Planet path using netwon's law with forward method

Given the initial position (ie x1,y1) and the velocity (ie vx,vy) of the planet.

How to plot a graph of the path of the planet around the center point (0,0) assuming the center is Earth, using time step of 10s for 500000s?

formula for forward method:

x(t+dt)=x(t)+v(t)*dt

v(t+dt)=v(t)+a(t)*dt

a=GM/r^2

G = 6.67e-11, M = 5.97e24

Many thanks.

[James Tursa]

What code do you have so far?

[Walter Roberson]

Where is "r" defined?

If I recall correctly, this kind of forward prediction is unable to handle the orbit of Mercury, which has notable influence from drag of the rotational gravitational frame.

[James Tursa]

@Walter: Well, OP has Euler's method listed which isn't going to do all that great with *any* orbit.

Answer 1

[Gregory Vernon]

You should look into velocity verlet methods.