Programming Assignment Checklist: N-Body Simulation


Frequently Asked Questions

What preparation do I need before beginning this assignment? Read Sections 1.4 and 1.5 of the textbook.

Any advice on completing this programming assignment? Warning: this program is more involved than the previous ones, and you should budget more time accordingly. The best advice we can give you is to carefully test, debug, and re-test your code as you write it. Do not attempt to write the whole program at once—if you do, then you will have no idea where to find the error if the program doesn't work. Proactive testing will save you enormous amounts of time in the long run. Trust us!

What's the easiest way to copy the nbody directory from the COS 126 ftp site to my computer?

DrJava doesn't let me redirect standard input. What should I do instead? DrJava does not support redirection or piping; instead, you must use the command line.

Do I have to follow the assignment specifications for reading input from command-line arguments and standard input, and writing output to standard drawing and standard output? Yes, or you will lose a substantial number of points.

Where can I find the APIs for StdIn, StdOut, StdDraw, and StdAudio? They are on p. 716–718 of the textbook. They are also available online in this Java cheatsheet.

I did not use the installer. How do I install stdlib.jar? We highly recommend using the Windows installer or the Mac OS X installer. If you choose not to, you can refer to the standard libraries, which includes instructions on downloading and using them.

When I compile, it says "cannot resolve symbol StdDraw." Any thoughts? You do not have our standard libraries properly installed. See the question above. If you tried to install stdlib.jar and still get this message, please consult a staff member (preceptor or lab TA) to fix this.

I do not have my own computer, so I am using a university computer cluster machine. How do I access the COS126 standard libraries? Refer to the instructions on using the standard libraries. The lab TAs can help you with this.

How do I plot a picture using StdDraw? The command StdDraw.picture(x, y, filename) plots the image in the given filename (either JPEG, GIF, or PNG format) on the canvas, centered on (x, y).

Do I need to write my own functions (static methods)? It's not required. If you want to modularize your program, here are two possibilites.

// return Euclidean distance between (x1, y1) and (x2, y2)
private static double distance(double x1, double y1, double x2, double y2)

// return the magnitude of the gravitational force between two bodies
// of mass m1 and m2 that are distance r apart
private static double force(double m1, double m2, double r)

My computer doesn't display the animation smoothly. Is there anything I can do? Use to turn on the animation mode of standard draw. Call it once at the end of each time step, not after each drawing command.

What is the argument in The number in the parentheses is a time delay in milliseconds (or close to it) before the next screen update. Use it to adjust the animation speed to a pleasing rate. Values between 10 and 30 work well for this simulation.

Can I combine Steps 1, 2, and 3 into one massive loop? No! You must do Step 1 (compute all of the forces) before Steps 2 and 3 (moving and drawing them); otherwise, you will be computing the forces at time t using the positions of some of bodies at time t and others at time t + Δt. Of course, the three steps comprise the body of the main simulation loop.

I draw the bodies, but nothing appears on the screen. Why? Use StdDraw.setXscale() and StdDraw.setYscale() to change the coordinate system to use the physics coordinates instead of the unit box.

My bodies 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: (x[j] - x[i]) vs. (x[i] - x[j]). Note that Δx and Δy can be positive or negative so do not use Math.abs(). Do not consider changing the universal gravitational constant G to patch your code!

What is Δx? It's the change in x-coordinate between two bodies (not between a body at time t and at time t + Δt).

How many steps should my program simulate if T is not a multiple of ΔT? Simulate the universe as long as t < T. For example, if T is 50,000 and ΔT is 25,000, you should simulate the system for two steps (t = 0 and 25,000). If T is 60,000 and ΔT is 25,000, you should simulate the system for three steps (t = 0, 25,000 and 50,000).

Does my program need to plot anything if T equals 0? No, you do not need to plot anything.

How do I submit the extra credit? Submit the extra credit file in the Additional Files dropbox window. Document what you did in your readme.txt file.

Everything works until I add"2001.mid") then everything hangs. What do I do? On some machines there may be a race problem between sending things to the drawing window and sending things to the sound card. Try moving to a place in the program after your initial calls to StdDraw.setXscale() and StdDraw.setYscale().

