According to models of stellar evolution, the diameter of the Sun just after its formation about 5 thousand million years ago was about 87/100 of its present size. This means that the Sun should be growing at a rate of about 1.5 inches a year. To see a difference of 1.5 inches at the distance of the Sun would require a telescope of about 1500 miles in diameter, or a system of telescopes at least 1500 miles apart, and would also require a measurement accuracy of one part in about four million million -which seems far beyond our current capabilities. We might be able to notice the size change if we observe the Sun for a thousand years or so.
At the moment the Sun gets its energy from turning hydrogen into helium. When the Sun's hydrogen runs out in the hot and dense center, then the Sun will expand into a red giant, about 100 times bigger than it is now, and will start turning helium into carbon in the center, and hydrogen into helium in a shell around the center. This phase will last about one thousand million years. Toward the end of the red-giant phase, when the Sun has run out of both hydrogen and helium in the hot center, the Sun will shed most of its outer layers. These layers will blow away from the Sun and form a planetary nebula. Only the very dense core of the Sun, which then consists of mostly carbon, will remain behind: the Sun will then be a white dwarf. The diameter of the white dwarf will be about one hundredth of the diameter of the current Sun: about as big as the Earth.
The
Sun is not heavy enough to get temperatures in its center that are
high enough to start turning carbon into something else and get
energy that way, so once the Sun turns into a white dwarf it will
no longer generate energy, but will very slowly cool down for the
rest of its days. The Sun will not "explode", though it will blow
away most of its outer layers -- but that time is still very far
away.
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