grumpymarie

ADDED PULSAR PRESET!
  
but first,
WHAT ARE PULSARS?
pulsars are neutron stars, remnants of collapsed massive stars, that spin realy fast and fire jets of charged particles from their magnetic poles. the jets spin around as the star spins. many also have an “accretion disk” which is just material from a different star or nearby gas that spirals in wards due to gravity.
  
SHELLS:

• added 6 shells, with increasing angular speeds and decreasing ejection speed.
• added randomised jitter to each shell so its not perfectly ring like, and more similar to a real life event. also, you see a different variation everytime you reload the preset cuz of this.
• added a precAngle and precessionStep which adds a bit of randomness to the initial conditions as well.
• the shells are also assigned different colors based on temperature, i did it for the supernova, and it looked really nice, so i added it here as well.
   
  ACCRETION DISK AND STAR:
• accretion disk: there are 5 rings which grow bigger.
• circular velocity is √(G·M/r), where M is the neutron star mass.
• each body gets a random eccentricity as well, using √((1-e)/(1+e)), so the orbits are elliptical, and follow physics.
   
• i also added auto-zoom and auto grid to this preset as well, like the supernova preset
• added pulsars config to DENSE_PRESETS with initial conditions and camscale set to 45.
   
• please see attached video (also you can add new bodies in this sim as well, i didnt show that in this video, but i have for other presets, and you should try it out for yourself!)
   

Changelog

• added pulsar preset

MADE BARNES-HUT SLIGHTLY BETTER!
 

• PROBLEM: if two bodies were at nearly the same place, the tree was recursing infinetely trying to subdivide them. this was causing it to sometimes freeze, which shouldnt matter much, but with galaxy collisions having 500+ it did.
• FIX: i just merged their mass into the existing node and return early.
   
• PROBLEM: child nodes were being created with half = node.size * 0.5 as both their offset and size, which is wrong cuz the offset should be a quarter of the parent to place the child’s centre correctly, and the size should be half
• FIX: renamed it to quarter and fixed the placement. nodes are now correctly placed!!
   
• PROBLEM: opening angle was using node.size / dist < THETA but i should be using the the full width not the half width stored in node.size.
• FIX: so (2 * node.size) / dist < THETA is the correct approximation threshold.
   
  (edit 1: i rly dont know what to add over here for the attachment, so I just i added a video of the pulsar preset)

• added readme and favicon
   

Changelog

• replaced favicon with transparent one
• fixed favicon
• fixed typo and added diff. favicon sizes
• updated readme and added favicon
• added readme

ADDED MP3’s for the tracks!
 

• added the mp3’s for the music tracks, I tried several approaches for this like using cloudinary and git LFS, but those were having play/pause issues and storage issues so I just committed all of them to git, not the most efficient idea, but it works!
   

Changelog

• added mp3’s for the music tracks

REMOVED SPOTIFY INTEGRATION, AND REPLACED IT WITH AN EMBED!
 

• I tried using ai for the Spotify integration but it didnt work because I need Spotify premium for the WebAPI so a lesson to not use ai I guess. I replaced it with a spotify embed.
• I also rewrote the playTrack function properly. before, it was just showing a the toast, and audio wasnt playing ;(
• I also updated the tracks - cafe scape, forest scape, lofi, white noise and classical music on a deadline and also added art for the tracks (this art is not mine, just images found on the internet- the rest of the art mentioned is my art tho).
   

Changelog

• removed spotify integration and added an embedded playlist

SPOTIFY INTEGRATION, and CAT WIDGET!
 

• I rewrote the css to use custom properties instead of the hardcoded colors.
• added a custom art background overlay of coffee beans.
• added a theme switches to support both the dark and light colors. also added three new background colors, mist, dark roast, and forest.
• added a spotify integration (that doesnt currently work), I did use AI for this cuz I couldnt for the life of me figure out why. (FUTURE UPDATE: its for Spotify Premium users only- the API, so I scrapped that completely later on, and just switched to an embed)
• added task per sessions, so you can allocate the no. of session required for a particular task.
• added a cat widget in the corner, on click, it bounces? and shows a random message using toast!!
   
  FIXES:
• fixed the cup update so that it only swaps the image when the image actually changes and now unnecessary DOM changes arent required.
• fixed the toast function, it was creating a new element instead of updating the existing one.
   

