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/
“...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?
Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field
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Can someone explain how a magnetic field creates radiation?