During the Voyager 2 flyby of Uranus, strong electron plasma oscillati
ons (Langmuir waves) were detected by the plasma wave instrument in th
e 1.78-kHz channel on January 23-24, 1986, prior to the inbound bow sh
ock crossing. Langmuir waves are excited by energetic electrons stream
ing away from the bow shock. The goal of this work is to estimate the
location and motion of Uranus' bow shock using Langmuir wave data, tog
ether with the spacecraft positions and the measured interplanetary ma
gnetic field. The following three remote sensing analyses were perform
ed: the basic remote sensing method, the lag time method, and the trac
e-back method. Because the interplanetary magnetic field was highly va
riable, the first analysis encountered difficulties in obtaining a rea
listic estimation of Uranus' bow shock motion. In the lag time method
developed here, time lags due to the solar wind's finite convection sp
eed are taken into account when calculating the shock's standoff dista
nce. In the new trace-back method, limits on the standoff distance are
obtained as a function of time by reconstructing electron paths. Most
of the results produced by the latter two analyses are consistent wit
h predictions based on the standard theoretical model and the measured
solar wind plasma parameters. Differences between our calculations an
d the theoretical model are discussed.