Astronomy math question...please help!?

Question

If each star has a radius equal to that of the Sun (700,000 km), calculate the volume of 1 star. If the cluster contains 500,000 stars within its 10 parsec radius, calculate the total volume that all 500,000 stars occupy.

Divide the volume the stars occupy by the total volume of the cluster to figure out what fraction of the cluster is filled with stars.

Is this a large number or a small number? Does the result surprise you, why or why not?

*** please help me, my teacher is awful

Answer 1

V = 4/3 pi r^3 where r is radius.

1 parsec = 30.857 x 10^12 km

The rest is just arithmetic. Find V for the cluster, and V for one star.

Answer 2

this question has been asked, word for word, half a dozen times in the last couple of days. what's the problem? it's just volumes of spheres.

the conclusion is that, despite appearances, the average density of a globular cluster is a hard vacuum.

Answer 3

Ok so 1 star volume = 4/3*pi*r^3, where r=700,000km.  (assuming a sphere)

So the sun = 1.43676*10^18 cubic km

500,000 of those = 7.18379*10^23 cubic km taken up by the stars.

1 Parsec = 30.857 petameter (10^12 km)

10 parsec radius sphere = 1.2307*10^44 cubic km

So dividing the volume of the stars by the total size of the cluster we get:

5.83718*10^-21, which is a really really small number (move the decimal left 21 times so 20 zeros before that 5).  It doesn't surprise me at all - that's why it is called "space" instead of "dense."  It is just difficult to visualize how small and how large that really is using the exponential notation - becomes a little more blatant how large that cluster is when you realize that 1 light year is just 0.3066 parsecs.  That means your cluster is a good 65 light years across - and given that the light will cross the diameter of one of your stars in just a few seconds you can see the scope of how tiny they really are compared to the cluster.  Now try to imagine the space between several clusters and compare that to the stars!

You might want to double check my math I clicked through it pretty fast on a calculator, but I think I got the gist of the question right.

Answer 4

good luck, that's way 2 advanced 4 me.