Introduction

This demo shows the orbit of a planet around sun. The equation of a planet is determined by the following initial value problem. $$-\frac{d^2x(t)}{dt^2} = \frac{x(t)}{r(t)^3}, \quad -\frac{d^2y(t)}{dt^2} = \frac{y(t)}{r(t)^3}, \quad r(t)=\sqrt{ x(t)^2+y(t)^2}$$ The initial conditions are taken as $$x(0) = 0.5, y(0)=0, x'(0)=0, y'(0)=\sqrt{3}.$$ Such a setting has a period of obit as $2\pi$.

How to compute?

To run the simulation, please make sure the computing server is ready. Please click "Initialize computing" if the computing server IP is empty.

Control panel

 Time　(unit: 2$\pi$): Step size: Method selection: Backward Euler

Animation

Plot setting

X Range:
Y Range:
Axis options:

Contact: Xuefeng LIU (xfliu.math@gmail.com)