physics

The sun rotates around the center of the milky way galaxy at a distance of about 30,000 light years (1ly= 9.5*10^15m). if it takes about 200 million years to make one rotation, estimate the mass of our galaxy. Assume that the mass distribution of galaxy is concentrated mostly in a central uniform sphere.

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  1. G M m /r^2 = m v^2/r
    so
    M = v^2 r/G

    r = 3*10^4 * 9.5*10^15 meters = 28.5*10^19 = 2.85*10^20 meters

    circumference = 2 pi r = 17.9 *10^20 meters

    time = 200*10^6 yr *365d/yr*24h/day*3600s/h = 6.31*10^15 seconds

    speed v = 17.9*10^20/6.31*10^15 = 2.84*10^5 meters/second

    so
    M = v^2 r /6.67^10^-11
    = 2.84^2 * 10^10 * 2.85*10^20 / 6.67*10^-11
    M = 3.44 * 10^41 kg

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