  The Doppler shift of a radio signal is caused by the relative motion between
the transmitter and receiver. The change in frequency of the signal over time
is called drift rate. In the studies of radio SETI (Search for Extraterrestrial
Intelligence), extraterrestrial narrowband signals are expected to appear
"chirped" since both the exoplanet and the Earth are moving. Such planet
rotation and orbital revolution around the central star can cause a non-zero
drift rate. Other relative motions between the transmitter and receiver, such
as the gravitational redshift and galactic potential, are negligible. In this
paper, we mainly consider the common cases that the drift rate is contributed
by the rotations and orbits of the Earth and exoplanet in celestial mechanics
perspective, and briefly discuss other cases different from the Earth-exoplanet
one. We can obtain the expected pseudosinusoidal drifting result with long-term
observations, shorter orbital periods of exoplanets. Exoplanets with higher
orbital eccentricities can cause asymmetric drifting. The expected result
should be intermittent pseudosinusoidal curves in long-term observations. The
characteristics of pseudo-sinusoidal curves, as another new criterion for
extraterrestrial signals, can be applied to long-term SETI reobservations in
future research.
