How does the Gravity Tractor method alter a comet's trajectory?

Using the spacecraft's minute gravitational pull over many years.

The Gravity Tractor is one of the theoretical methods proposed for nudging a threatening object off course, particularly favored for smaller or loosely aggregated bodies. This technique relies on patience and orbital mechanics rather than brute force. It involves positioning a massive spacecraft to orbit the comet over an extended duration, sometimes spanning decades or even centuries in idealized projections. During this prolonged proximity, the spacecraft exerts its own minuscule gravitational pull on the comet, gradually changing its orbital path just enough to ensure a safe miss when the time comes. This gentle, continuous tug requires significantly long lead times to be effective.