Milo's Solar System: quantitative replacement for the PHET "my solar system" orbit simulator

 

As 2020 dies, so does flash animation. I only care about two sites that will no longer be functional after flash is deprecated: homestarrunner.com, and PHET's "my solar system" orbit simulator (screenshot shown).  

Here's a link to the 2021 replacement: Milo's Solar System.  Read on for details.

See, I can't do live experimentation with gravitation. I can *predict mathematically* how to retain a circular orbit when the mass of the central planet is doubled:  Set the formula for gravitational force equal to the centripetal force.  Solve for speed v - you get root (GM/d).  So by Bertha's Rule of Ones*, doubling the mass means the factor of change for the speed is root(1*2/1) = root 2.

*Also known as the Factor of Change method

My students expect that the next step after any mathematical solution is to provide experimental evidence.  How to do that?  I can't very easily double the mass of the Earth, then speed up the moon by 40% to see if it still orbits in a circle.  And the gravitational force is too weak to set up a small-scale solar system in the lab.

For years, I've used the free PHET simulation linked above to show, if not real experimental evidence, at least something that has the look and feel of an experiment.  You can see me performing several calculations and experiments as quantitative demonstrations in this College Board video.  

Now that flash is gone, we need a replacement for the phet simulation.  We have one.

For his senior community service project, Milo Jacobs has essentially replicated "my solar system."  I'll call it "Milo's Solar System" for now.  Open it and press play - you'll see the yellow planet in a circular orbit.

To solve the "double the central planet's mass" problem I posed above, click on the big blue central planet.  You'll see its mass as "100,000" arbitrary units.  Change that to 200,000 and hit play - the yellow planet glides off the screen, obviously not in a circular orbit.  But, we know that the speed has to be root-2-times bigger than before to keep a circular orbit!  So, click on "undo motion", and change the vy value from 100 to 141.  Press play again... and you see a circular orbit again!  Yay!

I've written out twelve different versions of this question in this file.  I use it as a "come and show me" exercise - I give one randomly to each student.  They come to my desk to show me their solution.  I check that they've used Newton's law of gravitation and circular motion methods; then whatever their answer, I have the student use the simulation to check whether they in fact get a circular orbit with their result.  The student brings me a screenshot of a circular orbit with their new values of mass and/or speed and/or planet position.  If their solution was incorrect, they find out for themselves!  They either redo their prediction, or they come back to ask for help.  (Or most likely, they ask for help from a classmate.)

Milo's Solar System works best with chrome as your browser.  It works well for me on either my windows PC or my iPhone in chrome.  

Please explore - just as on the original PHET, it's possible to drag the velocity arrow, to add additional planets, and generally to explore trajectories.  The main benefit of Milo's simulation over the others I've seen online is that it's easy and fast to make quick quantitative changes to the initial speed, radius, and mass values to check whether an orbit is circular.  

(If you have operation requests or if you find bugs, please post a comment or email me - I can ask the author for changes.  We each tested the questions in the "come and show me" exercise, and they all seemed to work fine!)