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One can understand a subject better in physics by trying to solve as many problems as one can from a textbook say. When it comes to experimental physics and data analysis, no book on experimental (high energy or astrophysics or cosmology) physics comes with free data that one might analyze to test his understanding.

Are there sites online, for experiments in cosmology or astrophysics (I know that particle physics data would be overwhelming), where such data is available for free that one can play with (i.e. to be able to make cuts and reproduce simple histograms...etc)? may be to reproduce roughly the CMB curve?

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I would think it highly improbable. All data gathered come with a meta level that involves the detectors. Somebody not in the know of the experiment cannot fathom how to untangle these data without introducing biases and errors because of ignorance. – anna v Aug 12 '11 at 15:35

The Sloan Digital Sky Survey is very open. You can browse their dataset online, you can query it using SQL over the CAS, they even have tutorials to get you started.

The SDSS was one of the big surveys of the 2000s, with thousands of publications based on the data.

I don't think you can actually download the raw data, as it is several terabytes long. It's usually transported by copying it to hard drives and flying it home, or using dedicated fat pipes between institutions.

Some quick links:

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Cosmic microwave background data, particularly from WMAP, are publicly available.

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You can use anonymous FTP to get data from the VLA in Socorro, New Mexico, USA. Look in The NRAO Data Archive System.

You will need to use some data processing software like AIPS or something. It's not exactly user friendly and it is a lot of data, but it shouldn't be too hard to get going if you're interested. The only thing is that this is just RF data.

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SIMBAD - Portal for data (and Tools) from several astronomic catalogs

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LHC did a new update with their BOINC software and they release a lot of data that can be analyzed, I actually haven't seen myself what data is being analyzed but essentially BOINC divides the data released from LHC into packets and then it is send to the users who download BOINC, and it does computations on those by using the user's resources who downloaded it and later the computers send the data back. I think looking into what BOINC does with the LHC's data maybe the best shot at realizing what LHC itself does with the collected data.

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There are some projects over at Zooniverse that are open to public participation.

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