Posted on 05/06/2024 4:02:36 AM PDT by AdmSmith
Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.
In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft can’t orbit the moon itself. Instead, it will slide into an eccentric orbit around Jupiter and gather data by repeatedly swinging by Europa—53 times in total—before retreating from the worst of the radiation. Every time the spacecraft rounds Jupiter, its path will be slightly different, ensuring that it can take pictures and gather data from Europa’s poles to its equator.
The team put together a number of tools that they hope will be useful to mission planners. One of the tools is a number called the Conley-Zehnder index that can help determine when two orbits belong to the same family. To calculate it, researchers examine points that are close to—but not on—the orbit they want to study. Imagine, for instance, that a spacecraft is following an elliptical orbit around Jupiter, influenced by gravity from Europa. If you nudge it off its path, its new trajectory will imitate the original orbit, but only crudely. The new path will spiral around the original orbit, coming back to a slightly different point after it circles Jupiter. The Conley-Zehnder index is a measurement of just how much spiraling goes on.
Surprisingly, the Conley-Zehnder index doesn’t depend on the specifics of how you nudge the spacecraft—it’s a number associated with the entire orbit. What’s more, it’s the same for all orbits in the same family. If you compute the Conley-Zehnder index for two orbits, and you get two different numbers, you can be sure that the orbits are from different families.
One of the most important events in science dates back to 1687, when Newton published the Philosophiæ Naturalis Principia Mathematica. In this masterpiece of human thought, the famous second law of motion is laid out, which concretely and beautifully expresses the relationship between the motion of a classical particle and the forces exerted on it. This work contains the solution to the two-body problem, concerning the motion of two massive bodies under gravitational interaction. However, when a third mass is added, known as the three-body problem, there is no such concrete solution, as Henri Poincaré exhibited in 1892. Since then, the role of celestial mechanics has been central to modern scientific discourse, in view of its connections with astronomy and space exploration. Symplectic geometry, the geometry underlying William Rowan Hamilton's reformulation of classical mechanics, serves as the modern mathematical framework instrumental to addressing these classical problems. This talk will attempt to thread together bits and pieces of this beautiful story, from the (inevitably biased) viewpoint of a modern practitioner.
The article https://www.quantamagazine.org/geometers-engineer-new-tools-to-wrangle-spacecraft-orbits-20240415/
Cool article and presentation on how to calculate orbits in space.
hour long video. will watch later today.
Yes, the article is interesting. If I read it right, some very abstract mathematics has produced a tool not for computing orbits, but for finding new and otherwise unexpected orbits to compute.
Yes
Bkmk
Will come in real handy next time I’m in space!.......................
“...mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation...”
Am I missing a contradiction here?
Yes, se you “next year in space!” ;-)
Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field
+++++++++++++++++++
Can someone explain how a magnetic field creates radiation?
I does not create radiation, but:
Jupiter’s particle radiation field is 20,000 times larger than Earth’s Van Allen belts, and 1,000 times more intense than Saturn’s. The collosal planet rotates once every 10 hours (a Jupiter day). Jupiter pulls its magnetic field right along with it. The magnetic field hauls charged particles around Jupiter at blistering speed. And Europa orbits Jupiter in the heart of that torrent of particles.
Jupiter’s magnetic field is the largest and most intense in the solar system, aside from the Sun. Its magnetotail sometimes reaches Saturn’s orbit. The magnetic field traps electrons and protons – charged particles. Europa Clipper’s radiation monitors will study those particles.
https://europa.nasa.gov/spacecraft/instruments/radiation-monitoring-study/
sorry sloppy writing
se => see
I does not => It does not
It’s going to be a fascinating mission.
Hi Thank You.
I suppose most radiation is charged particles, and therefore feel a force from a magnetic field.
The radiation is charged particles (protons and electrons) whipped to high energies by the planet's and magnetic field's rotation. Some particles that are trapped by the magnetic field come from the planet itself or the solar wind.
The source of most of the particles is the moon Io, which dumps massive amounts sulphur dioxide into space. The molecules break up in space into more charged particles.
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