Gravitation

Question : 5

Total: 25

Let us assume that our galaxy consists of 2.5×1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 105 ly.

Solution:

Using, M=

4π2R3

GT2

or T= (

4π2R3

)

Given, M=2.5×1011
Solar mass =2.5×1011×(2×1030)kg
=5.0×1041kg
and R=50,0001y
=50,000×9.4×1015m
=4.73×1020m

∴T=[

4×(3.14)2×(4.73×1020)3

(6.67×10−11)×(5.0×1041)

]1∕2

T=1.12×1016s
=3.54×108‌years

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