Programming Assignment Checklist: N-Body Simulation

Goals

• Learn about a scientific computing application.
• Learn about reading from standard input using StdIn.
• Learn about redirecting standard input to read from a file.
• Learn about plotting using Turtle graphics.
• Learn about arrays.

Frequently Asked Questions

The submission system says my program exceeds the 80 character limit, but I don't see which line it's on. Can you help? The program WidthChecker.java and helper library CharStdIn.java print out all lines longer than a command line input N. Please note that all tabs are converted to 4 spaces during submission.

My computer it too slow to display the animation smoothly. Is there anything I can do? Here are a few suggestions. First, be sure that you are only calling Turtle.pause once at the end of each time step, instead of after each Turtle.spot command. You might also try increasing the delay parameter in Turtle.pause to prevent hoarding system resources. Or do several updates, say 20, before calling Turtle.pause.

Can I combine Steps 1, 2, and 3 into one massive loop? No! This will simultaneously screw up the physics and make your card harder to understand and debug.

I draw the planets, but nothing appears on the screen. Why? Make sure that the drawing coordinates are between 0 and 512. If not, rescale them so that they are. Also, be sure that you call Turtle.pause at the end of each time step.

How do I scale the bodies so that they stay inside the 512-by-512 Turtle graphics window? The first number in the data file is the radius R of the universe. You can assume all of the x and y coordinates of the planets remain between -R and R. Your job is to compute scaled and translated coordinates that are always between 0 and 512. Compute turtleX and turtleY with ax + b and ay + b for appropriate constants a and b. Note: you should not actually change the x and y coordinates of each planet (this will ruin the physics); instead use the temporary variables turtleX and turtleY to temporarily store the scaled coordinates you intend to plot.

I'm confused about all of the &Delta t / 2 terms. Do I need to worry about them to get the physics right? No! The update formulas for velocity and position already take this into account.

What should I use for the initial velocity in the leapfrog method? Use the value from the input file. As a technicality, the leapfrog method should be initialized with the velocity at time t = -Δt / 2, so we'll assume this is the value in the input file.

My planets repel each other. Why don't they attract each other? Make sure that you get the sign right when you apply Newton's law of gravitation. Note that Δx and Δy can be positive or negative.

How should I compute x²? Use x * x. Don't use Math.pow(x, 2).

I can't compile Turtle.java. Any thoughts? Be sure you are running Java 1.4 and not some older version.

Input, Output, and Testing

Input. Copy the nbody directory from the COS 126 ftp site to your computer.

• Windows NT using IE. Click the ftp link above, then right click the nbody folder, and select Copy To Folder.

• OS X using Safari. Click the ftp link above to mount the ftp site, then drag-and-drop the nbody folder from the ftp mount.

• Arizona Unix cluster. Type the following command:

  cp -pr /u/cs126/files/nbody .
  

Compilation.  Your program must be named NBody.java. The capatilization is important. Compile your program with:

javac NBody.java

Execution.  To redirect standard input from a file, execute your program with:

java NBody < planets.txt

You might also be entertained to substitute dance.txt for planets.txt. This universe was submitted by a Princeton student 5 years ago, and is absolutely wonderful! Set dt = 2500 and (i) either run on a fast computer or (ii) only call Turtle.pause after every 50 updates.

Also try out binaryStars.txt, courtesy of your classmate David Costanzo.

Reference solutions.   For reference, we provide our executable code on Windows, Solaris, and OS X.

Submission

readme.txt. Use the following readme file template and answer any questions.

Submission.  Submit NBody.java. Don't forget to hit the "Run Script" button on the submission system to test that it compiles cleanly.

Possible Progress Steps

These are purely suggestions for how you might make progress. You do not have to follow these steps.

• Review the Bouncing Ball program from lecture and the Student Precept List program from Section 2.5.

• Copy the following files from /u/cs126/files/nbody into your working directory. It contains sample input files, Turtle.java, StdIn.java, and reference solutions.

• Read in the data file planets.txt using StdIn.java, and print the information back out using System.out.println.

• Now, read in the data file and store the information in several arrays. Let px[i], py[i], vx[i], vy[i], and mass[i] be real numbers which store the current position (x and y coordinates), velocity (x and y components), and mass of planet i. Let image[i] be a string which represents the filename of the GIF image used to display planet i. Print the information back out.

• Step 3. Plot the background starfield.jpg image. Recall that Turtle.spot centers the image at the current location, so use Turtle.fly to pre-position the turtle. Write a loop to plot the data using Turtle graphics. Be sure that you scale and translate the data so that it fits within the 512-by-512 Turtle graphics window. Don't forget to call Turtle.pause(20) after the loop to allow the turtle some some time rest and display the picture on the screen. You should now see the four stationary planets and the sun.

• Step 2. Write a loop to calculate the new velocity and position for each body. (This code goes before the stuff you wrote in Step 3.) Assume Since we haven't yet incorporated gravity, assume the acceleration acting on each planet is 0. Add an outer loop to repeat Steps 1 and 2 forever. You should now see the four planets moving off the screen in a straight line, with constant velocity.

• Step 1. Now, calculate the net force acting on each body. (This code goes before the stuff you wrote in Step 2.) You will need two additional arrays fx[i] and fy[i] to store the net force acting planet i. First, write a loop to initialize all the net forces to 0.0. Then write two nested for loops to calculate the net force exerted by planet j on planet i. Add these values to fx[i] and fy[i], but skip the case when i = j. Once you have these values computed, go back to Step 2 and use them to compute the acceleration (instead of assuming it is zero).

• At the beginning of the simulation (outside of any loop), use Turtle.grunt to play the 2001 theme.

Enrichment

• Here's some information about our solar system.

• Here's a wealth of information on N-body simulation.

• Here's some of the N-body physics.