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

Corona million times fainterthan the photosphere

Image: Luc Viatour

X-ray imageYohkoh Soft X-ray Telescope (SXT).

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)

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

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

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.

Heliosphere

100 AU

Image Source NASA/JPL/JHUAPL