Changelog

• integrated spotify, added cat widget and some fixes

ADDED SIDEBAR TABS, SETTINGS, AND BACKGROUND COLORS!
 

• added tabs to the sidebar for settings, music and tasks.
• added settings tab with editable timer durations for focus, short break and long break. session dots are rebuilt according to the no of sessions.
• added notifications
• added background swatches to choose from for the background color in the settings panel. also added toggles for auto start break after focus and auto start focus after break.
• added a music tab, with tracks like lofi, jazz, cafe scape, classical.
   

Changelog

• added music, and the settings panel

ADDED CUP ART, CUPS FILLING AS THE SESSION PROGRESSES AND BUG FIXES!
 

• added the coffee cups (yes, I drew them- rather poorly, but nonetheless)
• the cup fills up as the session progresses (the images change based on the % of the session, so the cup is filled 25% of the 25% mark, so on and so forth)
• made the cup also clickable as play/pause button cuz why not? I felt like it should do something.
• fixed the borders, made them a bit bigger
• added checkboxes, hover and strikethrough (when completed) for tasks.
   
  BUGS FIXES:
• I put break-msg in one place, and break-message, I think somewhere in HTML and somewhere in JS, dont remember where I put which, but in short there was a mismatch in the id and the function wasnt working, so I fixed that.
• fixed the sidebar, it had a wrong color value (dot instead of a comma in the rgba) which was causing the section title to be not visible.
   

Changelog

• added cup art and fixed bugs

I was so burnt out from my last project so I wanted to make something that didnt need a whole ton of maths and physics, this is supposed to be that, something that brings me joy <3.
⠀
its a coffee themed pomodoro timer.

• added modes (focus- 25 mins, short break- 10 mins, long break- 15mins), and after every session a pop up asks you to take a break.
• after every 4 session, you’ll be asked to take a long break- 15 mins.
• added session dots at the bottom, they track where you are in the cycle of 4 sessions.
• task list right now, is a plain array and re-renders on every change, so ill fix that in the next commit
• basically added all the groundwork, the actual timer, some of the foundational css, js and stuff.
  ⠀
  TODO:
• the task list re-renders when a new task is added, so fix that
• add custom cups that fill up as the session progresses
  ⠀

Changelog

• first commit

UPDATED README, AND POLISHING!!
 

• updated readme to include info. about the new presets (figure-8, galaxy collisions and supernova scatter), barnes-hut algorithm and velocity verlet integration
• made minor changes to barnes-hut algorithm to make it more efficient
• fixed the barnes-hut toggle (css fix: display: block to flex)
   
  IMP. NOTES
  this is my last devlog, before shipping, so a couple things to note:
• the attached videos include how to use this website. some people found it difficult, and conveyed it during voting, so I attached these videos again (these are only for n-body and for some specific presets, but the rest of the website works similarly and I hope you can figure it out, if not, you can go back a couple devlogs and videos are attached for everything thats been added) . and if there’s anything else I can do to improve, lemme know!!
   
• please try using chrome with the website, all other browsers work, but I have found they lag a bit more (safari especially) for one specific n-body preset: galaxy collisions, with trails toggled on. basically, it works with all major browsers, but please try using chrome if you experience any issues (tho you wont, I tested it with all major browsers- Firefox, safari, brave and chrome)
   
• if the galaxy collision preset is lagging for you quite a bit (tho some lag is expected- its 500+ bodies, so dont worry about that), please toggle off the trails. dont toggle off barnes hut or velocity verlet while using this preset. it will lag A LOT. ive only given the option to toggle it off for people who wanna see what happens. but you have been warned, your browser will lag alot.
   
• toggle states are retained even when preset is reset. so make sure that if you toggled smthing like auto-zoom off, to toggle it on again for the experience? idk what to call it. but you should try it for the supernova preset included in n-body. just dont scroll or drag if you want auto-zoom (cuz I assume you’re trying to zoom into or look at smthing specific) so auto-zoom toggles off automatically (and remains toggled off til you toggle it on again).

