我必须为我的物理课程制作太阳系的模拟。我已经制作了一个非常基本的代码，使用欧拉方程模拟Sol和地球相互绕过。
然而，使用牛顿万有引力定律产生的加速度是错误的，我不知道为什么。
public class SolarSystemSim
{
public static void main(String[] args)
{
PhysicsVector EarthPos= new PhysicsVector(4.39e10,1.42e11,-2.44e7);
PhysicsVector EarthVel= new PhysicsVector(-2.89e4,8.71e3,-8.36e-1);
double EarthMass= 5.972e24;
PhysicsVector SunPos= new PhysicsVector(2.93e8,8.96e8,-1.85e7);
PhysicsVector SunVel= new PhysicsVector(-9.75,9.01,2.34e-1);
double SunMass= 1.989e30;
/**PhysicsVector MercuryPos= new PhysicsVector(5.791e10,0,0);
PhysicsVector MercuryVel= new PhysicsVector(0,47400,0);
double MercuryMass= 3.285e23;**/
Particle Earth= new Particle(EarthPos,EarthVel,EarthMass);
Particle Sun= new Particle(SunPos,SunVel, SunMass);
//Particle Mercury= new Particle(MercuryPos,MercuryVel,MercuryMass);
Scanner s1= new Scanner(System.in);
System.out.println("Enter a timestep i.e 1 second");
double TimeStep= s1.nextDouble();
System.out.println("Enter a total time i.e There are 86400 seconds in a day");
double FinalTime=s1.nextDouble();
Particle[]Planets={Sun,Earth/**Mercury**/};
PhysicsVector acc= new PhysicsVector();
PhysicsVector[]PlanetAccelerations= new PhysicsVector[Planets.length];
for(int t=0;t<FinalTime/TimeStep;t++)
{
for(int k=0;k<Planets.length;k++)
{
PhysicsVector PlanetPos= Planets[k].GetPos();
acc= new PhysicsVector(0,0,0);
for(int i=0;i<Planets.length;i++)
{
PhysicsVector r= PhysicsVector.subtract(PlanetPos,Planets[i].GetPos());
System.out.println(Planets[k].GetMass());
System.out.println(Planets[i].GetMass());
Gravity Grav= new Gravity();
acc.increaseBy(Grav.GravitySim(r,Planets[i].GetMass()));
acc.print();
}
PlanetAccelerations[k]=acc;
}
for(int j=0;j<Planets.length;j++)
{
PhysicsVector ac= new PhysicsVector();
ac= PlanetAccelerations[j];
Planets[j].Euler(TimeStep,ac);
}
}
Planets[0].GetPos().print();
Planets[1].GetPos().print();
//Planets[2].GetPos().print();
}
}
public class PhysicsVector {
private static final int vectorSize=3;
private double[] vectorComponents = new double[vectorSize];
public PhysicsVector()
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] =0.;
}
}
public PhysicsVector(double x, double y)
{
vectorComponents[0] = x;
vectorComponents[1] = y;
vectorComponents[2] = 0.;
}
public PhysicsVector(double x, double y, double z)
{
vectorComponents[0] = x;
vectorComponents[1] = y;
vectorComponents[2] = z;
}
public PhysicsVector(double [] x)
{
if (x.length == vectorSize){
for (int i=0; i<vectorComponents.length; i++)
{vectorComponents[i] = x[i];}
}
else if (x.length == vectorSize-1 ) {
for (int i=0; i<x.length; i++)
{vectorComponents[i] = x[i];}
vectorComponents[vectorComponents.length-1] = 0.;
}
else {this.setVector(new PhysicsVector());
System.out.println(
"WARNING: PhysicsVector(double [] x) " +
"requires an array of length " + vectorSize);
}
}
public PhysicsVector(PhysicsVector v)
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] = v.vectorComponents[i];
}
}
public void print()
{
String text = this.returnString();
System.out.println(text);
}
public void setVector(double x, double y, double z)
{
vectorComponents[0] = x;
vectorComponents[1] = y;
vectorComponents[2] = z;
}
public void setVector(double x, double y)
{
