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Juno perijoves 2 and 3, October 19 and December 11, 2016
Gerald
post Dec 18 2016, 09:07 AM
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This gif shows an attempt to fit the images into a mask which simulates a Jupiter spheroid, assuming a constant rotation period of 30.33740 seconds for Juno, and neglecting light travel time:
Attached Image

The rotation period is inferred from PJ3 images 103 and 126. You'll see a black margin at the top or bottom of Jupiter of variable thickness with respect to the ugly turqoise background mask. The most distant images of this sequence are taken from a distance of a little more than 100,000 km. Light takes about 0.3 seconds for this distance. So we get a shift of very roughly 100 pixels in the raw images due to light travel time. This appears to be similar to the observed error. So this will be one of the things which I'll include into my model. If you're using NAIF/SPICE libraries and kernels, this effect should already be considered.

Edit: ...hmm, I'm a bit hesitant, whether General Relativity (equivalence principle) allows for this simplification. May be I'd better adjust the angles manually, and then look which physical model fits.
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fredk
post Dec 18 2016, 03:50 PM
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QUOTE (Gerald @ Dec 18 2016, 10:07 AM) *
I'm a bit hesitant whether General Relativity (equivalence principle) allows for this simplification.

Which simplification?
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mcaplinger
post Dec 18 2016, 05:03 PM
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AFAIK, GR effects have never been part of the NAIF toolkit, but stellar aberration is: https://naif.jpl.nasa.gov/pub/naif/toolkit_...ice_spkezr.html
Although I doubt it makes much difference in this case.

Mods: IMHO this technical discussion belongs in some other thread.


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Gerald
post Dec 18 2016, 06:32 PM
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I was just looking for a simple solution to adjust for possible relativistic effects regarding spacecraft rotation. Since Juno's trajectory isn't an inertial system, but accelerated in a Newtonian understanding, we get into GR. I'd think, that this is implicite in SPICE by Ephemeris time (ET) - UT transformations.
I've been considering, that Juno's time-dilated rotation by GR might be equivalent to an offset by light travel time. But discussing this -- as M.Caplinger says -- would be an extra thread.
Since I can't be sure yet, to which degree relativistic effects play a role, and how complicated those considerations might become, I decided to adjust rotational offsets manually in a first step.

Edit: After these adjustments, the fitting looks better:
Attached Image

Maybe worth to create an animation (video) with black background and interpolated frames.
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mcaplinger
post Dec 18 2016, 07:14 PM
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QUOTE (Gerald @ Dec 18 2016, 10:32 AM) *
I'd think, that this is [implicit] in SPICE by Ephemeris time (ET) - UT transformations.

I don't think so. If this was the case then all time conversions would require knowledge of position. I think the full extent of SPICE's treatment of GR is in the mapping from ET=TDB to TDT, which applies only to the Earth and is not something I've ever used. See https://naif.jpl.nasa.gov/pub/naif/toolkit_...ound%20Material

I'd guess, without having worked it out, that in the total error budget of spacecraft pointing, GR effects are several orders of magnitude down in the list, at least for spacecraft and targets like the ones we deal with now. In the future, if mission planners are flying relativistic spacecraft to black holes, the SPICE toolkit will have to be enhanced.


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fredk
post Dec 18 2016, 07:20 PM
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QUOTE (Gerald @ Dec 18 2016, 07:32 PM) *
Since Juno's trajectory isn't an inertial system, but accelerated in a Newtonian understanding, we get into GR.

Newtonian mechanics can handle acceleration - that's the "a" in F = ma! GR effects are only noticible in rare circumstances, when either the velocities are large (relative to c), the gravitational potential is large (black holes etc), or when the precision is extremely high (Mercury perihelion measurements, GPS, gravity probe B.). I can't imagine that GR will be anywhere close to detectible in junocam. And being in a rotating frame does not imply time dilation.
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Gerald
post Dec 18 2016, 07:59 PM
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Well, in order to solve the question about whether relativistic effects might be relevant or not, I did a short SR calculation assuming velocities up to 1e-4 the speed of light, and got a relative effect of about 6.8e-9, which can't explain the offset, which I resolved only up to about 1e-7.
The effects I'm considering are often assumed to belong to SR, but they are better described by GR, like the twin paradox.

