Inferring the dynamics of stellar streams via distance gradients

We present a simple result in which the distance gradient along a stream can be used to derive the transverse velocity (i.e. proper motion) along it, if the line-of-sight velocity is also known. We show its application to a mock orbit to illustrate its validity and usage. For less extended objects, such as globular clusters and satellite galaxies exhibiting signs of tidal disruption, the same result can be applied in its small-angle approximation. The procedure does not rely on energy or angular momentum conservation and hence does not require a Galactic model; the transverse velocity can therefore be calculated even if the stream is not following an orbit.