The narrow GD-1 stream of stars , spanning 60 deg on the sky at a distance of \sim 10 kpc from the Sun and \sim 15 kpc from the Galactic center , is presumed to be debris from a tidally disrupted star cluster that traces out a test-particle orbit in the Milky Way halo .
We combine SDSS photometry , USNO-B astrometry , and SDSS and Calar Alto spectroscopy to construct a complete , empirical 6-dimensional phase-space map of the stream .
We find that an eccentric orbit in a flattened isothermal potential describes this phase-space map well .
Even after marginalizing over the stream orbital parameters and the distance from the Sun to the Galactic center , the orbital fit to GD-1 places strong constraints on the circular velocity at the Sun ’ s radius V _ { c } = 224 \pm 13 km/s and total potential flattening q _ { \Phi } = 0.87 ^ { +0.07 } _ { -0.04 } .
When we drop any informative priors on V _ { c } the GD-1 constraint becomes V _ { c } = 221 \pm 18 km/s .
Our 6-D map of GD-1 therefore yields the best current constraint on V _ { c } and the only strong constraint on q _ { \Phi } at Galactocentric radii near R \sim 15 kpc .
Much , if not all , of the total potential flattening may be attributed to the mass in the stellar disk , so the GD-1 constraints on the flattening of the halo itself are weak : q _ { \Phi,halo } > 0.89 at 90 % confidence .
The greatest uncertainty in the 6-D map and the orbital analysis stems from the photometric distances , which will be obviated by Gaia .