RK4 Solver Issue: Shoot the Moon with C Program

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A user is developing a 4th order Runge-Kutta program in C to simulate a spacecraft's trajectory to the moon but is encountering issues with the RK4 implementation. The user has shared the code file, specifically recommending the "shoot_the_moon3.c" version, which includes a .plt file for generating output data in .png format. The spacecraft is intended to follow a circular orbit but is instead exhibiting behavior akin to a massed spring. The user suspects that the problem may be related to an initial value issue and is seeking assistance from those more experienced in C programming to identify the errors in the code.
Illuminati
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Hey Folks,

So I've been making an 4th order Runge-Kutta program for finding a way to shoot the moon with a spacecraft . However for some reason the RK4 part of the program does not work and I cannot figure it out.

I've written it in C and attached the file. If someone who is more well versed in C could take a look at it and let me know what I'm screwing up I would be greatly appreciative.

Thanks!

Edit: I've attached a couple different methods to this post. If viewing try using shoot_the_moon3.c, it should have a working .plt file to output a .png of the data
 

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I suppose I should add that the spacecraft is supposed to have some kind of circular orbit, instead it acts more like a massed spring

it might be an initial value problem
 
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