To Save the Sun - Ben Bova

ANCIENT EARTH IS DOOMED...
Earth's Sun will explode, not millions of years hence but in mere lifetimes—violently enough to scour Earth clean and leave the Empire of the Hundred Worlds adrift.
The Empire's scientists deem that nothing can be done. The age of heroism is past: this is the long, stagnant afternoon of the human race.
Until—over massive opposition—a single young woman makes her way to the Emperor with that rarity, a new scientific insight... and a plan, flowing from its implications, to mobilize humanity's slumbering energies toward a thousand year effort of applied astrophysics. Of engineering carried out on the hearts of stars. A plan to save the Earth. To save the Sun.
By six-time Hugo Award winner Ben Bova.