Eventually, the presumed fluctuations of the angular velocity seem to be of a different cause, either some spacecraft operation, which I've considered as less likely during flyby, interaction with Jupiter's environment, which looked also less likely at that height, unconsidered image processing effects, or some inaccuracies in the data, which I also assumed to be considerably smaller.
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fredk
post Dec 18 2016, 08:33 PM
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Taking this thread even farther from Jupiter, the twin paradox is special relativistic. It occurs on flat (Minkowsky) spacetime, which is what defines SR. It would also occur on curved spacetime, but curvature (ie gravity) is not needed.
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Gerald
post Dec 18 2016, 09:17 PM
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By the equivalence principle "acceleration = gravity", for a non-inertial observer a Minkowski space looks curved, and we are in GR, at least in my understanding.
Investigating Jupiter's gravity field extremely accurately is part of the Juno mission. Otherwise I wouldn't have replied once more.
That said, essentially, GR doesn't solve or simplify the labor in my JunoCam processing in the way I had hoped for.
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mcaplinger
post Dec 19 2016, 04:28 PM
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QUOTE (Gerald @ Dec 18 2016, 01:17 PM) *
Investigating Jupiter's gravity field extremely accurately is part of the Juno mission.

Some reading on this topic:

https://www.lpl.arizona.edu/~showman/public...i-etal-2010.pdf

No mention of GR. Here's a paper on gravitational lensing by Jupiter:
http://iopscience.iop.org/article/10.1086/378785/meta
or https://arxiv.org/abs/astro-ph/0302294

The radial deflection was 1190 microarcsec = 0.0058 microradians. Lost in the noise for imaging systems.


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Gerald
post Dec 19 2016, 06:33 PM
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For those, who like to use the MSSS version of the PJ3 RGB images, but color-corrected, i.e. with much less color striping artifacts, and adjusted color weights.

====
Re Juno and GR:
There are even people, who think, that measuring the very subtle Lense-Thirring effect, aka frama dragging, might be feasible during the Juno mission:
https://arxiv.org/pdf/1302.6920v5.pdf
https://arxiv.org/pdf/0812.1485v3.pdf

But the effect I've been thinking about, is much more crude: It's the relative effect of velocity to clocks. And I'm keen enough to use Juno's rotation as a clock. Seen from Jupiter (barycenter), we get velocity changes of about +/- 1e-4 c. For a constant angular velocity, even small to tiny time-dilation sums up to a a small angle, which might be detectable by JunoCam. But as I've calcuated above, we are below 1 pixel per perijove. However displacements well below 1 pixel, in some cases down to less than 1e-2 pixels, are feasible for measurements. We are then in the same order of magnitude as relativistic effects. I've attributed these effects to GR, since we aren't in two inertial systems in a flat spacetime regarding Juno and Earth. But reasonable calculations should be possible with means of Special Relativity.
My very first crude presumption without calculations has been, that a velocity of 1e-4 c might result in relativistic effects near 1e-6, but as mentioned above, it's only near 0.5e-8. I was two orders of magnitude off, since the 1e-4 c need to be squared in the calculation for the relativistic effects.
The idea came during pondering about the root cause of an angular offset observed during PJ3 image processing.

Btw.: Regarding SPICE: Probes close to the Sun may experience considerably stronger relativistic effects.
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Gerald
post Dec 21 2016, 08:00 PM
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Crescent Jupiter:
For the PJ3 Approach sequence, I'm currently running a calibration process. This required some software adjustment, since the background seems to be a little brighter than for Marble Movie. Previously this has been hard-coded. Now it's a program parameter. This calibration batch will run a few hours. So I found some time to enhance one of the intermediate images, image #2 of the PJ3 series:
Attached Image
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Ant103
post Dec 21 2016, 08:31 PM
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All I want to tell you Gerald : you are doing an AMAZING work ! I don't understand clearly the process behind (because you know, mathematics and me are not in very good terms…) but I admire you for this, and thanks for being so generous about it smile.gif


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scalbers
post Dec 21 2016, 09:09 PM
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Regarding GR, in my numerical integration software used for solar system planet orbit calculations, I employ a GR correction. It can be thought of as an "anomalous" acceleration to be applied to the otherwise Newtonian formulation of determining the acceleration of a planet. I suppose this correction can be checked in the Jupiter setting to see if it appears to be significant.


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Gerald
post Dec 21 2016, 09:33 PM
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QUOTE (Ant103 @ Dec 21 2016, 09:31 PM) *
All I want to tell you Gerald : you are doing an AMAZING work ! I don't understand clearly the process behind (because you know, mathematics and me are not in very good terms…) but I admire you for this, and thanks for being so generous about it smile.gif

Thanks a lot Damia! That's particularly precious, when those words come from one of the world's leading image processing experts. smile.gif

@scalbers: Fully nailing this down for Juno's extremely elliptical orbit would be really great! Might be, you could even determine the accurate relativistic effects on clocks travelling with Juno. I guess, that only +/- a few hours around perijoves need to be considered, where we get high velocities, and a tiny gravitational red shift.
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