  When a massive object crosses a star stream velocity changes are induced both
along and transverse to the stream which can lead to the development of a
visible gap. For a stream narrow relative to its orbital radius the time of
stream crossing is sufficiently short that the impact approximation can be used
to derive the changes in angular momenta and radial actions along the star
stream. The epicyclic approximation is used to calculate the evolution of the
density of the stream as it orbits around in a galactic potential. Analytic
expressions are available for a point mass, however, the general expressions
are easily numerically evaluated for perturbing objects with arbitrary density
profiles. With a simple allowance for the velocity dispersion of the stream,
moderately warm streams can be modeled. The predicted evolution agrees well
with the outcome of simulations of stellar streams for streams with widths up
to 1% of the orbital radius of the stream. The angular momentum distribution
within the stream shears out gaps with time, further reducing their visibility,
although the size of the shear effect requires more detailed simulations. An
illustrative model indicates that shear will limit the persistent gaps to a
minimum length of a few times the stream width. In general the equations are
useful for dynamical insight into the development of stream gaps and their
measurement.