vectorComponents[0] = x;
vectorComponents[1] = y;
vectorComponents[2] = 0.;
}
public void setVector(PhysicsVector v)
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] = v.vectorComponents[i];
}
}
public void increaseBy(PhysicsVector v)
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] += v.vectorComponents[i];
}
}
public void decreaseBy(PhysicsVector v)
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] -= v.vectorComponents[i];
}
}
public double magnitude()
{
double mag = dot(this,this);
mag = Math.sqrt(mag);
return mag;
}
public double getX()
{
return vectorComponents[0];
}
public double getY()
{
return vectorComponents[1];
}
public double getZ()
{
return vectorComponents[2];
}
public PhysicsVector getUnitVector()
{
PhysicsVector unit = new PhysicsVector(this);
double magnitude = this.magnitude();
if (Math.abs(magnitude) > 1.e-34)
{unit.scale(1/magnitude);}
else
{unit = new PhysicsVector();}
return unit;
}
public void scale(double x)
{
for (int i=0; i<vectorComponents.length; i++)
{
vectorComponents[i] *= x;
}
}
public static PhysicsVector scale(double x, PhysicsVector v)
{
PhysicsVector scaled = new PhysicsVector(v);
for (int i=0; i<(scaled.vectorComponents).length; i++)
{
scaled.vectorComponents[i] *=x;
}
return scaled;
}
public static PhysicsVector subtract(PhysicsVector u, PhysicsVector v)
{
PhysicsVector sum = new PhysicsVector(u);
sum.decreaseBy(v);
return sum;
}
public static double SumArray(double[] a)
{
double sum= 0;
for(int i=0;i<a.length;i++)
{
sum+=a[i];
}
return sum;
}
public static void PrintArray(PhysicsVector[] b)
{
for(int i=0;i<b.length;i++)
{
b[i].print();
}
}
}
public class Gravity
{
private double G=6.67408e-11;
private PhysicsVector position= new PhysicsVector();
private double Mass;
public Gravity(PhysicsVector x, double M)
{
position= new PhysicsVector(x);
double Mass= M;
}
public Gravity()
{
position= new PhysicsVector();
double Mass= 0.0;
}
public PhysicsVector GravitySim(PhysicsVector r, double M)
{
if(r.magnitude()!=0)
{
double g=-(G*M)/(r.magnitude()*r.magnitude());
PhysicsVector acc=new PhysicsVector(r.getUnitVector());
acc.scale(g);
return acc;
}
else
{
PhysicsVector zero= new PhysicsVector();
return zero;
}
}
}
public class Particle
{
private PhysicsVector velocity= new PhysicsVector();
private PhysicsVector position= new PhysicsVector();
private PhysicsVector TempV= new PhysicsVector();
private PhysicsVector TempV1= new PhysicsVector();
private PhysicsVector TempV2= new PhysicsVector();
private PhysicsVector TempP= new PhysicsVector();
private PhysicsVector TempP1= new PhysicsVector();
private double Mass;
public Particle()
{
position= new PhysicsVector();
velocity= new PhysicsVector();
Mass= 0.0;
}
public Particle(PhysicsVector x,PhysicsVector y,double M)
{
position=new PhysicsVector(x);
velocity=new PhysicsVector(y);
Mass=M;
}
public void Euler(double t,PhysicsVector ac)
{
position.increaseBy(PhysicsVector.scale(t,velocity));
velocity.increaseBy(PhysicsVector.scale(t,ac));
}
public PhysicsVector GetPos()
{
return position;
}
public double GetMass()
{
return Mass;
}
}
我一直在TimeStep = 1和FinalTime = 2进行模拟，并得到结果：
太阳加速度= 5.6e-9 m/s^2
地球加速度= -1.8e-3 m/s^2
什么时候应该：
太阳加速度= 1.8e-8 m/s^2
地球加速度= - 5.9e-3 m/s^2