  Synchronous satellites of Venus have long been thought unstable, but we use
Poincare's surface of section technique to show that synchronous
quasi-satellites orbiting just outside Venus' Hill sphere are quite stable, at
least for centuries. Such synchrosats always remain within a few degrees of
Venus' equator, and drift very slowly in longitude. These synchrosats could be
useful for continuous monitoring of points on Venus' surface, such as active
landforms or long-lived landers.