ADDED SPIRAL ARMS, AUTO-ZOOM and FIXED THE GALAXY PRESET LAG!!
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SPIRAL ARMS:

• the galaxy rings were perfectly circular before, and every star was placed at exactly the same radius, and evenly spaced. not how galaxies actually look.
• real galaxies have “arms” because of density waves and orbital resonance. you can achieve/fake it in an artificial setting by offsetting each ring’s starting angle by a certain amount (spiralTwist) and add a jitter.
• also increased the number of stars per galaxy, it was looking too sparse, and with more bodies you can see tidal trails become more apparent.
   ⠀
  GALAXY PRESET LAG:
• PROBLEM: with 500+ bodies, drawScene was calling ctx.createRadialGradient once for every body, and every frame. for 500+ bodies, so that’s a radial gradient created, filled and erased 500+ times per frame. so it lags. A LOT.
• FIX: very obvious, to only render the glow for a certain amount of bodies, and skip for galaxy collision preset (we are not rendering the gradient for 500+ bodies) .
  ⠀
• PROBLEM: the trails were doing the same thing, recording a trail every dubstep for every body. for more than 500 bodies its 500 * 8 =4,000 trail points written and drawn.
• FIX: added a trailSkip variable that only records trail points every 5th frame for the galaxy preset.
  ⠀
  SUPERNOVA PRESET UPDATES:
• added two more shells
• added a noMerge flag to the remnant and the fragments. previously, the collision handling was treating slow inner fragments as colliding with the remnant and absorbing it. this was wrong. so, noMerge skips mergeCollisions.
  ⠀
  AUTO-ZOOM:
• the supernova ejecta travels upto 12AU/yr . at the default timescale the outer shell exits the view within a few seconds and then you have to manually zoom out.
• added auto-zoom, which tracks the furthest ‘alive’ fragment from the origin and adjusts camScale toward a target thats keeps everything in frame (well actually, it tries to keep the outermost fragment at 35% of the canvas width).
• VERY IMP NOTE: auto-zoom auto disables when you manually drag or scroll (because you clearly wanna zoom in and out and see something) so, when then if you wanna enjoy the ‘experience’?? of auto-zoom you should toggle it on again and stop manually dragging or scrolling.
• on reset, the toggle state is preserved.

ADDED GALAXY COLLISION AND SUPERNOVA PRESET!!
  
so the last two devlogs, and commits, were for this. we have a lot of bodies in play for these two presets, so O(n log n) is actually worth the effort!
 
GALAXY COLLSIONS:

• each galaxy has a core and eight rings of stars. 282 bodies per galaxy. the initial conditions are a prograde -retrogade pair where galaxy A spin clockwise and galaxy B spins counterclockwise. this produces tidal stream. the prograde disc stretches during approach and retrograde gets compressed.
• circular orbital velocity for each star is set at √(G·M/r) where M is the core mass only, as starMass = 0.003 is negligible. this gives each ring a stable orbit around the core before the collision starts.
   
  SUPERNOVA SCATTER:
• When a massive star exhausts its fuel, the core collapses and the outer later are blasted outward. Left behind, is a dense remanant (neutron star or black hole). This preset starts right after that explosion, with a remanant at the centre, and shells of debris flying outward. The remanant’s gravits gradually pulls some of it back, but the fastest fragments escape.
   
• 4 ejecta shells at diff speed, a slower inner shell, an iron-group middle shell, a carbon layer, and then a outer layer. each shell has a different mass per fragment. the spread within the shell is randomised so its more like a cloud and less like a ring.
   
  MINOR FIXES:
• substeps added to verlet (4 to 8). the galaxy collision preset needed the extra subsets to maintain accuracy during closest approach.
• updated panel so that it now skips noLabel bodies when more than 60 bodies are alive so it actually remains useful and its not showing 500+ bodies named ‘star’.

FIXED BARNES-HUT AND VERLET INTEGRATION, ADDED FIGURE-8 PRESET!!
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first, let’s cover figure-8 and then we’ll cover my stupid mistakes.
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FIGURE-8 PRESET:

