We can calculate the mass of a galaxy by observing how fast stars are moving around...

We can calculate the mass of a galaxy by observing how fast stars are moving around its edge. Further we can estimate how many stars are in that galaxy using an average star mass of around 1/2 solar mass. NGC 253 (image below) is a flat spiral galaxy with a diameter of about 60,000 ly. If a star on the edge of NGC 253 is observed to have an angular velocity of about 7.8x10-16 rad/s, (a) calculate the mass of the galaxy and (b) estimate the number of stars in it.

Solutions

Expert Solution

(a)

Consider there is a gravitational attraction between the galaxy and the star on the edge.

The radius of the galaxy is

r = 60, 000 ly

= (6000 ly) (9.46 x 10¹⁵ m / 1 ly)

= 5.7 x 10¹⁸ m

The star moves as the centripetal force is provided by the gravitational force.

Thus,

Centripetal force = gravitational force

This gives the mass of the galaxy.

Substitute 5.7 x 10¹⁸ m for r, 7.8x10^-16 rad/s for w and 6.67x10^-11 Nm²/kg² for G in the above equation

Rounding off to two significant figures, the mass of the NGC 253 galaxy is 1.7 x 10³⁶ kg.

(b)

It is given that the stars in the galaxy are ½ solar mass.

Solar mass is equal to 1.99 x 10³⁰ kg.

Thus, mass of each star is

m = 1.99 x 10³⁰ kg /2

= 0.995 x 10³⁰ kg

Now, the number of stars in the galaxy is equal to the mass of the galaxy divided by mass of each star. Thus, it is

n = M /m

= 1.7 x 10³⁶ kg / 0.995 x 10³⁰ kg

= 1.7085 x 10⁶

Rounding off to two significant figures, the number of stars in the NGC 253 galaxy is 1.7 x 10⁶ stars.

genius_generous answered 1 year ago

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