The orbit of P/Swift-Tuttle is investigated by way of a long-term inte
gration forward to AD 2392 and backward to 703 BC. Two of its previous
returns prior to the telescopic period, in AD 188 and 69 BC, are iden
tified in Chinese records. No other observations of P/Swift-Tuttle hav
e been found. The non-gravitational forces that affect the motion of m
ost active comets appear to be negligible for this comet, suggesting t
hat either the comet outgasses radially toward the Sun and in a symmet
ric fashion about perihelion and/or it is far more massive than period
ic comets of comparable activity (e.g. P/Halley). Our successful integ
ration is consistent with all the observed returns of the comet. The u
nobserved returns between AD 188 and 1737 are easily explained, as the
comet did not approach the Earth closely enough to allow naked-eye vi
sibility. Our integration and the observing conditions at each return
suggest that the comet has maintained about the same intrinsic brightn
ess for more than two millennia. The lack of non-gravitational effects
for this comet and the relative constancy of its intrinsic brightness
place constraints upon the lifetime of its active area(s) and its spi
n state. Our prediction of the comet's return in 2126 places it well a
way from the Earth's position at the nodal crossing.