This article presents and discusses a method for measuring the proper motions of the Galactic dwarf spheroidal galaxies using images taken with the Hubble Space Telescope .
The method involves fitting an effective point spread function to the image of a star or quasi-stellar object to determine its centroid with an accuracy of about 0.005 pixel ( 0.25 milliarcseconds ) — an accuracy sufficient to measure the proper motion of a dwarf spheroidal galaxy using images separated by just a few years .
The data consist of images , dithered to reduce the effects of undersampling , taken at multiple epochs with the Space Telescope Imaging Spectrograph or the Wide Field Planetary Camera .
The science fields are in the directions of the Carina , Fornax , Sculptor , and Ursa Minor dwarf spheroidal galaxies and each has at least one quasi-stellar object whose identity has been established by other studies .
The rate of change with time of the centroids of the stars of the dwarf spheroidal with respect to the centroid of the quasi-stellar object is the proper motion .

Four independent preliminary measurements of the proper motion of Fornax for three fields agree within their uncertainties .
The weighted average of these measurements is \mu _ { \alpha } = 49 \pm 13 milliarcseconds century ^ { -1 } and \mu _ { \delta } = -59 \pm 13 milliarcseconds century ^ { -1 } .
The Galactocentric velocity derived from the proper motion implies that Fornax is near perigalacticon , may not be bound to the Milky Way , and is not a member of any of the proposed streams of galaxies and globular clusters in the Galactic halo .
If Fornax is bound , the Milky Way must have a mass of at least ( 1.6 \pm 0.8 ) \times 10 ^ { 12 } ~ { } \mathcal { M } _ { \odot } .