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https://texercises.raemilab.ch/exercise/mass-of-milky-way/
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Exercise:
The Sun is at a distance of about dkilo pc from the galactic centre and moves around the galactic centre in a circular path with a velocity of about vkilometerpersecond. Make a rough estimate of the mass of the Galaxy.

Solution:
We can get a very rough estimate of the mass of the Galaxy by making the asption that most of the Milky Way mass will lie in its centre and that we can therefore neglect the mass at larger distances from the galactic centre than the Sun. By equating the gravitational and the centripetal force at the position of the Sun we have GfracM_odotM_textMWd^ M_odotfracv^d Using pc.emeter and M_odot .ekilogram we obtain M_textMW fracv^dG &simeq .eM_odot Compare this to the experimental value M_textMWsimeq . - .eM_odot shows that the calculation underestimates the mass of the Galaxy. This means that we cannot simply neglect the mass located further away from the galactic centre than the Sun just because we don't see it.
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Exercise:
The Sun is at a distance of about dkilo pc from the galactic centre and moves around the galactic centre in a circular path with a velocity of about vkilometerpersecond. Make a rough estimate of the mass of the Galaxy.

Solution:
We can get a very rough estimate of the mass of the Galaxy by making the asption that most of the Milky Way mass will lie in its centre and that we can therefore neglect the mass at larger distances from the galactic centre than the Sun. By equating the gravitational and the centripetal force at the position of the Sun we have GfracM_odotM_textMWd^ M_odotfracv^d Using pc.emeter and M_odot .ekilogram we obtain M_textMW fracv^dG &simeq .eM_odot Compare this to the experimental value M_textMWsimeq . - .eM_odot shows that the calculation underestimates the mass of the Galaxy. This means that we cannot simply neglect the mass located further away from the galactic centre than the Sun just because we don't see it.
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Attributes & Decorations
Tags
astrophysics
Content image
Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator rk
Decoration