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Because of its very high sensitivity, Nustar could solve some long-standing puzzles, such as whether "nanoflares" exist.
These proposed smaller versions of the Sun's giant flares could help explain why its outer atmosphere is many times hotter than its surface - a decades-old question.
Physicists first thought of using Nustar to study the Sun when it was already under construction.
"At first I thought the whole idea was crazy," said the mission's principal investigator Prof Fiona Harrison, from the California Institute of Technology.
"Why would we have the most sensitive high energy X-ray telescope ever built, designed to peer deep into the universe, look at something in our own back yard?"
But she was eventually convinced by Prof David Smith, a solar physicist at the University of California, Santa Cruz.
"Nustar will give us a unique look at the Sun, from the deepest to the highest parts of its atmosphere," said Prof Smith, a solar physicist at University of California, Santa Cruz.
Nanoflare impulsive bursts of heating, none of which can be individually detected