It works on all computers because it works in your browser.  I can even run it on my cell phone.
It doesn't have nearly all the bells and whistles of the Windows version.  You can't even save your simulations (at least not yet!)
It also behaves quite differently on different computers.
 
This is a recreation of the solar system barycenter simulation:
http://orbitsimulator.com/gravitySimulatorCloud/ssBarycenter.html
 
This traces the pentagram of Venus caused by the near 13:8 resonance between Venus and Earth
http://orbitsimulator.com/gravitySimulatorCloud/venusPentagram.html
 
This shows all the Moons of Jupiter
http://orbitsimulator.com/gravitySimulatorCloud/joviansystem.html
 
This shows the motion of the Spitzer Space Telescope.  Scroll down for a rotating frame version.
http://orbitsimulator.com/gravitySimulatorCloud/spitzer.html  
 
Voyager 1 approaches Jupiter.  It makes very close flybys of Io, Ganymede and Callisto before heading off for Saturn.
http://orbitsimulator.com/gravitySimulatorCloud/voyager1JupiterApproach.html
 
Super-massive black hole at the center of the Milky Way
http://orbitsimulator.com/gravitySimulatorCloud/mwbh.html
 
This one is user-controlable!
Deflecting Apophis.  Apophis won't hit Earth in 2029, but it will make a very close approach.  During this approach, if it passes through a "keyhole", it will return to strike Earth in 2036.  Scientists are certain that it won't pass through this keyhole.  But "what if"?  
 
This simulation begins in 2014.  This simulation gives you 3 Apophises.  The one called Apophis is based on Apophis' actual trajectory.  But a mere 10 kilometers away sits a pair of 'keyhole Apophises'.  They will pass through the keyhole.  They will return to strike Earth in 2036.  The "Vectors" interface lets you control them.  Leave one of them alone to act as your experimental 'control'.  See how much delta V it takes to nudge the other one off course so it misses the 2029 keyhole.  Just edit the velocity, and it will take off on a new trajectory.
 
This simulation controls the time step for you.  It also pauses prior to Apophis' close approaches to Earth.  You can override the time step, but don't.  If you go faster than 2048, and 32 when Apophis is in Earth's vicinity, you will not get accurate results.  The simulations takes care of this for you.  It takes some time for this simulation to develop, so be patient.  The sim will automatically pause a few days before Apophis' close approaches, so you won't return to your computer to discover you've missed it.
http://orbitsimulator.com/gravitySimulatorCloud/apophis2014.html
 
Trojan planet
Adjust the mass of a planet and its trojan companion to see what mass ratios are stable.
http://orbitsimulator.com/gravitySimulatorCloud/trojanratio.html
 
Turn off Sun's gravity
In demonstrating Newton's Laws, it seems to be a common conceptual question:  What path would the planets follow if the Sun's gravity were somehow turned off? With the press of a button the students can find out.
http://orbitsimulator.com/gravitySimulatorCloud/turnOffSunGravity.html
 
A binary star system with planets
This is one of the original Gravity Simulator simulations.
http://orbitsimulator.com/gravitySimulatorCloud/casella.html
 
If the Moon orbited the Earth in a polar orbit, it would crash to the Earth in under a decade due to the Kozai Mechanism.
http://orbitsimulator.com/gravitySimulatorCloud/kozaiMoon.html
 
Earth captures an asteroid.  In 2006, Earth captured 2006 RH120,  It spent just over a year orbiting Earth before escaping back into interplanetary space.
http://orbitsimulator.com/gravitySimulatorCloud/capturedmoon.html

Same here , works when the ">" button is pressed under "time step" .  
Wonder how Tony did this !

Yes, this is HTML5 with javascript.
I probably should have began this sim unpaused.
 
I might try to save the trajectories, but there are a few other things higher on the priority list at the moment.
 
You can't save the sim as you figured out.  When you close it you lose it. Javascript doesn't allow you save files on a user's hard drive for security reasons.
There's 2 work-arounds:
1. Save the simulation to a text box.  The user copies the contents, pastes it into a text editor and saves it as a text file with an html extension.
2. Use PHP or Perl to save a user's simulation to my server.  This would require users have an account ($$) with me as server space is not free.
 
I made this because I work in a school where all the students have iPads.  I wanted to give them some assignments using Gravity Simulator that would work on their iPads.  It's worked fine for that purpose.  It's simple.  There's nothing to install.  The HTML5 version might not ever be as powerful as the Windows version.  Browsers don't like being thrown into what they perceive as an endless loop.  Any attempts I've made to speed it up result in a "script not responding" error.
 
So for the moment, this is just an attempt to recreate some of Gravity Simulator's simulations on a platform anyone can access.  I'll post a few more in the coming days.

Quote from frankuitaalst on 10/02/14 at 13:18:54:

Yes, I had to reprogram.
But keep in mind, the RK-4 routine that powers Gravity Simulator is already coded in C++, which is virtually identical in syntax to javascript (at least for the stuff I'm doing).
And the orbital elements code was already translated into javascript code on my orbitsimulator.com/formulas page.
 
So it was more of a piecing together of stuff that already existed, and making slight modifications rather than coding from scratch.
 
The code is executed in your browser.  You can save it to your computer and run it offline.  Do a "view source" and you can see the code.
 
Here's another one: http://orbitsimulator.com/gravitySimulatorCloud/spitzer.html
This shows the Spitzer Space Telescope in a rotating frame.

I really like this work Tony ! especially the Jovian system .  
I guess we ( users ) cannot (yet ) select existing simulations and let them run on this app ?

I've added a few more to the first post in this thread.

Again , amazing achievement Tony !
 
I ran the http://orbitsimulator.com/BA/1435715518034_aprelease.html simulation and have following info :  
 
* Apophis crashes to Earth in 2029 . Is this also what you get ?  
* The time slice is 2048 , I can't change it to lower or higher values . The "reverse" however works .  
* Two input buttons seem to interact : pushing the "star field " sometimes triggers the "pre-orbit "feature . Sometimes the "pre-orbit" button doesn't seem to react also .

Thanks , I wasn't aware there was an "optimal" time step avalable .  
Curious : how did you code for this ??? Taking into account the minimum actual distance between bodies ?  
 
I was talking about the buttons :
"stars " and the "pre-trails" which interfere .