By DENNIS OVERBYE

In the end, there won’t even be fragments.
If nature is left unhindered, about 7.59 billion years from now Earth will be dragged from its orbit by an engorged red Sun and spiral to a rapid vaporous death.
That is the forecast according to new calculations by a pair of astronomers, Klaus-Peter Schroeder of the University of Guanajuato in Mexico and Robert Connon Smith of the University of Sussex in England.
Their report, to be published in the Monthly Notices of the Royal Astronomical Society, is the latest and gloomiest installment yet in a longrunning debate about the ultimate fate of our planet.
Only last year, the discovery of a giant planet orbiting the faint burned-out cinder of a star in Pegasus had suggested that Earth could survive the Sun’s death.
Dr. Smith called the new result “a touch depressing” in a series of e-mail messages.
But “looked at another way,” he added, “it is an incentive to do something about finding ways to leave our planet and colonize other areas in the galaxy.
” Earth’s basic problem is that the Sun will gradually get larger and more luminous as it goes through life, according to widely held theories of stellar evolution.
In its first 4.5 billion years, according to the models, the Sun has already grown about 40 percent brighter.
Over the coming eons, life on Earth will become muggier and more uncomfortable and finally impossible.
“Even if the Earth were to marginally escape being engulfed,” said Mario Livio, an astronomer at the Space Telescope Science Institute, “it would still be scorched, and life on Earth would be destroyed.
” About a billion years from now, the Sun will be 10 percent brighter.
Oceans on Earth will boil away.
The Sun will run out of hydrogen fuel in its core about 5.5 billion years from now and start burning hydrogen in the surrounding layers.
As a result, the core will shrink and the outer layers will rapidly expand as the Sun transforms itself into a red giant.
The heat from this catastrophic event will transform the solar system; it will briefly be springtime in the Kuiper Belt out beyond Neptune.
Mercury and Venus will surely be swallowed, but the Earth’s fate has always been more uncertain.
According to Dr. Smith and Dr. Schroeder, the chance of the earth’s surviving is nil.
Is there any way out of this fiery end for the robots or cockroaches or whoever will be running the Earth in a billion years- One option is to leave for another planet or another star system.
Another option, Dr. Smith said, is to engage in some large-scale highstakes engineering.
In the same way that space probes can get a trajectory boost by playing gravitational billiards with Venus or Jupiter to gain speed and get farther out in space, so the Earth could engineer regular encounters with a comet or asteroid, thus raising its orbit and getting farther from the Sun, according to a paper in 2001 by Don Korycansky and Gregory Laughlin of the University of California, Santa Cruz, and dim.
and Fred Adams of the University of Michigan.
Dr. Laughlin said that when their paper first came out, they were praised by some people for forward thinking.
But he said they were not advocating the orbit-shifting project, noting that a miscalculation could lead to the comet’s hitting the Earth.
“There are profound ethical issues involved,” he wrote in an e-mail message, “and the cost of failure (an Earth-sterilizing impact) is unacceptably high.
” Anyway, such a maneuver would prolong the viability of the Earth for only a few billion years.
After that, the planet would be stranded in the cold and dim.