﻿ Let us assume that our galaxy consists of 2.5 × 1011stars 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. from Physics Gravitation Class 11 Manipur Board

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Let us assume that our galaxy consists of 2.5 × 1011stars 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.

Mass of our galaxy Milky Way, M = 2.5 × 1011 solar mass

Solar mass = Mass of Sun = 2.0 × 1036 kg

Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036

= 5 × 1041 kg

Diameter of Milky Way, d = 105 ly

Radius of Milky Way, r = 5 × 104 ly

1 ly = 9.46 × 1015 m

∴                             r = 5 × 104 × 9.46 × 1015

= 4.73 ×1020 m

A star revolves around the galactic centre of the Milky Way.

Time period is given by the relation,

=

=

=

= 1.12 × 1016 s

1 year = 365 × 324 × 60 × 60 s

1s = years

Therefore,

1.12 × 1016 s =

=  3.55 × 108 years.
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The position co-ordinates of two particles of masses m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

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Let the position coordinates of the centre of mass be (X, Y, Z).

Therefore the position vector of centre of mass is,

Since,

Comparing the coefficients of  , we get

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