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The Total Mass of the Milky Way

For the more mathematically inclined, there is an excellent discussion of how astronomers found the lower limit of the Milky Way's mass in an "Extending Our Reach" box on page 461 in your text. Since the math confuses some students, there is a simple step by step explanation here: Math.

In the early part of the 20th Century, astronomy Harlow Shapley used the light curves of Cepheid variables (pages 398 & 442 in your book) in the many globular star clusters that enshroud the Milky Way to determine the Sun's distance to the center of the Galaxy. The modern refinement of Shapley's results is about 8.5 kpc or 8.5 kiloparsecs from the center of the Galaxy. Since a kiloparsec is 3260 light years, that puts the Sun about 28,000 light years from the center of the Milky Way.

The interesting thing is that beginning just outside the Sun's orbit the velocity of revolutions doesn't fall off as would seem normal under Kepler's Laws. Instead, the value stays nearly the same ("the rotation curve goes flat). The best interpretation of this is that there is a great deal of unseen matter beyond the Sun in the Milky Way.

Recent estimates are that the period of rotation around the Galaxy's Core range from about 227 to 240 million years. Your text favors the longer period. Try using those values in the Javascript form below to determine the mass of the Galaxy.

 

Enter distance from the galactic core in light years:
(Note: current estimates are that the Sun is about 28,000 light years from the core. Enter your numbers without commas, i.e.: 28000)

Enter period of revolution in millions of years:
(Note: current estimates are that the Sun revolves around the galactic core in about 240 million years.)


The resulting mass would be times the mass of the Sun.
(Note: using the current estimates, this figure should come out to be about 96 billion, but the figure you will get from the calculation will not be adjusted for significant figures, and thus will appear more precise than just"96 billion.")

Or, if you have the distance in parsecs (pc) and the velocity in kilometers per second (km/s):
Enter distance from the galactic core in parsecs:
(Note: current estimates are that the Sun is about 8,500 parsecs from the core. Enter your numbers without commas, i.e.: 8500)

Enter the orbital velocity in kilometers per second:
(Note: current estimates are that the Sun orbits the galactic core at about 220 km/s.)


The resulting mass would be times the mass of the Sun.
(Note: this also does not account for significant figures and thus appears more precise than it should. In addition, even when using the standard suggested figures, the results in the first part (using light years and the period in millions of years) and the results in the second part (using parsecs and rotational velocity) are not exactly equal due to rounding and the above-mentioned situation with significant figures.)

Based on the data in Figure 15.26 (page 462 of your text), what would you find for the Galaxy's mass if you used the motion of stars at 16 kpc (kiloparsecs), nearly twice the Sun's distance from the core. Is it higher or lower? Why?

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