  The Sun's gradual brightening will seriously compromise the Earth's biosphere
within ~ 1E9 years. If Earth's orbit migrates outward, however, the biosphere
could remain intact over the entire main-sequence lifetime of the Sun. In this
paper, we explore the feasibility of engineering such a migration over a long
time period. The basic mechanism uses gravitational assists to (in effect)
transfer orbital energy from Jupiter to the Earth, and thereby enlarges the
orbital radius of Earth. This transfer is accomplished by a suitable
intermediate body, either a Kuiper Belt object or a main belt asteroid. The
object first encounters Earth during an inward pass on its initial highly
elliptical orbit of large (~ 300 AU) semimajor axis. The encounter transfers
energy from the object to the Earth in standard gravity-assist fashion by
passing close to the leading limb of the planet. The resulting outbound
trajectory of the object must cross the orbit of Jupiter; with proper timing,
the outbound object encounters Jupiter and picks up the energy it lost to
Earth. With small corrections to the trajectory, or additional planetary
encounters (e.g., with Saturn), the object can repeat this process over many
encounters. To maintain its present flux of solar energy, the Earth must
experience roughly one encounter every 6000 years (for an object mass of 1E22
g). We develop the details of this scheme and discuss its ramifications.
