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.

Orbital Crystals

I'm now calling these Orbital Crystals, being inspired by a friend who's into rock crystals.  These images/structures I'm creating with the JPL Horizons data have similar characteristics:

1. They form regular patterns with occasional "flaws" that adds complexity to the piece
2. They take time to form

So the orbital crystal shown below is sort of a mind-bender.  It is a plot of the angular distance (as seen from Earth) from Jupiter to Io in arc seconds (the x-axis) versus the angular distance (also as seen from Earth) from Jupiter to Europa in arc seconds (the y-axis), over the course of the year 2015.  Time resolution is 1 hour, which means 8760 data points were used to make this plot.





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I also created another ribbon today using the orbits of Io and Europa.  I played with the angles in gnuplot until it looked like something sort of interesting.

Seven Mutual Events At Jupiter

On the 9th of February 2015, there will be seven mutual events at Jupiter.  This is the most number of mutual events this season, as far as I'm aware.  All four Galilean moons will be at play.

05:26 - 05:29: Io occults Europa.  Visibility for this event will be North and South America

05:32 - 05:34: Io eclipses Europa.  Visibility for this event will also be North and South America

10:34 - 10:40: Ganymede occults Europa.  Visible from western North America, all of the Pacific (including Hawaii), and some of east Asia.

10:47 - 10:50: Ganymede eclipses Europa.  Also visible from western North America, all of the Pacific (including Hawaii), and some of east Asia.

13:33 - 13:41: Callisto eclipses Europa.  Visible from the western Pacific, east Asia, and Australia.

20:56 - 21:01: Ganymede occults Io.  Visible from west Asia, all of Europe, and all of Africa.

21:06 - 21:13: Ganymede eclipses Io.  Also visible from west Asia, all of Europe, and all of Africa.

Dust off your photometers and take some data!

I'll post more information on my 'Jupiter Today' podcast for 2/9/2015.

https://www.youtube.com/channel/UCYDhvZYNk09bE28HE1BI65w

Five Mutual Events At Jupiter For Groundhog Day

Groundhog day is my fifth favorite day of the year, after the Solstices and Equinoxes.

On that day, the moons of Jupiter are involved in five "Mutual Events" which means that some kind of interaction (from Earth's point of view) goes on -- either one moon eclipsing or occultating another moon.

This is the most number of mutual events on a single day in this season on Jupiter (an equinox) sofar.  More to come.

The maps of the Earth below shows the visibility of each event.  The small dot in the center of the image marks the location on the Earth where Jupiter will be at the zenith at the time of the event.

All four moons are involved in these five events.  Here are the details:

01:32-01:46 Ganymede eclipses Callisto.  This is a 13.7 minute event

View from Earth

Visible in Europe, Africa, some of South America

03:29-03:33 Io occults Europa.  This is a 3.6 minute event

View from Earth

Visible in Africa, North America, South America

07:53-07:59 Ganymede occults Europa.  This is a 5.7 minute event

View from Earth

Visible in North America, South America

18:17-18:24 Ganymede eclipses Io.  This is a 7.2 minute event

View from Earth

Visible in Asia, Australia, and some of Europe

18:32-18:37 Ganymede occults Io.  This is a 5.3 minute event.

View From Earth

Visible in Asia, Australia, and some of Europe

Send your images and data to jupitertoday AT gmail DOT com

Color Adds Depth

This is using the same data as in my last post, but just colorized.  It adds a nice sense of depth.  I'll have to play with different colors as time goes on.  But for now, the default ones: