An electronic "notebook"... Please treat this as "work in progress". --Amara

Jovian Dust Stream and Io Location Calcs

"Back-of-the-Envelope" Dust Stream Rate Calcs.

These calculations find the dust stream mass rate from Io as detected by the Galileo DDS (dust detector) instrument.

In this program, one can try different values of the "wedge angle" (which gives a surface cross-section for dust particles detected by Galileo), a distance from Io, particle density, particle radius, DDS rate, DDS sensitivity.

I calculate for a range of values for the mass rate of particles from Io:

0.01 kg/sec (11 deg wedge, 0.2 particles/min average rate) to
10.0 kg/sec (45 deg wedge, 30 particles/min average rate)

Where is Io?

Here, I'm asking the question, "Where is Io?" when we see peaks in the Galileo rate data that we think are "Io peaks". The "peaks" were seen by eye, after binning the Galileo DDS data in 10-hour bins, which removed the strong 10 hour Jupiter magnetic field rotation signature.

Some of the peaks are quite strong, and some of them are simply clear, and some of them are barely visible. I used a subjective criteria to distinquish between the peaks, to help us choose which points are good indicators of Io and which are not. My subjective criteria is (1=poor, 2=ok, 3=good).

The results show that there seems to be a trend in the plotted results, and the linear trend may say something about the "Io torus" extended source of dust particles, rather than a local Io source.

I found a handy reference to Io that shows me a global view of the complexities of the Io system HERE. Note that the Galileo spacecraft orbits around Jupiter on average every two months, and Io orbits around Jupiter every 1.8 days.

My/Our Method to Locate Io

  1. I picked out by eye approximately 60 places in the Galileo DDS data, where Harald/we think that we have "Io peaks".

  2. From the time shown on the x-axis of Harald's graphs (resolution of tenths of a day), I found Galileo's position in Harald's SPICE Galileo orbital trajectory file: "glrtn.dat".

  3. From Eberhard's dust particle trajectory file, where he calculated the position, and time of a dust particle to travel, I found the number of seconds for a charged dust particle to move from a position near Io to a position near Galileo. Eberhard's model assumed: 
           s (m)        m (g)        U (V)        q (C)    QM (C/kg)        phase
  8.929E-009   2.982E-021   3.000E+000   2.982E-018   1.000E+003   1.200E+002

    Eberhard's model has the main physics of the dust particle dynamics. We have to assume that the acceleration doesn't change (or change much) from the Io position to the Galileo position. Further out in the Jupiter system, this assumption won't hold. Eberhard assumed a charged particle of a particular Q/m ratio, a simple dipole magnetic field for Jupiter, and a size of 10 nanometers and Lorentz force. Other assumptions are listed above.

  4. I subtracted the dust particle travel time from Galileo's "Io event" time.

  5. Taking care to have the same reference longitudes (comparing positions in spherical coordinates), see where Io is located using Harald's SPICE Io orbital trajectory file: "iortn.dat".

Something About the Uncertainty

"Event times" for Io peaks were gathered by eye, and are uncertain by tenths of a day. So if a "peak" is determined to be at day 200.1, it could really be Day 200.0 to 200.2. What does this translate to in the results?

Roughly: Galileo's position could move about 2Rj during the .2 Day. The particle trajectory time could change about 300 secs (~.1 Hour) during the .2 Day. Io's longitude position could change about 20 degrees in longitude during that time.

Output

My output looks like this (for ~60 different events). 
************************************************************
Event: Year:       1996.00 Day:       177.200

Spherical Galileo coords at event =
gal_long (deg) =       -65.959251
gal_lat (deg) =       -2.8264236
gal_r (Rj) =       34.991103

The time for particle to travel from 6Rj to
Galileo position at event =       14312.5(secs)

The longitude of particle at this source time
for (Galileo time - trajectory time) =       -227.96225(deg)

Spherical Io coords at particle source time =
io_long (deg) =        44.270428
io_lat (deg) =       0.44495973
io_r (Rj) =       5.9235472

Quality: 3
************************************************************
These numbers can be easily translated into a table form. The values we are most interested in are "The longitude of particle at this source time for (Galileo time - trajectory time)" and "io_r (Rj)". In fact we subtract the two to see where Io is, and if any clustering or correlations appear.

Results

The data plotted for the Galileo-Particle-Io Trajectory Longitude versus the Galileo-Particle Trajectory Longitude.

Scatter Plot

Plots from our table of all ~60 events, colored in terms of quality of the data points.

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Histograms binned by Longitude

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Separating the Results based on the Point Quality



The "Poor Quality" (1) Points.

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The "OK" Quality (2) Points.

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The "Good Quality" (3) Points.

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WaveButton MPI-K Dust Group

Created by Amara Graps.
Last Modified by Amara Graps on 15 March 1999.