Thinking About Motion

The last section of my daily Jupiter Today podcasts is a summary of the position of Jupiter relative to the Earth and the Sun.  One of the values I report is the daily change in velocity (in km/hour).  What I've noticed after these few months is that the change in velocity itself is changing.

So I decided to finally look into this a little more.

Below are six plots.  The x-axis in every case is the number of days past 2015-Mar-22.  The y-axis is the value of the parameter in the units described below.

The 1st plot is the distance from Jupiter to Earth (in km) over the course of ten years, sampled every day.

The 2nd plot is the difference in distance over the course of that day.

The 3rd plot is the radial velocity between Jupiter and Earth (in km per day).

The 4th plot is the change in the change in that radial velocity.

The 5th plot is the radial acceleration between Jupiter and Earth (in km per day per day)

The 6th plot (the one I'm most interested in) is the change in that radial acceleration.

To put this into language, what this last plot is showing is that not only is the change in velocity changing, but that change is changing too!!!! Confused?????  So am I.

I've been trying to figure out a way to describe what this would feel like in our ordinary life.  The best I can come up with is that we're driving a car over bumps that are changing their shape over time.  So the amplitude (and frequency????) of the bumping is changing as we drive over them.

Looking at the plot itself, what do the maxima and minima represent?  My best guess is superior conjunction and opposition.  But which is which ... and why?  Why does this plot have a "sawtooth" shape and not a sine wave shape?  I'm fairly certain that the smaller wiggles are caused by Jupiter's moons.

For sure I need to look at this closer and in as many perspectives as I can.

If any of you have any ideas on how to interpret these plots, please comment!

Mimas and Enceladus

A suggestion was made that I take a look at some of the Saturn moon orbital crystals so I did just that, but got a little distracted by my first one taking orbit data of Mimas and Enceladus (the two large inner moons of Saturn).  This is what I came up with:

but then I simply rotated the image by 10 degress and saw an interesting motion effect totally being created by my brain.  So I made a little movie taking the original image and rotating it through 180 degrees at 10 degree intervals.  Doing this, I got this:

Please note that the gif movie above is NOT a representation of the motions of these moons along their orbits around Saturn, but rather is a kind of optical illusion.  Rather, consider this an alternative perspective on how the moons are connected in space and time.

Hope you enjoy.

Galilean Moon Orbital Crystals for March 2015

Here are the orbital crystals of the four Galilean moons of Jupiter for March 2015.  This is using data taken from the JPL Horizons website.

First, the individual pairs:

Io and Europa

Io and Ganymede

Io and Callisto

Europa and Ganymede

Europa and Callisto

Ganymede and Callisto

So then I can combine all of these into one image and colorize each one differently to come up with this:

Orbital Crystal for March 2015

Here's the same image, but showing the orbits:

Orbital Crystal showing orbits

And then I can zoom in a few times:

I hope you find these as beautiful as I do.