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Our Sun - NASA and other Space Based Missions
There are two NASA and NASA ESA space-based satellite missions studying the Sun.
In addition, you may want to check out AeroSpaceGuide. This site has some interesting facts as well as mission summaries.
The most popular mission is the SOHO (SOlar and Heliospheric Observatory). This orbiting satellite has provided some of the most remarkable images of the Sun. There are a number of specialized instruments on the SOHO spacecraft:

CDS Coronal Diagnostic Spectrometer
CELIAS Charge, Element, and Isotope Analysis System
COSTEP Comprehensive Suprathermal and Energetic Particle Analyzer
EIT Extreme ultraviolet Imaging Telescope
ERNE Energetic and Relativistic Nuclei and Electron experiment
GOLF Global Oscillations at Low Frequencies
LASCO Large Angle and Spectrometric Coronagraph
MDI/SOI Michelson Doppler Imager/Solar Oscillations Investigation
SUMER Solar Ultraviolet Measurements of Emitted Radiation
SWAN Solar Wind Anisotropies
UVCS Ultraviolet Coronagraph Spectrometer
VIRGO Variability of Solar Irradiance and Gravity Oscillations

The above SOHO image is taken by the MDI. This image is also using the MDI, but emphasizes the sunspot magnetic fields.
The LASCO image above allows a view of the corona. The large occlusion in the center is called an occultation disk. This LASCO image is of a wider field. The occultation disk is in place. The circle within the disk is the diameter of the Sun.

The following images are taken with the EIT. The images are focused at a particular frequency which corresponds to levels of atmosphere. The higher the wavelength, the higher up the atmosphere is imaged, and the hotter the temperature.

EIT Image at 171 angstroms - 1 million degrees EIT Image at 195 angstroms - 1.5 million degrees
EIT Image at 284 angstroms - 2 million degrees EIT Image at 304 - this image is focused more towards the surface - 60,000 to 80,000 degrees

Nearly all of these experiments cannot be performed here on Earth. The atmosphere safely filters out the Ultraviolet - the primary wavelength observed by SOHO - and the gravity oscillations are better studies in space without the contamination of oscillations present on Earth (like earthquakes, traffic jams and so on).

The Ulysses:
In its 12 year mission, the Ulysses studied the solar maximum conditions as well as studies of the polar regions to better understand the solar atmosphere (the photosphere and chromosphere).

The mission of the Ulysses spacecraft has been extended until 2008.

Primary mission results (care of

Solar Wind Speed from North and South Poles The Solar Winds emanating from the polar regions of the Sun are faster than the equatorial regions - around 800 km/s for the poles and 600 km/s for the equator.
Solar Magnetic Field Strength The strength of the magnetic field increases towards the polar regions of the Sun.
Different Compositions between Fast and Slow streams The ratio of Mg/O (Mg = magnesium, O = oxygen) are larger in low speed solar winds. Additionally, the amount of Mg/O is lower in faster speed solar winds. This means the temperature of the chromosphere is affecting the ionization of the elements thereby affecting the temperature of the corona.
Cosmic Rays diffused in the Heliosphere Cosmic rays are thought to travel along magnetic field lines. Since the magnetic fields from the Sun are strongest near the poles, it was thought that cosmic rays would be greater in these regions. Ulysses discovered no such increase.

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