## Wednesday, November 26, 2014

### tidal stretching of Palomar 5

the globular cluster Palomar 5 orbits the Milky Way and is stretched by tidal forces. on what time-scale would the tidal arms reach all around the Milky Way?

1. the equilibrium condition would be $\upsilon^2=GM/R$ with the distance $R$ from the Milky Way centre to Palomar 5 and with the mass $M$ of the Milky Way. the variation in velocity between the close and far edges of Palomar 5 would be
and therefore, the time scale $t$ needed for the slower moving far edge to circle the Milky way at the velocity $\Delta\upsilon$ results as
with the distance $R=23~\mathrm{kpc}=10^{21}m$, the mass $M=10^{12}M_\odot$ and the size $\Delta r = 10^{19}m$ of Palomar 5. comparing this to the orbital time $T = 2\pi R/\upsilon=10^9\mathrm{yr}$ shows that the arms will reach all around the Milky Way after 100 orbits.