• in 1993, mathematician Cris Moore discovered that three equal masses can follow each other in a figure-8 forever. and it’s perfectly periodic as well.
• but it can only happen in very special initial conditions, and its the most sensitive among the three-body problem cases, which is why barnes-hut has to be disabled for this. even minor errors cause the orbits to drift, and the figure-8 pattern to be break.
  ⠀
• initial published conditions had G = 1, but sine this simulation uses G= 4π² (AU). velocities should then scale by, √G, so the published values needed to be multiplied by 2π.
  ⠀
  BARNES-HUT FIX: (see the prev. devlog before reading this to understand the Barnes-Hut Algorithm)
• BUG: In bhInsert , when a leaf node needed to be sub-divided, I was calling bhInsert recursively on the existing body to push it down, which re-updated the COM a second time. the existing body’s mass was being counted twice in every ancestor node.
• FIX: I had to separate the functions properly . bhInsert now only updates COM and mass, and then bhSubInsert routes the body to the correct child quadrant. I also added a depth limit of 50 for the recursion, for the edge case that two bodies end up in almost the same place.
  ⠀
  VELOCITY VERLET FIX:
• BUG: ax and ay weren’t being initialised when loading a preset, so on frame verlet would use whatever was in memory and bodies would jump to random positions. verlet needs to store accelaration b.w steps, the first half-kick uses the acc. from the previous step so you cant recalculate it as well.
• FIX: added ax and ay fields to Body.

ADDED BARNES-HUT ALGORITHM AND VELOCITY VERLET INTEGRATION!!
⠀
THE PROBLEM:

• before this update, every body in the simulation would calculate the gravitational pull from every other body, which is n² force evaluations per step.
• I am thinking of adding galaxy collisions next, and for a galaxy with a 100 stars, O(n²) isnt great, it would lag a lot and would even more on a higher timescale.
  ⠀
  THE SOLUTION: BARNES-HUT
• good news tho! this problem has already been solved cuz its really well known in astrophysics.
• the solution is to treat distant groups of stars as a single mass. a cluster of stars about 50 AU away pulls on an object almost the same way whether you calculate each one individually or use the entire cluster’s total mass at its centre of mass (COM). the error is miniscule. and it becomes O(n log n).
  ⠀
  BARNES HUT ALGORITHM:
• barnes-hut requires building a quadtree over all the bodies at the start of each step. then the tree sub-divides into quadrants until each cell contains at most one body. then for each body, you walk the tree. if a cell is far enough that its angular size is below a threshold θ (0.5 in this case), you stop recursively calling and treat the whole cell as a point mass. if its too close, you continue. the approximation error is a great deal under 1% and its O(n log n) from O(n^2). a great deal faster!
  ⠀
  THE PROBLEM:
• energy conservation using RK4 integration is very accurate but not symplectic. in a conservative system you want an integrator that preserves the geometric structure of the physics. without that, the errors leak energy in and out of the system, which means if you run a two-body orbit for a long time, with a non-symplectic integrator and it would spiral or drift because of floating point errors adding up over time.
  ⠀
  THE SOLUTION: VELOCITY VERLET is symplectic.
• velocity verlet is a lot simpler than RK4, half-kick the velocity with the old accelaration, drift the position, recalc. acceleration, and then half kick again.
• its called “symplectic” because it conserves energy for a long time which means orbits stay stable which is important for galaxy collisions.
  ⠀
• toggles for both barnes-hut and velocity verlet are independent and you can run any combo of integrator and force method. RK4 and direct force calculation stay the same, but you do get the option to switch! (velocity verlet and barnes-hut will be auto-toggled on for some presets, but you can toggle it off, at your own risk ofc- your browser will lag).
  ⠀
• minor bug fixes- the velocity vectors were a bit too small, so I scaled them a tiny bit up, there was also a bug in the energy panel readout, so I fixed that aswl.

UPDATED README, REPLACED PLACEHOLDER TEXT, AND FIXED CSS BADGES
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• updated readme to reflect new simulation “Lagrange Points” being added.
• replaced all mentions of placeholder text or lorem ipsum dorem with appropriate text.
• changed nbody, hohmann and index to include lagrange points page in the nav-bar.
• fixed orbit and stability of L4/L5 not being shown in the system panel readout.
  ⠀
  UPDATE: I removed the animation toggle, because the animation playing or not can be paused or played using the speed slider. I couldn’t devlog this change as it was less than 15 mins. (images do not reflect this change, but it is a minor one, so you can test it in the demo)

SOME POLISHING AND CSS CHANGES:

• the newton() function defined inside solveLP() got redefined on every call, so I moved it out. I also added a condition to avoid singularities.
   
• fixed the canvas zooming in infinitely on refresh - that took maybe an hour :(

ADDED ORBIT ANIMATION, POTENTIAL HEATMAP AND MORE SYSTEMS!!
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EFFECTIVE POTENTIAL HEATMAP:

• in the rotating reference frame, you can define an effective potential, a scalar field that adds the gravity from both bodies with the centrifugal term (Ω(x,y) = -½(x² + y²) - (1-μ)/r₁ - μ/r₂). the five Lagrange points, as stated in the prev. devlog, are the saddle points of this field.
• this allows to visualise why the points exist, cuz bfr I was only showing their positions.
   
