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Re: Orbit Physics - Kepler's Laws for Planetary Motion

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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 02:11 PM
I want to take a part and have it orbit around another part - with all the factors of the three laws Kepler had created.

Unfortunately, my Physics year for astro-physics doesn't hit until the next season. I am wondering if anyone here has gone through enough in this field - or just happens to know how it works - to give me an accurate answer.

The farthest, and only accurate equation I have gotten to, is simply using Newton's laws to find the force of attraction between two bodies.

local g = 196.2
local F = g((p1:GetMass() * p2:GetMass())/((p2.Position-p1.Position).magnitude)^2))
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1waffle1 is not online. 1waffle1
Joined: 16 Oct 2007
Total Posts: 16381
16 Jul 2013 02:21 PM
Kepler's laws describe the geometry of gravity based on Newton's laws. They describe how the planets move, not why.
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ukwarrior6 is not online. ukwarrior6
Joined: 06 Sep 2009
Total Posts: 485
16 Jul 2013 02:34 PM
You'll need to "create" an orbit, at the moment, if you apply your force in any way, those two bodies will merely move towards each other. You need to apply Keplers Law, as you've stated above.

But, it depends how indepth you're going with this,if you want a true gravity simulator, you need to include things like foci for elliptical orbits.

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ukwarrior6 is not online. ukwarrior6
Joined: 06 Sep 2009
Total Posts: 485
16 Jul 2013 02:37 PM
@1waffle1, Presumably he is going to include Newtons laws of Gravity and motion into his equations anyway?
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Oysi is not online. Oysi
Joined: 06 Jul 2009
Total Posts: 9058
16 Jul 2013 03:20 PM
[ Content Deleted ]
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Radioaktiivinen is not online. Radioaktiivinen
Joined: 25 Apr 2009
Total Posts: 18629
16 Jul 2013 03:38 PM
Using an alogirthm specifically designed to describe an orbit will likely work only for a single gravitational body and wont likely cooperate with other gameplay features too well.

So go with the force approach.

Then the only problem is the stability of the orbit. If you were making your own physics you would have to worry about properly integrating the force/velocity/position stuff, but roblox probably does something like that so if you use BodyForce or something, it might be stable enough already.
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1waffle1 is not online. 1waffle1
Joined: 16 Oct 2007
Total Posts: 16381
16 Jul 2013 03:41 PM
BodyForce would be the least stable of all options.
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Radioaktiivinen is not online. Radioaktiivinen
Joined: 25 Apr 2009
Total Posts: 18629
16 Jul 2013 03:43 PM
I dont think BodyPosition would work, and i dont see any other options either for more complex systems.

If theres only a single gravitational body you can use your fancy orbit formulas to get a 100% stable orbit.
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Oysi is not online. Oysi
Joined: 06 Jul 2009
Total Posts: 9058
16 Jul 2013 03:45 PM
[ Content Deleted ]
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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 04:50 PM
"Kepler's laws describe the geometry of gravity based on Newton's laws. They describe how the planets move, not why."

You're always so helpful. And smart. Smart as can be.

Anyways, none of this is too helpful in being able to use his equations to duplicate one body orbiting another based on things such as velocity, gravity (which both are obtained from another string of equations based on mass and distance), mass, and distance (though distance would correlate to velocity).

So thanks for all your attempts, but it would have been easier to say "I don't understand Kepler's laws enough to do this"
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Charl3s7 is not online. Charl3s7
Joined: 07 Dec 2007
Total Posts: 4146
16 Jul 2013 05:24 PM
I thought the gravitational constant (G) was 6.67384e-11
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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 05:40 PM
"I thought the gravitational constant (G) was 6.67384e-11"

Not in ROBLOX.
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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 05:41 PM
Unless it is.....?
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Charl3s7 is not online. Charl3s7
Joined: 07 Dec 2007
Total Posts: 4146
16 Jul 2013 05:41 PM
idk. I remember learning about this stuff in my physics class I took, but I never applied it to roblox.
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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 05:43 PM
^^^

Physics is my major, but it's too bad I haven't touched planetary things yet.
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Oysi is not online. Oysi
Joined: 06 Jul 2009
Total Posts: 9058
16 Jul 2013 05:52 PM
[ Content Deleted ]
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MrNicNac is not online. MrNicNac
Joined: 29 Aug 2008
Total Posts: 26567
16 Jul 2013 06:09 PM
^^^

The reason I'm using the laws is because I'm making a solar-system sandbox game where you can in real time edit the elliptical orbits of planets or have the planets collide with things such as the sun or something. I want people to be able to edit say, the velocity, to have the planet slow down and slowly (from the KL equations) start to spiral into the sun because of lack of speed.
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Oysi is not online. Oysi
Joined: 06 Jul 2009
Total Posts: 9058
16 Jul 2013 06:38 PM
[ Content Deleted ]
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1waffle1 is not online. 1waffle1
Joined: 16 Oct 2007
Total Posts: 16381
16 Jul 2013 06:42 PM
Kepler's laws are more geometry than they are physics. If your intention is to understand the math rather than apply it practically, the equation to find the position of the planet relative to the star as a function of time can be calculated by:

perihelion = closest point on the ellipse to the star
center = center of the ellipse
time = time since the planet was at the perihelion

major=|center*perihelion| -- semi-major axis
eccentricity=|center*position of the star|/major

E=sin(E)*eccentricity + sqrt(gravitational_constant(mass_of_star+mass_of_planet)/major^3)*time -- eccentric anomaly

angle = 2*atan(sqrt((eccentricity+1)/(eccentricity-1))*tan(E/2))
radius=major*(1-eccentricity^2)/(1+eccentricity*cos(angle))
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Aerideyn is not online. Aerideyn
Joined: 16 Jan 2010
Total Posts: 1882
16 Jul 2013 09:06 PM
There is a fair amount of information on orbital(kepler) elements which are a system used to uniquely define a orbit - you can also convert them directly back to state vectors to use in your bodyforce though i think just adding the state vectors to it's current cframe would be more stable.

I got most of the way through the conversion between elements and vectors before moving on to other projects - it takes a fair bit of messing but you will get there.

Ill try and finish it off in the next day or so - if you still need a hand then just let me know,
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shadow350 is not online. shadow350
Joined: 17 Aug 2009
Total Posts: 38153
16 Jul 2013 11:34 PM

ogm nerds




~Oh boy, here we go again~
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Radioaktiivinen is not online. Radioaktiivinen
Joined: 25 Apr 2009
Total Posts: 18629
17 Jul 2013 03:50 AM
Just calculate the force exerted by the gravitational bodies. Use bodyforce to apply it to take advantage of robloxs force integration and stoof.
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a1u1 is not online. a1u1
Joined: 24 Mar 2013
Total Posts: 452
17 Jul 2013 03:13 PM
@Oysi that thing where it's like m1 reminds me about Albert's Theory Of Relativity. It's cool, and a bit catchy. It's simply e = mc2. BUT THAT'S NOT FULL! ALBERT SHOULD WORK MORE (but he died)! BUT HERE:
http://www.youtube.com/watch?v=NnMIhxWRGNw

That's proof e=mc2 isn't full O_O (above is the proof, the youtube link)
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thedestroyer115 is not online. thedestroyer115
Joined: 19 Dec 2010
Total Posts: 11546
17 Jul 2013 10:01 PM
I am sorry if I am derailing this thread, but why did MNN ragequit from MS?
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1waffle1 is not online. 1waffle1
Joined: 16 Oct 2007
Total Posts: 16381
18 Jul 2013 10:25 AM
the members were no longer a fan of having a dictator and he recognized that.
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