The fate of a planetary system like our own, as the parent star expands thr
ough the red giant phase and becomes a white dwarf (WD), has been a topic o
f some discussion. For an Earth-like inner planet, the conducting core may
remain intact, even though severe ablation occurs of the outer layers. We a
rgue that a planetary core in orbit around a WD may reveal its presence thr
ough its interaction with the magnetosphere of the WD. As the planet moves
through the magnetosphere, electrical currents will be generated, which wil
l heat the atmosphere of the WD near its magnetic poles. The results of suc
h a heating may be detected in the optical as H alpha emission. Ohmic dissi
pation will result in the slow decay of the planetary orbit, and such a pla
net will merge with the WD in less than a Hubble time, unless the initial o
rbital separation is greater than about 10 solar radii. We propose that the
peculiar emission-line WD GD 356 may be a system in the process of such a
merger.