• the potential is sampled at every pixel on the grid and mapped to a blue color ramp and then written to an offscreen canvas usingImageDAta, pixel by pixel (doing it using shapes takes too long)
    
  ORBIT ANIMATION:
• added orbit animation!!! now m2 moves around m1. the lagrange points also move since theyre relative to both bodies.
• also added a stability indicator, L4 and L5 are only stable if the mass ratio is > 25. below thats the equilateral points are also unstable. the panel shows green or red if the system selected satisfies this.
   
  ADDED 4 SYSTEMS:
• added Earth-Moon, Sun- Jupiter Sun-Mars and Sun-Venus systems as well. the sidebar also shows examples and a bit about each lagrange point in the system as well!

ADDED LAGRANGE POINTS!!
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WHAT ARE LAGRANGE POINTS?
yet again, im so happy you asked this!

• in a two body system, lets consider the sun and earth there are five special positions where a third smaller body (think asteroids, satellites) can sit in a stable (or semi-stable) position relative to the system. this basically means it doesnt move, without requiring constant engine burns.
• eg: at L2:- James Webb Telescope, L4/L5- Trojan asteroids.
  ⠀
  ROTATING REFERENCE FRAME:
• Lagrange points only exist in a rotating reference frame, this means that if you look at the sun-earth system from a frame that rotates with the Earth’s orbit, both bodies appear at rest.
• in this frame, you get pseudo-forces, centrifugal force and the coriolis force, and when they are added to gravity, the resulting effective potential has five saddle points. those are Lagrange points.
  ⠀
  L1, L2, L3:
• L1, L2, L3 lay on the line connecting the two bodies. there positions come from the variations of the equation of effective potential, again, there is no closed form solution for these equations so I solved them numerically using Newton-Raphson method (see devlog for Hohmann transfer, its used for Kepler eq.).
• for L1 and L2 the initial guess uses Hill sphere radius (∛(μ/3)), which is the approx radius of the sphere where m2’s gravity is dominating. this allows for a starting point for the iteration to converge.
   
  L4/L5
• L4 and L5 sit at the vertices of equilateral triangles formed with the two masses, so their positions are (0.5 - μ, ±√3/2). there is no further solving required for these.
  ⠀
  MU PARAMETER:
• everything in the frame is normalised using one parameter, mu (reduced mass ratio- μ = m₂ / (m₁ + m₂))
• for the sun-earth system, mu will be very small as the sun is so much bigger in comparison.
• all five langrange points are then functions of mu which means the same thing works for any two body by changing the mass ratio.

SMALL FIXES, FAVICON AND README!! FINAL DEVLOG BEFORE SHIPPING
⠀

• replaced placeholder text
• fixed minor css bugs (gravitas, written on the navbar of the Hohmann page, was grey instead of intended green)
• added favicon
• added README

ADDED ANIMATIONSS KEPLER SOLVER AND BADGES!!
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ANIMATIONS:

• finally added the canvas animation!! now you can see the bodies involved in the transfer moveee
  ⠀
  KEPLER SOLVER:
• PROBLEM: I was moving the spacecraft at a const. angular speed along the ellipse. because of that, it was moving too fast near the sun, and too slow at the far end.
• ideally, the spacecraft should move fast at periapsis and slower at apoapsis (Kepler’s 2nd law: equal areas swept in equal times)
  ⠀
• FIX: I needed to convert mean anomaly to true anomaly, because mean anomly increases linearly with time, which is what I had. true anomaly is the actual angle.
  ⠀
• the relationship between them goes thru eccentric anomaly thru Kepler’s eq. (M = E - e·sin(E)). but you cant solve directly for E so I had to implement Newton-Raphson Iteration.
  ⠀
• also added a trail, which draws the last N steps of the path with increasing opacity.
  ⠀
  BADGES:
• also added a phase badge that shows current state of the mission (WAITING, BURN 1, BURN 2, ARRIVED.)
  ⠀
  SLIDER:
• added animation speed slider to control the speed of the animation.
• I had to scale the the real elapsed time by speedMult × (transferDays / 20) so a slow transfer and a fast one would take about the same time real life time (at normal speed). otherwise, earth to mercury wld barely be visible and earth to Neptune would take FOREVER.
  ⠀
  BUG FIXES:
• fixed the scaling bug which was causing the centre body become massive and eat the inner orbit. clamped the body radius to 35% of the inner orbit radius.

