2 rotating body in C++

Question

I have this code in C++ that is suppose to simulate the rotation of a body (body2) around another one (body1) in the xy plane, and save the x and y position of body2 in a file:

#include<iostream>
#include <vector>
#include<math.h>
#include <fstream>
using namespace std;

class Body{
    private:

    double G= 1;
    double rx;
    double ry;
    double rz;
    double vx;
    double vy;
    double vz;
    double mass;
    double fx;
    double fy;
    double fz;
    double dt=0.01;


    public:

    Body(double rx, double ry, double rz, double vx, double vy, double vz, double mass){
        this->rx=rx;
        this->ry=ry;
        this->rz=rz;
        this->vx=vx;
        this->vy=vy;
        this->vz=vz;
        this->mass=mass;
    }

    void update(){
        vx=vx+dt*fx/mass;
        vy=vy+dt*fy/mass;
        vz=vz+dt*fz/mass;
        rx=rx+vx*dt;
        ry=ry+vy*dt;
        rz=rz+vz*dt;
    }


    double get_x(){
        return rx;
    }

    double get_y(){
        return ry;
    }

    double get_z(){
        return rz;
    }

    double get_fx(){
        return fx;
    }


    void resetForce(){
        fx=0.0;
        fy=0.0;
        fx=0.0;
    }

    void addForce(Body b){
        double dx=b.rx-rx;
        double dy=b.ry-ry;
        double dz=b.rz-rz;
        double dist = sqrt(dx*dx+dy*dy+dz*dz);
        double F=G*mass*b.mass/dist*dist;
        fx=fx+F*dx/dist;
        fy=fy+F*dy/dist;
        fz=fz+F*dz/dist;
     }


};



int main(){

    Body body1(0,0,0,0,0,0,1000), body2(100,0,0,0,10,0,10);

    ofstream pos;
    pos.open ("Position.txt");


    int N=10000;
    for(int i; i<N;i++){
        body2.resetForce();
        body2.addForce(body1);
        body2.update();
        pos<<body2.get_x()<<" "<<body2.get_y()<<endl;


    }
pos.close();

}

I expected the plot to look like a circle around the origin (where body1 is located), but it looks like this:

I assume it is something wrong with the way I update the speed and force at each step but I couldn't find the mistake, so I appreciate any help.

Thank you!

Answer 1

First mistake is in line

double F=G*mass*b.mass/dist*dist;

This line will be interpretated like this double F=(G*mass*b.mass/dist)*dist; so as you see it will we incorrect result and you need this one

double F=G*mass*b.mass/(dist*dist);

Second you're increasing force on each simulation step in this lines

    fx=fx+F*dx/dist;
    fy=fy+F*dy/dist;
    fz=fz+F*dz/dist;

But I suppose you shouldn't do so you need this change it like this

    fx=F*dx/dist;
    fy=F*dy/dist;
    fz=F*dz/dist;

Third I also suppose that your bodies actually are located to far from each other in initial configuration you can decrease initial distance like this:

Body body1(0,0,0,0,0,0,1000), body2(10,0,0,0,10,0,10);

Actually you also should take into account force with which body2 is affecting on body1 but yes you can say that is too small.