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Fluid Equations

Fluid Equations. Continuity Equation. Euler Equation. Energy Equation. Gravitational Acceleration. Gravitational Potential. Poisson Equation. Solution. Hydrostatics. All time derivatives – zero Fluid velocity – zero Heat Loss - zero. Solar Corona. 1999 Total Eclipse

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Fluid Equations

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  1. Fluid Equations Continuity Equation Euler Equation Energy Equation

  2. Gravitational Acceleration Gravitational Potential Poisson Equation Solution

  3. Hydrostatics • All time derivatives – zero • Fluid velocity – zero • Heat Loss - zero

  4. Solar Corona 1999 Total Eclipse Corona million times fainter than the photosphere Image: Luc Viatour

  5. X-ray image Yohkoh Soft X-ray Telescope (SXT).

  6. Solar Corona • Extremely tenuous and hot plasma • At ~1.2 Solar radius • Temperature ~ 1.4 million Kelvin • Electron number density ~200 million/cc • Hotter than the surface of Sun (5800 K)

  7. Heat Source • Possibly small patches of magnetic field • Found across entire Sun • Possibly not the big Solar flares • Energy transfer through magnetic reconnections • Still an unresolved issue

  8. Solar Wind • Proposed by Parker 1958 • Discovered ~1960, Soviet satellite Luna 1 • Mainly electrons and protons • Near the Earth: • Number density 3 – 10 particles/cc • Flow Speed 400 km/s • Temperature 150,000 Kelvin

  9. Solar Wind • Occasionally streams 750 km/s • Occasional Impulse Events 1000 km/s • Solar wind can also have a measurable effects on the flight paths ofspacecraft.

  10. Heliosphere 100 AU Image Source NASA/JPL/JHUAPL

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