Galilean Moon Mutual Shadows and Mutual Transits

Dave Dickenson recently published his annual Top 101 Astronomical Events for 2016 and I was surprised to see that (at least according to this article) the shadows of pairs of moons (he calls them 'double shadows') was visible from Earth twenty-seven times!  Wow so that takes up 26.73% of all the events for this year!

"Dave!", I thought, "why did you mention these events if for no other reason than filler so you could get up to your famous 101 events?"  You were actually very very lucky to have just the right number of double shadow events to fill what would otherwise be a big gap in your list.

Mutual events involving two or more moons plus Jupiter itself is pretty exciting, but aren't there any other things -- perhaps more interesting -- going on there?  What about actual moon transits?  Too many or too few to fit into your pre-determined number of top events for 2016?

I, for one, don't think that the moon transits should be left out, especially if you're already looking for moon shadow transits anyhow.  But listing shadows and transits would have made the list way too unbalanced, so maybe this is why Dave chose just the shadow events -- because they fit.

So I decided to take a look and see what else is happening at Jupiter this year from Earth's POV.  Plus, like any good scientist, I wanted to check Dave's work.  I'm happy to announce that, for the most part, our results agrees.

So I found Galilean moon event predictions at the IMCCE and wrote a program to parse the data and tell me when each moon is transiting and when it's shadow is transiting.

I then produced these plots.  The first shows the shadow events and the 2nd shows the transit events.

Shadow Events

Transit Events

The y-axis is an arbitrary value that allows me to separate events.  The x-axis is the day number for this year (2016).  I've labeled the events.

According to this data, there are 25 'double shadow' events and 30 'double transit' events.  The two events that Dave has on his list that I don't have on mine are:

12 April double shadow Io - Europa
08 November double shadow Ganymede - Europa

Not quite sure where Dave got his data, but this is clearly a case of "your results are only as good as your data".

Here are the events I found (EV=event, MM=month, DD=day, HH=hour, MM=minute):

Shadows (under the EV column: I = Io, E = Europa, G = Ganymede, C = Callisto):

    EV MM DD HH MM   MM DD HH MM Comment
----------------------------------------------
 1. IE  2 22 20 42 -  2 22 20 46
 2. IE  2 26  9 38 -  2 26 10  4
 3. IE  2 29 22 35 -  2 29 23 22
 4. IE  3  4 11 32 -  3  4 12 40
 5. IE  3  8  0 29 -  3  8  1 59
 6. IG  3  9 18 57 -  3  9 19 11
 7. IE  3 11 13 26 -  3 11 15 17
 8. IE  3 15  2 23 -  3 15  4 35
 9. IG  3 16 20 51 -  3 16 23  6 Io Passes Gan
10. IE  3 18 15 19 -  3 18 17 35 Io Passes Eur
11. IE  3 22  4 24 -  3 22  6 32
12. IG  3 23 23 48 -  3 24  1  0
13. IE  3 25 17 42 -  3 25 19 29
14. IE  3 29  7  1 -  3 29  8 26
15. IE  4  1 20 19 -  4  1 21 23
16. IC  4  3 15 12 -  4  3 15 51
17. IE  4  5  9 38 -  4  5 10 20
18. IE  4  8 22 56 -  4  8 23 17
19. IC  5  7  4 40 -  5  7  5 43
20. IG  8  7  5 32 -  8  7  6 34
21. IG  8 14  7 33 -  8 14  9 41
22. IG  8 21 11 31 -  8 21 11 36
23. EG 10 17 20 59 - 10 17 22 14
24. EG 10 24 23 33 - 10 25  2  8 Eur Passes Gan
25. EG 11  1  3 20 - 11  1  4 41

Transits:

