The explanation of astronomers believe that fusion is going in sun after knowing that fusion takes average 14 billion year to undergo and sun is just 5 billion year old is that there are few protons in the sun who undergo fusion by few collisions only and not have to wait 14 billion years.
Thus we can say as their exist few protons inside sun who can undergo the fusion after few collisions only, the astronomers believe that fusion is going on there now also.
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