Gravity problems: a) The Large Magellanic Cloud is a dwarf galaxy that orbits th

Question

Gravity problems:

a)     The Large Magellanic Cloud is a dwarf galaxy that orbits the Milky Way with a

velocity of about 300 km/s. If it is at a distance of 160,000 light years, how massive is the Milky Way?

     b) Suppose you observe a star orbiting the center of a galaxy at a distance of 20 light days

          and a velocity of 1000 km/s. What is the mass of the black hole in solar masses?

     c) Stars in the outskirts of a globular cluster are typically about 50 light years from the

     cluster

Explanation / Answer

orbital speed, v = sqrt(G*M/r)

==> r = v^2*r/G

a) v = 300000 m/s

r = 160,000*3*10^8*365*24*60*60

= 1.514*10^21 m


M = v^2*r/G

= (3*10^5)^2*1.514*10^21/6.67*10^-11

= 2.0428*10^42 kg



b)

v = 1*10^5 m/s

r = 20*3*10^8*365*24*60*60

= 1.892*10^17 m


M = v^2*r/G

= (1*10^5)^2*1.892*10^17/6.67*10^-11

= 2.837*10^37 kg

= 2.837*10^37/2*10^30 msun

= 1.418*10^7*Msun

c)
v = 1*10^4 m/s

r = 50*3*10^8*365*24*60*60

= 4.73*10^17 m


M = v^2*r/G

= (1*10^4)^2*4.73*10^17/6.67*10^-11

= 7.09*10^37 kg

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