Juno, perijove 12, April 1, 2018 |
Juno, perijove 12, April 1, 2018 |
Mar 28 2018, 04:10 AM
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Junior Member Group: Members Posts: 71 Joined: 12-December 16 Member No.: 8089 |
So, according to the voting page, apparently the spacecraft's being spun around to get the instruments pointed directly at the planet. Io and Ganymede will also be imaged during this pass, as they'll come into view of JunoCam two hours before and twelve hours after closest approach, respectively. For Io, the team are "planning to take two pictures - one exposed nominally and one that over-exposes Io to look for volcanic plumes extending above the surface." The Great Red Spot is also expected to come into view during the spacecraft's departure.
Here's a logo for Perijove 12 I threw together, by the way. |
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Jun 2 2018, 02:47 AM
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Senior Member Group: Members Posts: 2346 Joined: 7-December 12 Member No.: 6780 |
What I've implemented has been pretty simple. I just inferred a bandpassed displacement field. This could be interpreted as an approximation of a velocity field. Everything is given only numerically.
More generally, this displacement field can be understood as a field of 1st order tensors, given explicitely. Each pair (x,y) of the plane is assigned a vector (dx/dt, dy/dt), describing which infinitesimal amount (dx,dy) a vector (x,y) is to be displaced after an infinitesimal time step dt. Write this assignment as (dx/dt, dy/dt) = f(x,y). I'd classify this as a first-order partial differential equation. So. for each pixel position in the image plane, an approximate velocity is assigned. That's essentially the DE, represented only numerically. This DE can be integrated forward, or backward in time. I've implemented both by the Euler method, the most simple numerical method to integrate DEs. Other than the 1-dimensional case described in Wikipedia, the settings here are 2-dimensional. And we don't have a time-dependency of the tensor field. It's assumed stable, instead. All the derivatives are infered numerically from the displacement field (approximate velocity field). They aren't required for the integration of the DE on the above level, but are subject to a separate investigation. I didn't make assumptions constraining curl, divergence, or Laplace operators, but instead just calculated them numerically from the displacement field. Any assumptions about these operators could be made, but they would define results that should better be determined from the data instead of being presumed. Up and downwelling are well possible and shouldn't be ruled out by assumptions. Even a zero Laplacian may be plausible under idealized conditions. But how can we assume these conditions without trying to measure or infer them? I think, that any unnecessary assumption should be avoided, and we should instead measure and infer everything we can from actual data. I think, the most significant approach of criticism of the method implemented thus far is the implicite assumption of a stable velocity field. I.e., the integration over the displacement field is assuming, that the displcement field doesn't change over the integration time interval. This simplification, and likely oversimplification, should be verified, at least, or better be refined, by investigating not just a pair of images, but a longer time-series. Such a time series may allow to detect and model changes of the velocity field over time, and result in more accurate particle trajectories than just in flow lines. Another possibly relevant point is the difficulty to properly determine vectors with a non-zero component normal to Jupiter's "surface", or to the image plane. Once the numerical representation is fully elaborated, including the reduction to physically meaningful units, this representation can be checked against Navier-Stokes, simplifications to special cases, or extensions. |
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