Programming Assignment Checklist: N-Body Simulation


Frequently Asked Questions Part 1: Operating System Questions

At the terminal/command prompt, Java is not compiling, saying it "cannot resolve symbol StdIn" (or StdDraw, etc) even though I used the introcs installer. Why is this? To use the standard libraries, someone has to tell the Java compiler and runtime where to find them. The introcs installer should have configured DrJava to do this automatically when compiling or running in DrJava. But when using the Command Prompt/Terminal, use java-introcs and javac-introcs in place of java and javac. These are modified commands that tell Java where to find the standard libraries. With the older, more intrusive installers, it may be the case that java/javac were automatically reconfigured to do this.

I used the installer and neither of these commands worked, why is that? Check with a lab TA or preceptor first (you may simply be running things in the wrong directory). If you moved any of the files that the installer added, the environment variables and DrJava preferences set up by the installer will no longer be accurate. If you think you did this, you may reinstall. If this was not the issue, it may be an installer bug which you should diagnose through the lab TAs and on Piazza.

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.

I am a power user and installed everything myself. Where do I get stdlib.jar? Here on the booksite (scroll to top of page) and make sure you add it to both the classpath of DrJava and your CLASSPATH environment variable.

I do not have my own computer, so I am using a university computer cluster machine, and cannot install there. How do I access the COS126 standard libraries? It may work automatically but if not, directly download copies of,, and into your assignment work directory (the same folder as from the booksite (scroll to top of page). Compile them and then you can use them. (You'll have to copy them into future weeks' assignment folders too.) The lab TAs can help you with this.

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 Prompt/Terminal.

How do I get the files needed to complete the assignment? There are two approaches: download a single compressed .zip file and then decompress it on your computer to the right location; or, grab the folders themselves using the File Transfer Protocol (FTP). If you've never used either of these tools, follow one of the methods below. (You'll need to do a similar process each week from now on.)

  1. Zip files on Windows. Download the file listed on the assignment page. In Explorer, view the directory that you downloaded the zip file to. Right-click on the zip file and "Extract All..." which will ask you to choose the extraction location. (Don't double click the zip file, since it browses the contents but does not extract them.) A new subdirectory nbody will be created at the extraction location, with the files inside of it.

  2. Zip files on OS X. Download the file listed on the assignment page. In Finder, view the directory that you downloaded the zip file to. Some browsers will automatically have extracted the zip file and created an nbody folder for you with the extracted files inside of it. (Some also will delete the original .zip file.) Otherwise if you see but no nbody folder, double-click on the .zip file to extract its contents. Finally, drag or copy-and-paste the nbody folder to your desired location.

  3. FTP on Windows. Click Run (Windows-R) and enter explorer which will let you browse our FTP site. Right-click on nbody (the folder for this week) and select "Copy to Folder...". A new subdirectory nbody will be created at the target, with the files inside of it.

  4. FTP on OS X. Either (a) in Safari, navigate to or (b) in Finder, press Command-K and enter this as the Server Address. If prompted for a name and password, choose to Connect as a Guest. This lets you browse our FTP site. Drag-and-drop the nbody folder to your desired location on your computer to make a copy of it.

  5. Linux. Execute wget -r at the command line.

Frequently Asked Questions Part 2: Programming Questions

What preparation do I need before beginning this assignment? Read Sections 1.4 and 1.5 of the textbook. You also should get familiar with using the command-line.

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!

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.

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).

May I write my own functions (static methods)? It's not required and not expected for this assignment, but it is permitted if you want. Here are two possibile ways to modularize your program.

// 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)

May I write my own objects/classes? There are organizational advantages to using objects, which we'll explore later. However, for this assignment, for full credit, you must adhere to the parallel array data structure specified in the assignment. Many well-used programming languages do not allow data abstraction and it is good to be able to write readable, well-organized code subject to that limitation.

My computer doesn't display the animation smoothly. Is there anything I can do? Use void msec) to use the animation mode of standard draw and pause for msec milliseconds. Call it once at the end of each time step (frame), not after each drawing command. A typical delay time would be between 10 and 50 milliseconds, but use whatever looks good on your computer.

Can I combine Steps 1, 2, and 3 for each body? You must separate Step 1 (compute all of the forces) from Step 2 (moving 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.

My animation looks fine, but the numbers are off a little bit when I follow the tests below, what could be causing this? Read the question just above — this is the most common cause. Double-check that you followed the assignment instructions exactly in the order of how positions and velocities are updated.

I draw the bodies, but they do not appear 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. Since we want it centered on the origin with a "square radius" of R, the minimum of each axis should be –R and the maximum should be +R.

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 timing conflict (known in computer science as a "race") between 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.

When I add the music, I get this weird error. How can I fix it?

java.util.prefs.WindowsPreferences (init). Could not open/create prefs root node Software\JavaSoft\Prefs at root 0x80000002. Windows RegCreateKeyEx(...) returned error code 5.
Try running your command prompt as administrator (right-click on the shortcut icon). Then use it as before and try again. If this doesn't help, contact the course staff.

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",
                   px[i], py[i], vx[i], vy[i], mass[i], image[i]);
Here are our results for a few sample inputs.
% java-introcs 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-introcs 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-introcs 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-introcs 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-introcs 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.

Reviewing your Program