I can play MP3s using my favorite media player, but no sound plays in Java. What could be wrong? If you are running Windows XP, be sure that the audio stream that Java uses is not muted via Start -> Programs -> Accessories -> Multimedia -> Volume Control -> Wave Out.

Testing and Debugging

Inserting print statements is a good way to trace what your program is doing. Our input files were created with the following StdOut.printf() statements.

StdOut.printf("%d\n", N);
StdOut.printf("%.2e\n", R);
for (int i = 0; i < N; i++) {
    StdOut.printf("%11.4e %11.4e %11.4e %11.4e %11.4e %12s\n",
                   rx[i], ry[i], vx[i], vy[i], mass[i], image[i]);
Here are our results for a few sample inputs.
% java NBody 0.0 25000.0 < planets.txt           // zero steps
 1.4960e+11  0.0000e+00  0.0000e+00  2.9800e+04  5.9740e+24    earth.gif
 2.2790e+11  0.0000e+00  0.0000e+00  2.4100e+04  6.4190e+23     mars.gif
 5.7900e+10  0.0000e+00  0.0000e+00  4.7900e+04  3.3020e+23  mercury.gif
 0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  1.9890e+30      sun.gif
 1.0820e+11  0.0000e+00  0.0000e+00  3.5000e+04  4.8690e+24    venus.gif

% java NBody 25000.0 25000.0 < planets.txt       // one step
 1.4960e+11  7.4500e+08 -1.4820e+02  2.9800e+04  5.9740e+24    earth.gif
 2.2790e+11  6.0250e+08 -6.3860e+01  2.4100e+04  6.4190e+23     mars.gif
 5.7875e+10  1.1975e+09 -9.8933e+02  4.7900e+04  3.3020e+23  mercury.gif
 3.3087e+01  0.0000e+00  1.3235e-03  0.0000e+00  1.9890e+30      sun.gif
 1.0819e+11  8.7500e+08 -2.8329e+02  3.5000e+04  4.8690e+24    venus.gif

% java NBody 50000.0 25000.0 < planets.txt       // two steps
 1.4959e+11  1.4900e+09 -2.9640e+02  2.9799e+04  5.9740e+24    earth.gif
 2.2790e+11  1.2050e+09 -1.2772e+02  2.4100e+04  6.4190e+23     mars.gif
 5.7826e+10  2.3945e+09 -1.9789e+03  4.7880e+04  3.3020e+23  mercury.gif
 9.9262e+01  2.8198e-01  2.6470e-03  1.1279e-05  1.9890e+30      sun.gif
 1.0818e+11  1.7499e+09 -5.6660e+02  3.4998e+04  4.8690e+24    venus.gif

% java NBody 60000.0 25000.0 < planets.txt       // three steps
 1.4958e+11  2.2349e+09 -4.4460e+02  2.9798e+04  5.9740e+24    earth.gif
 2.2789e+11  1.8075e+09 -1.9158e+02  2.4099e+04  6.4190e+23     mars.gif
 5.7752e+10  3.5905e+09 -2.9682e+03  4.7839e+04  3.3020e+23  mercury.gif
 1.9852e+02  1.1280e+00  3.9705e-03  3.3841e-05  1.9890e+30      sun.gif
 1.0816e+11  2.6248e+09 -8.4989e+02  3.4993e+04  4.8690e+24    venus.gif

% java NBody 31557600.0 25000.0 < planets.txt    // one year
 1.4959e+11 -1.6531e+09  3.2949e+02  2.9798e+04  5.9740e+24    earth.gif
-2.2153e+11 -4.9263e+10  5.1805e+03 -2.3640e+04  6.4190e+23     mars.gif
 3.4771e+10  4.5752e+10 -3.8269e+04  2.9415e+04  3.3020e+23  mercury.gif
 5.9426e+05  6.2357e+06 -5.8569e-02  1.6285e-01  1.9890e+30      sun.gif
-7.3731e+10 -7.9391e+10  2.5433e+04 -2.3973e+04  4.8690e+24    venus.gif

Possible Progress Steps

These are purely suggestions for how you might make progress. You do not have to follow these steps. If you get stumped or frustrated on some portion of the assignment, you should not hesitate to consult a preceptor.