    EV MM DD HH MM   MM DD HH MM Comment
----------------------------------------------
 1. IE  2 19  8 11 -  2 19  8 18
 2. IE  2 22 21  3 -  2 22 21 27
 3. IE  2 26  9 54 -  2 26 10 34
 4. IE  2 29 22 46 -  2 29 23 43
 5. IE  3  4 11 38 -  3  4 12 50
 6. IE  3  8  0 30 -  3  8  1 58
 7. IG  3  9 18 55 -  3  9 18 59
 8. IE  3 11 13 21 -  3 11 15  6
 9. IE  3 15  2 13 -  3 15  4 14
10. IG  3 16 20 39 -  3 16 22 15
11. IE  3 18 15  5 -  3 18 17 20 Io Passes Eur
12. IE  3 22  3 57 -  3 22  6 12 Io Passes Eur
13. IG  3 23 22 23 -  3 24  0 38 Io Passes Gan
14. IE  3 25 16 52 -  3 25 19  4
15. IE  3 29  6  1 -  3 29  7 56
16. IG  3 31  1 40 -  3 31  2 22
17. IE  4  1 19 10 -  4  1 20 49
18. IE  4  5  8 19 -  4  5  9 41
19. IE  4  8 21 29 -  4  8 22 34
20. IE  4 12 10 40 -  4 12 11 28
21. IE  4 15 23 50 -  4 16  0 21
22. IE  4 19 13  2 -  4 19 13 15
23. IG  8 14  6 46 -  8 14  7 56
24. IG  8 21  9  5 -  8 21 11  2
25. EG 10 10 18 53 - 10 10 19 17
26. EG 10 17 21 41 - 10 17 23 42
27. EG 10 25  1 13 - 10 25  3  3
28. EG 11  1  5 40 - 11  1  5 49
29. IG 12 21 13 19 - 12 21 14 18
30. IG 12 28 16  1 - 12 28 17 26

What I think is very very cool about these events is that in some of them, one moon passes the other one while both are in transit!!!!!

In 2016, there are no triple or quadruple shadows or transits, unlike in 2015.  I looked ahead to 2017 and see pretty much the same as 2016.

Jupiter Moon Audio | 29 December 2015

Here once again are the sounds of Jupiter's moons as they revolve around the planet over the next 24 hours.

First, the sounds:

Jupiter Moon Audio | 29 December 2015

And then some plots.  Here are the orbits as seen from above.  Blue line pointing to the left is line of sight to Earth.  Red line pointing left is line of sight to the Sun:

Relative distances (in km):

Relative velocities (in km/min):

Relative accelerations (in km/min/min):

Line color code:

• Cyan - Io / Europa
• Pink - Io / Ganymede
• Yellow - Io / Callisto
• Green - Europa / Ganymede
• Red - Europa / Callisto
• Blue - Ganymede / Callisto

Playing IRIS Spectra Like A Player Piano

I took a sequence of calibrated IRIS spectra, identified the location of each peak, and then translated the location of the peak and the amplitide of a peak to an audio signal that we can hear.  The plots below show the peaks greater than a value of 25 (in ADU's).

Now -- how to read this plot:

Along the x-axis is the spectrum number.  In this dataset, there are 1168 spectra each taken 2 seconds apart.  So this entire dataset took 2336 seconds, or 38 minutes, 56 seconds.  Along the y-axis is the pixel location of the detected peaks.  So if you can imagine a player piano strip, the song will be played from left to right, with each dot representing a spacial location on the Sun.  In this case, the pixel range (0-548) corresponds to a nice audio frequency range, so I didn't transpose or spread out the frequency range in any way.  So a pixel location of 432 will correspond to a frequency of 432 Hz.  The amplitude of the sound corresponds to the brightness of the pixel value at that peak.

The first plot below shows the peaks above a data value of 25 ADU and as expected quite a few notes are being played at the same time.  The 2nd plot shows the peaks above a data value of 50 ADU where there are fewer notes being played.  Notice that starting at about spectrum 800 (along the x-axis) and ending about 900, the strip being played starts playing a lot more frequencies.  It also turns out that the amplitude of these tones increases by as much as a factor of 300!  What is this?  Well, it turns out to be IRIS moving through the South Atlantic Anomoly (SAA).  In the sound sample, the amplitude is obviously saturated, so I've decreased the volume of that section by 10 dB so your ears aren't blown out.

