In this section, we write an object-oriented program that dynamically simulates the motion of n bodies under the influence of mutual gravitational attraction.

Bouncing balls.

 The data type Ball.java represents a ball with a given position (rx,ry)$(r_x,r_y)$ that moves with a fixed velocity (vx,vy)$(v_x,v_y)$ in the box with coordinates between −1 and +1. When it collides with the boundary, it bounces according to the law of elastic collision.

The client BouncingBalls.java takes a command-line argument n and creates n random bouncing balls.

N-body simulation.

 The bouncing ball simulation is based on Newton's first law of motion: a body in motion remains in motion at the same velocity unless acted on by an outside force. Embellishing that example to incorporate gravity leads us to a basic problem that has fascinated scientists for ages. Given a system of n bodies, mutually affected by gravitational forces, the problem is to describe their motion.

• Body data type. The data type Body.java represents a body with a given position $(r_x,r_y)$, velocity $(v_x,v_y)$, and mass $m$. It appliesNewton's third law of motion (which explains the gravitational force between two bodies) to determine the net force acting on a body:

  $$\mathit{F}=G\frac{m_1{m}_2}{r^2}$$

  and Newton's second law of motion (which explains how outside forces directly affect acceleration and velocity).

  $$\mathit{F}=m\mathit{a}$$

  It uses the Vector.java data type to represent displacement, velocity, and force as vector quantities.

  

• Universe data type. Universe.java takes a command-line argument dt, reads in a universe from standard input, and simulates the universe using time quantum dt. Here is an example of the data file format:

  

  
  The following static images for 2body.txt, 3body.txt, and 4body.txt are made by modifying Universe.java and Body.java to draw the bodies in white, and then black on a gray background.