This weak decay of a proton to a neutron at the
temperature and density of the core of the sun is so rare a
process that it could never be duplicated on earth, so how do
we know it actually takes place in the sun? ALMOST EVERY KEY
STEP in the conversion of two protons into a helium nucleus
involves the emission of characteristic electron neutrinos. We
need to see those neutrinos arriving here on earth! About
65 billion solar neutrinos — roughly 6.5 × 10¹⁰ per cm² per
second — pass through every square centimeter of Earth’s
surface, including you, with the total flux including all
sources reaching ~10¹⁴ cm⁻² s⁻¹.
| Ray Davis (1914 - 2006), Nobel Prize 2002 |
John Bahcall (1934 - 2005) |
The Antarctic Muon And Neutrino Detector Array (AMANDA), buried in the ice beneath the South Pole, ultimately became part of the IceCube observatory. IceCube, which was completed in 2010, consists of a cubic kilometer grid of sensors embedded below 4,900 feet (1,500 m) of ice. In Europe, researchers are developing plans for KM3NeT, which will span 1.2 cubic miles (five cubic kilometers) in the Mediterranean Sea. And physicists at the Baikal Neutrino Telescope in Russia's Lake Baikal, the largest freshwater lake by volume in the world, are planning to build the Gigaton Volume Detector (GVD), which would be one cubic km.
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The instability of multi-body gravitational systems arises from the inherent chaos and sensitivity to initial conditions in systems with three or more bodies, leading to orbits that can change drastically over time. While some systems, like our solar system, show stability over long periods due to a hierarchical structure (large mass differences and separated orbits), many others are not stable. Instability can manifest as gradual orbital changes from secular perturbations, dramatic chaotic scattering events, or the ejection of bodies over millions or billions of years. Causes of instability include:
• Many-body problem: Unlike a two-body system, which has a stable orbit, systems with three or more bodies are inherently chaotic and lack simple, predictable long-term solutions.
• Secular perturbations: The slow, cumulative effect of gravitational nudges between bodies can gradually change orbital elements like semi-major axis, eccentricity, and inclination over long timescales.
• Resonances: Orbital resonances, where the orbital periods of two bodies are in a simple ratio, can cause chaotic diffusion. When these resonances overlap, the system can become unstable.
• Lack of hierarchy: Systems without a clear hierarchical structure, where the masses are more similar and the distances are not well-separated, are particularly prone to instability and rapid changes.