Peaks Above 25 ADU

Peaks Above 50 ADU

And here are a couple closeups.  The first is from the beginning of the dataset.  The 2nd is right before and through most of the detection of the SAA.  The closeups make it a bit easier to understand what's being played.

I should mention here that these sound samples SHOULD NOT BE PLAYED THROUGH A SPEAKER SYSTEM.  Frequencies and amplitudes might be too much for your system which could result in permanent damage.  Listen to this stuff with headphones and make sure you have control of the volume.


Here is the playlist:

IRIS Spectra Player Piano

Jupiter Moon Distance, Velocity, and Acceleration Audio | 25 December 2015

An overhead view of the orbits:

Distances (in km) over the next 24 hours:

Velocities (in km/min) over the next 24 hours:

Acclerations (in km/min/min) over the next 24 hours:

Listen to theses various forms of motion:

Jupiter Moon Audio 25 December 2015

Jupiter Moon Velocities & Accelerations, Plus More M13 Music

Today I've listened to the relative accelerations (changes in velocity) between the four Galilean moons of Jupiter as they orbit the planet.  As you can see from the plot below, the values for the accelerations don't go much above 3 km/min/min either accelerating or decelerating.  That translates to 0.83 m/s/s, which is about ten times "slower" than Earth's gravitational acceleration -- or 0.1g.  Pretty cool.

I also show the usual plots of relative velocities....

Line color code:

• Cyan - Io / Europa
• Pink - Io / Ganymede
• Yellow - Io / Callisto
• Green - Europa / Ganymede
• Red - Europa / Callisto
• Blue - Ganymede / Callisto

... and orbits:

Finally, here is the velocity and acceleration audio:

Jupiter Today | 21 December 2015 | Velocity and Acceleration Audio



Continuing study of SDSS image of M13

I took this image of M13 from the SDSS:

and found the 115 brightest stars:

I then calculated the distance, in pixels, between the position of the star and what I determined to be the center of the cluster.  Thus, my calculation is the radial distance of the star from the center of the cluster.  I then converted this distance to an audio frequency and the brightness to an amplitude, and added them all up to get this:
 
The Sound of M13's 115 Brightest Stars I

I then took the ten closest stars to the center and made a tone with them, and then the next ten, and then the next, and the next until I had eleven different tones each containing the audio distances of ten stars.  In what you're about to hear, I run each 10-tone sound for 14 seconds, with one second of overlap.  No idea what this means, if anything.  But I sure do like the sounds produced.

The Sound of M13's 115 Brightest Stars II

Jupiter Today | 18 December 2015 | Velocity Audio

Let's start with the sound of the relative velocities:

Velocity Audio | 18 December 2015

Here are the positions of the four Galilean moons of Jupiter as they orbit the planet over the next 24 hours.  This view is looking down on the system, and the moons are moving counterclockwise.  The blue line pointing towards the left is the line of site to Earth.  The red line pointing left is the line of site to the sun.

Here are the relative velocities between the four moons (six combinations):

The y-axis shows the velocity in kilometers per minute.  Negative values represent moons moving towards one another, positive values represent moons moving away from one another.  So for example, the blue line representing the relative velocity between Ganymede and Callisto shows that they are moving toward one another at a pretty constant velocity of 300-ish km/min.  Looking at the orbit plot above, you can see that Ganymede is "catching up" to Callisto just as the velocity plot shows.

Line color code:

• Cyan - Io / Europa
• Pink - Io / Ganymede
• Yellow - Io / Callisto
• Green - Europa / Ganymede
• Red - Europa / Callisto
• Blue - Ganymede / Callisto

Jupiter Today | 17 December 2015 | Velocity Audio

Here are the positions of the four Galilean moons of Jupiter over the next 24 hours:

This is a plot showing the relative velocities between the four moons:

Notice that at about 21:00 UTC, all but Io's motion relative to Ganymede is very nearly the same -- in this case, moving toward one another at about 200 km/minute.

