. Forced to quickly make up the numbers on his side, Zeke recruits several members of Shingeki’s site staff as replacements. Janitor Levi returns, only, he’s more than anyone expected.

For Levi Ackerman is secretly a genius.

Zeke’s strategy to fluster Hange and Erwin with his man candy seems to be working, but the competition continues until the Sudden Death round. Facing off against Levi, Hange’s attempts to distract him lead them to realise that playing on others’ insecurities will never be enough to win them the Physics Bowl cup…

[megline]

ᅠ- Who is newton?

ᅠᅠᅠᅠᅠᅠᅠ- Ah, good old Isaac! My friend from Earth. Discovered the law of universal gravitation. Well, I say discovered. I kind of helped him out a little bit.

ᅠᅠ- What did you do?

ᅠᅠᅠᅠᅠᅠ - Climbed a tree.

ᅠᅠ- And?

ᅠᅠᅠᅠᅠᅠᅠ- And threw the apple on his head.

ᅠᅠ- Ah, and that's how he discovered the law?

ᅠᅠᅠᅠᅠᅠᅠᅠ- No, he told me to get out of his tree. I explained the law to him later at dinner.

[aspiramy]

UNIVERSAL LAW OF GRAVITATION OR NEWTON'S SECOND LAW OF GRAVITATION

According to the law, every object in the universe attracts every other object in the universe with the force which is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force is directly proportional to the product of their masses, i.e, F ≈ m1 x m2.

F = (G x m1 x m2) / d²

where F is the force, G is the universal constant for gravity, m1 and m2 are the masses, and d is the distance.

IMPORTANCE OF THE LAW

It successfully explained several phenomena which were believed to be unconnected

The force that binds us to the Earth

The motion of moon around the sun

The tides due to moon and sun

The motion of planets around the sun

Rainfall and Snowfall due to this force

Atmosphere of earth is possible due to this.

The prediction of solar and lunar eclipse.

Galileo concluded that the bodies having different masses dropped simultaneously hit the ground at the same time if air resistance is neglected.

g

acceleration due to gravity

acceleration produced in a body freely falling under the actions of gravitational pull of the earth

the value of g is different at diff points of the earth

it decreases as we go higher from surface

G

universal gravitational constant

G is the gravitational force between 2 objects of unit masses seperated by unit distance

the value of G is 6.7 x 10¹¹ Nm² / km²

The value of G does not change with jeight or depth

MASS AND WEIGHT

Mass is the quantity of matter contained in an object. The mass of an object is constant an dir is the measure of its inertia. It can never be zero.

Weight is the force with which the earth attracts an object. It is measured in Newton and it can be zero at the centre of earth. It is a variable and vector quantity.

Sorry for typos !!