SATELLITE MODE!!!!
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PROBLEM: the planet to planet tab works in AU and yrs which is fine for interplanetary transfers but not for satellites cuz then AU doesnt work and you need km. so I added another mode.
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THE FIX:

• planet to planet remains the same but I added another tab: Satellite mode.
• added buttons to pick the central body
• add type in field to enter both altitudes and angle
• the vis-viva eq we discussed before remains the same but now uses μ instead of the AU version.
  ⠀
  INCLINATION:
• PROBLEM: the planet tab assumes that all orbits are coplanar , satellite manoeuvres however also require a plane change
• FIX: combined the plane change with the second burn. this can be done using the law of cosines √(vt² + vc² - 2·vt·vc·cos(Δi)) - vc
  ⠀
  DEFAULTS:
• each body has its default values when you select it.
  ⠀
  BUG FIXES:
• If you call offsetWidth on a panel that was just visible, it read zero. requestAnimationFrame delay fixed that.

HOHMANN TRANSFER!!
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What even is a Hohmann transfer?
THANK GOD YOU ASKED CUZ I HAVE A BUNCH OF UNTRACKED RESEARCH TIME TO SHOWCASE
⠀

• its the MOST efficient way to move a spacecraft b/w two circular orbits. you fire the engine twice, once to leave the first orbit and enter an elliptical transfer orbit, and once when you arrive at the second orbit to circularise.
• missions you know and have heard about use this. the mars transfer windows and stuff… this is it.
  ⠀
  MATH:
• the eq is the vis-viva eq. v = √(GM(2/r - 1/a)). it gives you the speed for the object at any point in the orbit. because for a circular orbit r = a, the equation can be simplified to v = √(GM/r).
• a Hohmann transfer has one focus at the sun, periapsis touching the inner orbit and apoapsis touching the outer one. so, on the canvas the sun is the centre, and the ellipse isnt centred but offset by a focal distance (c = ecc * a). so, to account for that we docx - c before drawing the ellipse.⠀
  ⠀
  PLANET BUTTONS:
• added buttons to pick the arrival and departure planet
• you cant pick the same arrival and departure planet (added classList.toggle('disabled'))
  ⠀
  CANVAS:
• started drawing the orbits for the transfer
• the two delta-v burn points are marked with points, amber for departure and blue for arrival (labelled).
• the arrival planet is placed at the phase angle (the angle is needs to be at so it arrives at the right spot)
• the stars on the canvas are seeded deterministically rather than than Math.random(), so they stop flickering every time the canvas redraws.

ADDED LANDING PAGE + BUG FIXES!!
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LANDING PAGE:

• added a landing page (finallyy!!)
• the background is a live canvas animation (see attached video)
• a twinkling stars background aswl
• a card list listing all the sims available (nbody, and Hohmann -to come)
  ⠀
  CUSTOM CURSOR:
• added a custom cursor, a small green dot
• on hover, it becomes bigger with a glow
  ⠀
  BUG FIXES:
• fixed the font in nbody + some other small fixes

for now, all the text is just placeholder text, but I plan on changing that right bfr shipping

CSS UPDATES, BINARY STAR PRESET, VELOCITY VECTORS… AND MORE
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CSS:

