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Gravitational acceleration calculation

None · 2022-08-10T15:36:27

I'm getting strange results when calculating the physics between two objects. My goal is to build a galaxy simulator that can simulate how galaxies consisting of 100s of stars might look when interacting. It's a fun little side project and I'm not even sure how it'll turn out (which is part of the fun). I have a really limited background in math and physics so this is a pretty big challenge for me atm. I'm starting with one star and a static object to attract it to nail down the basic physics. The problem I'm facing is that, as star one approaches the static object it's is accelerating as expected and when it passes the object I expect the velocity to slowly bleed to zero and the star to fall back in. However, after passing the static object the star is behaving oddly. Depending on my delta time variable It position sometimes shoots off crazy fast in one direction or another. I'm too new to all of this and there are too many variables for me to follow where exactly the issue lies. As an FYI this is a little web app written in javascript and not an actual video game. However, the concepts are similar to calculating video game physics and most web developer forums aren't helpful. Here is a link to the code in codepen. NOTE: If the “try me” button doesn't appear try shrinking your browser down in size or scrolling down to find the button. Finally, the rendering engine (canvas) doesn't appear to be the problem as I can see the issue in the console as being related to the calculations and not he rendering. let frameCount = 0; let stars; let dt; let gravConst = 6.674 * Math.pow(10, -11); // let solarMass = Math.pow(10, 30); // let lightYear = 9.5 * Math.pow(10, 15); let solarMass = 1; let lightYear = 1; let yearCounter; stars = [ { x: 250, y: 75, m: 1, v: 0 }, { x: 275, y: 75, m: 1, v: 0 } ]; dt = 50000; yearCounter = 0; const render = () => { let canvas = document.getElementById("canvasRef"); const context = canvas.getContext("2d"); let animationFrameId; frameCount++; animationFrameId = window.requestAnimationFrame(render); draw(context, frameCount); }; const draw = (ctx, frameCount) => { // console.log(frameCount) ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height); ctx.fillStyle = "#ffffff"; calculateGravAccel(stars[0], stars); drawStar(stars, ctx); }; let calculateGravAccel = (star, stars) => { // Force on current star by all other star sources (newtons) let m1 = stars[0].m * solarMass; let m2 = stars[1].m * solarMass; let distance = (stars[0].x - stars[1].x) * lightYear; let xDistance = stars[0].x - stars[1].x; let f = gravConst * (m1 * m2) / Math.pow(distance, 2); console.log(f); // Convert velocity to account for the fact that the force is now coming from behind // New velocity of current star star.v = distance < 0 ? star.v + (f / m1) * dt : star.v - (f / m1) * dt; // Position star.x = star.x + star.v * dt; // Ellapsed Time yearCounter += dt; }; const drawStar = (stars, ctx) => { console.log(`x:${stars[0].x} y: ${stars[0].y} v: ${stars[0].v}`); ctx.beginPath(); ctx.arc(stars[0].x, stars[0].y, 5, 0, 2 * Math.PI); ctx.arc(stars[1].x, stars[1].y, 5, 0, 2 * Math.PI); ctx.fill(); };

Math and Physics Programming gravity

Started by jonny-b May 10, 2022 05:04 PM

143 comments, last by taby 1 year, 10 months ago

jonny-b

Author

June 25, 2022 03:37 AM

@taby Cool. Thanks. I'll come back to this after I finish doing the UI! Thanks.

None

taby

1,511

June 25, 2022 04:44 PM

I should have my copy of Galactic Dynamics in hand tomorrow morning. Then we will get to the bottom of this galactic simulation.

jonny-b

Author

June 25, 2022 04:48 PM

@taby, Just for more info. I created the galaxy sim by writing a script for the solar system sim that would periodically output the ‘planets’ position and velocity. I used this data to hydrate the initial galaxy simulation. So the only difference between the two simulations is that there are more ‘planets’/'stars' in on than in the other.

None

taby

1,511

June 25, 2022 07:27 PM

Right. Well, there are falloff functions that are used to describe the mass density. It's these data that you use to initialize the galaxy in terms of point particles. Like, say the density is 0.5 at location x, then one gets a uniform random variable in the range of [0, 1], and if that value is less than than 0.5, then a star belongs there. Repeat 10,000,000 times for various x, or repeat until y stars are made.

taby

1,511

June 25, 2022 08:41 PM

In the meantime, check out:

https://arxiv.org/abs/1307.8215

taby

1,511

June 26, 2022 12:00 AM

Why are you doing this?

taby

1,511

June 26, 2022 06:12 PM

My buddy forgot to bring the book. :( There’s always tomorrow.

Nagle

June 27, 2022 07:16 PM

jonny-b said:
The problem I'm facing is that, as star one approaches the static object it's is accelerating as expected and when it passes the object I expect the velocity to slowly bleed to zero and the star to fall back in.

Orbital dynamics does not work like that. Go play Kerbal Space Program until you get some intuition about how that works.

taby

1,511

June 28, 2022 01:47 AM

There is something called escape speed.

Nagle

June 28, 2022 03:03 AM

You cannot reach escape velocity with gravity alone in a two-body situation. You may get a very elongated elliptical orbit, like a comet, but not an escape.

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Gravitational acceleration calculation

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