For example, we typically make use of Kepler's 3rd or harmonic law, viz.
M = (a) 3 / (P) 2
to make a mass estimate for the galaxy, where a = the semi-major axis (mean distance of Sun estimated from the galactic center), and P is the period for revolution about the galactic mass center. We estimate that a = 2 x 109 AU and P = 2 x 10 8 yrs , so that we can write for M:
M = (2 x 109 AU) 3 / (2 x 10 8 yrs) 2
M = (8 x 10 27) / (4 x 10 16 ) = 2 x 1011 (m) the mass of the Sun.
But examine it carefully! It essentially assumes the mean mass for all stars in the Milky Way is equal to one solar mass (2 x 10 30 kg ) which, if off, would mean the galactic mass is overestimated.
Anyway, what the UCSC researchers found is that stars in the far outer reaches of the Milky Way, between 260,000 and 490,000 light-years from the galactic center, are moving surprisingly slowly In some ways, this isn't suprising and merely discloses we jumped the gun in our assumptions. The precise parameters which defines this is the epicycle frequency ( ko ) which is in turn related a given star's orbital angular speed ( W ).
For example, in the Sun's case we first convert it's period (P - used in the Mass computation) to seconds, so: T(s) = (2 x 10 8 yrs.) (365.25 days/yr.) (86,400 s/ day) = 6.3 x 10 15 s
Then: W » 10 -15 rad s-1
But clearly if the UCSC data show slower stars than this parameter will be off. According to Alis Deason, one of the primary researchers:
"Because these velocities are so low, the mass of our galaxy may be much lower than we once thought,"
She added: "If we infer the properties of the stars that we think are reasonable, then we find the mass of the Milky Way could be half as massive as we currently believe,"
To be sure, Deason and her colleagues did far more than use seat of the pants estimates for angular velocity such as depicted above. Her team looked far out into the Milky Way's halo, which extends far beyond the 100,000-light-year-wide disk. They measured the radial velocities of a sample of distant halo stars using two different instruments: the European Southern Observatory's 8.2-meter telescope in
They found that the dispersion, or spread, of halo-star velocities was about half that seen for stars closer to the galactic center.
Using this information, the team calculated that the total mass of the Milky Way out to such extreme distances may be between 500 billion and 1 trillion times that of our sun — substantially lower than the current leading estimate. Note that if the upper limit here is accepted or 10 12 solar it means a total galactic mass of (2 x 10 30 kg ) ( 10 12) = 2 x 10 42 kg compared to 4 x 10 41 kg obtained from the Kepler's law value. Thus, the problem doesn't enter until the lower value of mass is used.
Even so, the research results must be confirmed, and that may also necessitate assessing the amount of dark matter in our galaxy, including the degree to which black holes (especially the putative central black hole) contribute to the Milky Way's mass.