• rewrote the css with a sticky navbar, blinking status, diff button types, panel components, badges, a scanline overlay, etc.
• also restructured nbody.html
  ⠀
  ENERGY PANEL:
• PROBLEM: now how would YOU know the simulation is working right?
• FIX: YOU TRACK ENERGY CONSERVATION! if the energy drifts too far from its initial value, then the integrator is accumulating error.
• added energy panel to show kinetic energy, potential energy, total energy and angular momentum.
• also added a little bar at the bottom of the panel that shows how much the total energy has drifted from its initial value
  ⠀
  BINARY STARS PRESET:
• added the binary stars preset
• this took A LOT of UNTRACKED time. It took so much research but I’ll try to summarise why this took me so much time.
  ⠀
  basically for this preset, two stars need to orbit their shared centre of mass, not the origin . so, you have to calculate where the star sits relative to its barycentre.
  the orbital velocities were also headache inducing to get right. you need the relative velocity of the circular orbit and then each star gets a fraction of that.
  ⠀
  VELOCITY VECTORS:
• each body gets an arrow showing the direction and the magnitude of its velocity.
  ⠀
  GRID:
• add a grid toggle because it gives a sense of scale, each square is one AU. (I got lost on the canvas and each body I placed was outside 50 AU and so I had to reset the sim.)
  ⠀
  COM Tracking:
• added centre of mass tracking. the camera follows the system,’s barycentre (barycentre: mass weighed av. position)
• I kept getting the sign wrong because of the flipped y-axis.
  ⠀
  ADAPTIVE SUBSTEPS:
• when bodies get close to each other the integrator auto. takes smaller and smaller step to maintain accuracy.
  ⠀
  CONTROLS?
• added play, pause, step, and a timescale slider.

COLLISIONS, SOFTENING, CLICK-TO-ADD BODIES AND TRAILS
‎⠀
COLLISIONS:

• PROBLEM: bodies were just passing through each other, so COLLISIONS.
• FIX: added inelastic merging for collisions. when a bigger body gets closer to the smaller one it swallows it and gets bigger (radius is capped however)
  ⠀
  BODY ESCAPING:
• also added a body ejection threshold and notification, so when a body escapes beyond 50AU, it disappears and you get a notification for the same.
  ⠀
  SOFTENING:
• PROBLEM: when two bodies got close to each other the force calculation would tend to infinity (dividing by distance approaching zero, causes acceleration to tend to infinity and bodies go ZOOMINGGG)
• FIX: add a ε² term (0.001) to the denominator of the force eq. , so it never reaches 0 (or tends to 0).
  ⠀
  CLICK-TO-ADD BODIES:
• when you click anywhere on the canvas (not beyond 50AU tho), a new body is added over there.
• I also added option for the size of the body (try adding a star, a lot of things happen then… OOOH GRAVITY)
• also added a dropbox to pick HOW the body is added. basically, most of the time a body with Zero Velocity will fall into the nearest star. so I added Random and Circular Orbit. The default mode, Circular Orbit computes circular orbital velocity at that point, relative to the nearest massive body. Orbit eccentricity can also be adjusted, which leads to more keplerian orbits.
  ⠀
  TRAILS:
• each body keeps a history of its prev. 500 positions and I connect them using a using a line. the trail also fades gradually as it is tied to how old the point is.
  ⠀

ADDED RK4 INTEGRATION AND CAMERA CONTROLS
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• Euler was causing energy drift so added replaced with fixed step RK4.
• getDerivs() temporarily overwrites positions so accel() can be evaluated at intermediate stages, then it restores them. (this took me so long to figure out… the bodies were teleporting because I forgot to restore.)
• you couldnt see outer planets before, so I added cursor anchored zoom and pan
  ‎‎
  so now…, you can see all the planets (and bodies in the future) cuz I added zoom and pan.
  orbits are now stable long term!!
  ‎‎‎
  TODO:
• add gravitational softening
• add new bodies on click
• add trails behind bodies

WE NOW HAVE 5 BODIES!!! AND THEY MOSTLY OBEY THE LAWS OF PHYSICS!!
‎

• added Sun, Mercury, Venus, Mars and Earth.
• labeled bodies
• gravity calculated b.w every pair of bodies
• set G = 4π², stable orbits.
• added integration using Euler method, so velocity and position update by (dt).
• real time to sim. time scaling (1 sec = 0.05yrs in sim. time)
• background changes (stars)
• sim. time in corner
  ‎
  basically we got more planets, stable orbits, with gravity working for multiple bodies anddd speeds look realistic relative to each planet.
  ‎
  TODO:
• SWITCH TO BETTER INTEGRATION METHOD FOR ENERGY STABILITY (RK4.. or velocity verlet)
• add trails behind bodies
• update and add back the navbar that I removed in this version
  ‎
  ramblings..
  I have a rough idea on how to add the bodies (like the user adds the bodies… the actual point of this sim). ive also kinda figured out how to implement binary stars, so in theory, at least, I know what to do!!

MADE BLUE DOT GO WHEE AROUND YELLOW DOT
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set up canvas and render loop now works!!
then added two bodies:

• sun in the middle
• small blue body orbiting it with sideways velocity.