Much of the mass of our Milky Way galaxy is concentrated in a central sphere of

ID: 1359504 • Letter: M

Question

Much of the mass of our Milky Way galaxy is concentrated in a central sphere of radius

r = 2 kpc,

where "pc" is the abbreviation for the unit "parsec";

1 pc = 3.26 ly.

Assume the Sun is in a circular orbit of radius

r = 8.0 kpc

around the central sphere of the Milky Way. The Sun's orbital speed is approximately 220 km/s; assume the central sphere is at rest.

(a) Estimate the mass in the inner Milky Way. Report your answer in kilograms and in solar masses.

(b) What is the escape speed of the Milky Way? (Assume the starting position is on the surface of the central sphere of radius 2 kpc.)

(c) CHECK and THINK: Do you believe that stars in the Milky Way have been observed to have speeds of 500 km/s? Explain.

given,

orbit radius of sun = 8000 pc or 2.4685 * 10^20 m

orbital velocity = 220 km/s ot 220 * 10^3 m/s

velocity = sqrt(G * M / r)

220 * 10^3 =sqrt(6.674 * 10^-11 * M / (2.4685 * 10^20))

M = 17.9 * 10^40 kg

mass of inner milky way = 17.9 * 10^40 kg

escape velocity = sqrt(2GM / r)

escape velocity = sqrt(2 * 6.674 * 10^-11 * 17.9 * 10^40/ (6.1714 * 10^19))

escape velocity = 6.22 * 10^5 m/s

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