Line color code:

• Cyan - Io / Europa
• Pink - Io / Ganymede
• Yellow - Io / Callisto
• Green - Europa / Ganymede
• Red - Europa / Callisto
• Blue - Ganymede / Callisto

And for fun and because these are usually so pretty, the orbital ribbons for today:

And finally, the sound of those velocities:

Velocity Audio | Jupiter Today 17 December 2015

The Sound of Velocity | Jupiter Today 11 December 2015

So instead of listening to the distances between the four Galilean moons of Jupiter, today I'm listening to the changes in distance -- otherwise known as velocity.

This first plot shows the orbits of the four moons as seen from above.  Rotation around Jupiter (which would be in the center) is counter-clockwise:

The blue line going left points to Earth.  The red line going left points to the Sun.

This next plot shows the changes in distance (velocity).  The y-axis units are in km/minute and the x-axis is the UT during 11 December 2015:

Line color code:

• Cyan - Io / Europa
• Pink - Io / Ganymede
• Yellow - Io / Callisto
• Green - Europa / Ganymede
• Red - Europa / Callisto
• Blue - Ganymede / Callisto

So in the plot above, the pink line shows the velocity between Io and Ganymede.  At 0h UTC, these two moons are moving away from one another at a velocity of about 800 km/minute.  By about 13:30 UTC, the relative velocities between the two moons is zero km/minute.  By the end of the day, the two moons are moving away from another at a velocity of almost 800 km/minute.

Also note that at about 16:11 UTC that the pink line and the yellow line cross.  This shows that at that moment in time, Io and Ganymede are moving away from each other at exactly the same velocity as Io and Callisto are moving away from each other.  HOWEVER, Io is accelerating (positive slope of velocity) towards Ganymede and decelerating (negative slope) towards Callisto!

Very very very coo, and mind blowing and dizzying.

And finally, the mixed sound itself:

The Sound of Velocity

Jupiter Today 09 December 2015

A nice day at Jupiter today.

Notice that at about 05:08 UTC, the distances between Ganymede / Callisto, Europa / Ganymede, and Io / Callisto are all about the same.  Pretty nice!  Notice also that this three-distance convergence involves all four moons.

Here are the orbits:

and here are the distances:

Here is the sound of the distances:

Jupiter Today 09 December 2015

Jupiter Today 07 December 2015

Jupiter Today is resuming but it probably won't be every day.

Listen to the sound of the distances between the four Galilean moons change over the next 24 hours.  Best heard with headphones!!!!

The Sound of Jupiter Today 07 December 2015

This first plot shows the positions of the moons as they orbit Jupiter over the next 24 hours.  We're looking from the top of the system, so all of the motion is counter-clockwise.  The blue line is the line of site to Earth.  The red lines are the lines of site to the Sun, and 90 degrees to that to designate quadrants.

The 2nd plot shows the distances between each of the moons (the y-axis) as a function of time (x-axis, number of minutes since midnight).

Cyan - Io / Europa
Pink - Io / Ganymede
Yellow - Io / Callisto
Green - Europa / Ganymede
Red - Europa / Callisto
Blue - Ganymede / Callisto

Listening to Varying Brightness

I took this blurred image of M13:

and looked at the pixel values (representing brightness in the SDSS u band) along column 115, which cuts more-or-less down the brightest part of the image.

I then created three sound files.  The first (shown in red in the plot below) represents the brightness of the pixel.  The second (shown in green in the plot below) represents the change in the brightness (1st derivative).  The third (shown in blue in the plot below) represents changes in the changes in the brightness (2nd derivative).

I've scaled all of the data to fall within a frequency range of 100-200 Hz, which is the y-axis of the plot.  The x-axis is the row number.

Once all three sound files were made, I mixed them into a single track.  Wear earphones for the best effect:

M13 Brightness Changes

What do you hear?

Jupiter Today

Check out my daily posts about the Jupiter system over at my new blog Curious Participants.

Galilean Moon Orbit Crystal for April 2015

Here are the orbit crystals for April 2015.  Watch Jupiter Today every day for your dose of Jupiter action over the next 24 hours.

Io / Europa

Io / Ganymede

Io / Callisto

Europa / Ganymede

Europa / Callisto

Ganymede / Callisto

All Moons Combined

All Moons Combined, with Orbit Lines (white)

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.