[HELP][DISCUSSION][WIP]ETA OF PLANET COLLISIONS

I did a few tests but as of now its late, I have work tomorrow (later today actually), and I don't feel like doing the math, as of now I have a text document attached here with my current findings, it will be updated but as for now I am letting you guys have at it for 18 ish hours then I will be back.

Wow, I am tired I almost forgot to say what I am trying to do even though I think the title explains it, I want to find the ETA of planet collisions in-game, I would like to use a mathematical equation so it can be incorporated into a UI mod. Here are my findings (attached and in the below code box)

Code:

"slower" planet
    position
        X:13625
        Y:1000

    velocity
        X:-11.4294
        Y:191.547

"faster" planet
    position
        X:12625
        Y:-1000

    velocity
        X:15.6892
        Y:198.076

at 0:53 planets collide

Time Relation Tests [System Editor to In-Game](APPROX):
First: 1.12
Second: 1.01
Third: 1.00
Fourth: 1.11
Fifth: 1.11

Average: 1.07

(**APPROXIMATION**): I could say that 1.07 seconds is equal to 53 seconds but for simplicity's sake I will say this --


  --1 Second of time in the System Editor is equal to 60 seconds of time in-game

        (I also chose those values because that would make sense, why program it with something weird when you can do 1 = 60?)
        I cannot prove this, but I believe that FPS has to be 60 in system editor for this to apply

Global Variables for the Equation​

Code:

e-T = Time in Editor

g-T = Time in-game

s-posX = Slower planet position X

s-posY = Slower planet position Y

s-velX = Slower planet velocity X

s-velY = Slower planet velocity Y

s-rad = Slower planet radius

f-posX = Faster planet position X

f-posY = Faster planet position Y

f-velX = Faster planet velocity X

f-velY = Faster planet velocity Y

f-rad = Faster planet radius

Helpful? Equations
Distance Formula for a straight line
Equation for a circle x² + y² = r² where x and y are the center and r is the radius
Circumference of a Circle C=2 π r where C is the circumference and r is the radius

Links
http://math.stackexchange.com/questions/534182/how-to-build-a-mathematical-formula
http://en.wikipedia.org/wiki/Fourier_analysis
http://en.wikipedia.org/wiki/Box–Jenkins
http://en.wikipedia.org/wiki/Akaike_information_criterion

Tools
https://www.desmos.com/calculator - Graphing Caclulator​

It's gonna be a nice challenge I guess planets not orbiting around the sun will give you some headache with their vector.

Oh man, I didn't even think about that last night. Let's just focus on planets orbiting the sun for right now

This idea has a lot of potential !

Quick thought sparkling in my head :
I could easily imagine a devious soul hosting a game using a rigged system that explodes the starting planet after let's say 7 minutes, not telling anyone and rushing orbital to save the commander for an easy win (has to be 3 planet system obviously). So it induce the following question :
I'm not an expert, and so far noticed server mods are mostly used to change game mechanics (balance, etc ...), but could a server mod be used for what you are planning to do in a UI one (ie to get all game participants to have that UI mod by being in that particular game). This is a naive question, but if possible, it could be an awesome game mode !

I have already made and tested a system like that on PTE but the problem is the two minute timer players get to choose where the commander lands. The planets move during that timer so the scenario will be different depending on how long people take to land.

Nice finding !
And what if that really devious soul ( ) was to use a mod like "In Game Timer" (or a simple stopwatch) set to a little less than 2 minutes, to be the last one to input its starting position (or let choose automatically) and have a good approximation of the collision ETA ?
I'm guessing this 2 minutes timer starts as soon as the system is created / loaded on server side, right ?

Bad trick aside, would a server mod be possible / suitable to let everyone one know collision's ETA ? Or it isn't their role at all ?

Yes it starts on the server side. This means you will have to sync the mod to the chronocam timer instead of making a client-side timer.

Have either of you looked into the math?

Okay, I will be adding it to the main post but I want it here too, when we start experimenting with equations I want everyone to use the same variables for the same thing

Code:

T = Time

s-posX = Slower planet position X

s-posY = Slower planet position Y

s-velX = Slower planet velocity X

s-velY = Slower planet velocity Y

f-posX = Faster planet position X

f-posY = Faster planet position Y

f-velX = Faster planet velocity X

f-velY = faster planet velocity Y

This might be helpful, I just skimmed it http://math.stackexchange.com/questions/534182/how-to-build-a-mathematical-formula

I am currently doing a test to see if planet speed stays the same regardless of distance from sun, I will post my findings when I am done

Okay, so we have a bit of a problem, according to my research a planet 30,000 units away from the sun moves ~30% slower than a planet 15,000 units from the sun, this is going to make the equation much harder

The math currently surpasses my intelligence, I will keep working at it but in the meantime I have updated the title to reflect that

Okay I am now doing some trials to find the relation of distance from the sun to speed, will be posting results in 10-ish minutes, still working on them

I timed how long each planet took to complete 1 entire trip around the sun and complete it's orbit

okay here are my findings, Planet 1 is the closest to the sun at positions y=0 and x=15,000

every panet is at y=0

Planet 1 x=15,000
Planet 2 x=20,000
Planet 3 x=25,0000
Planet 4 x=30,000

maybe someone will actually come and help me now that I have some more info

https://docs.google.com/spreadsheets/d/1vTBfHbktEvs_pBKsBn4JYfUqLAH0M_y4mRMjZus6UwE/edit?usp=sharing

Elliptical orbits are a thing BTW. Have fun with that.

I know that, but right now I am just focusing on normal circular orbits

Interesting... the farther away from the sun, the slower they travel.

Y is the speed of the planet.
X is the distance from the Sun.

The equation is somewhere around y = -0.15x + 10000

Thank you, this should help.