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Mass of the Milky Way's Halo. The Large Magellanic Cloud orbits the Milky Way at a distance of roughly 160,000 light-years from the galactic center and a velocity of about 300 km/s. Use these values in the orbital velocity law (Mathematical Insight 19.1) to estimate the Milky Way's mass within 160,000 light-years from the center. (The value you obtain is a fairly rough estimate because the orbit of the Large Magellanic Cloud is not circular.)

Respuesta :

The approximate mass of the galaxy within 160,00 light-years of the center is 2.0x10^42 kilograms.

To find the mass within 160,000 light-years of the center of the galaxy, we will use the orbital velocity law:

M(r)= (rv^2)/G

  • To use this law, we need to convert the radius and the speed of the Large Magellanic Cloud into meters and meters per second.
  • We are told that the orbital radius is 160,000 light-years. Since 1 light-year is 9.46x10^15 meters, this is the same as 1.51x10^21 meters.
  • The speed is given as 300 kilometers per second, which we can easily convert to 3.0x10^5 meters per second.
  • Putting the given values into the orbital velocity law, we learn that the approximate mass of the galaxy within 160,00 light-years of the center is 2.0x10^42 kilograms, or about 1 trillion times the mass of the Sun.

Hence, mass of the galaxy within 160,00 light-years of the center is 2.0x10^42 kilograms.

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