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Back to Math and Physics

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

taby

1,511

June 23, 2022 12:03 AM

Looking good. But, the galaxy components are moving too slow. Are you going to take dark matter into consideration?

I read the book Galactic Dynamics, but I lent it out.

taby

1,511

June 23, 2022 04:35 AM

P.S. The more I play with your simulations, the more impressed I become. Great job!

jonny-b

Author

June 23, 2022 02:56 PM

@taby No, I wasn’t considering dark matter. However, I was thinking of how to simulate spatial expansion. Especially for the random distribution scenario. I’d like to slow its collapse without weakening gravity.

None

taby

1,511

June 23, 2022 05:32 PM

Even without dark matter involved, the orbit speed is too slow to form circular orbit paths.

Do you remember my other post where I showed you how to calculate the orbit speed at perihelion?

jonny-b

Author

June 23, 2022 11:27 PM

@taby ya I was just too lazy to figure it out. I just wanted to get things going so I just got them as close as possible. also keep in mind the system drifts due to the rotational velocity of the planets in orbit. This prevents the orbits from looking perfect. Also if your browser is a different size than mine was when I calibrated the orbits they will be slightly off.

None

taby

1,511

June 24, 2022 12:11 AM

It sounds like you have a lot of work in the future. I will see about simulating a galaxy using my own code.

JoeJ

4,266

June 24, 2022 07:59 AM

taby said:
Even without dark matter involved, the orbit speed is too slow to form circular orbit paths.

Not sure what you mean, but maybe the reason is the distance clamping, called ‘constrain’ in the older code. The value was often set very high, like 100 pixels, iirc.
You surely want to make this value as small as possible with the simulation still stable and not adding too much energy from planets which come close to each other.
(The more realistic solutions we had discussed probably won't work, because the radius of plants is too small it would remain stable.)

jonny-b

Author

June 25, 2022 01:23 AM

@taby, I’m not sure I follow what you think the problem is. Can you clarify it a bit? Do you think the solar system is wrong as well?

None

taby

1,511

June 25, 2022 03:19 AM

Well, I suppose that orbits are likely to be elliptical. I just thought that you'd want to simplify the galaxy model by making the orbiting stars move in circular orbits.

taby

1,511

June 25, 2022 03:22 AM

taby said:
Ok, here is the formula:
If you want a circular orbit, you place the object r metres away and set it flying at:
v = sqrt(G*M/r) metres per second

If you want an elliptical orbit, you set it flying at a lesser speed. To calculate the desired speed based on how eccentric the orbit is:
v = sqrt((G*M/r)*(1 - e)/(1 + e))

Alternatively, if you place the object at periapsis:
v = sqrt((G*M/r)*(1 + e)/(1 - e))

This…