Home Table of Contents About the Authors Glossary Buy This Book Joseph Henry Press


SOLUTION TO EXERCISE 7

back to exercise

matter: TOC for Knowledge Concepts, Exercises, and Solutions



SOLUTION TO EXERCISE 7

(a) The mass of the Sun is 2.0 * 10^30 kg.  Also, the radius of the
Sun is r = 7.0 * 10^8 m, so the Sun's volume is (4/3) * pi * r^3.  You
can calculate that the Sun's volume is 1.43 * 10^27 m^3, and has density

       M             2 * 10^30 kg
  D = --- = --------------------------------- = 1400 kg/m^3
       V     1.333 * 3.14 * (7.0 * 10^8 m)^3

This is about 1000 times denser than air, 40% denser than water,
half as dense as rock, and about 5 times less dense than iron.  Based
on this information alone, I might conclude that the Sun is primarily
liquid, since its average density is most like water.  Some solid 
component, to bring the density up toward rock, could be reasonably
assumed to exist also; and since gas at terrestrial densities is so 
much less dense than the Sun on average, some of that could probably
exist too, and not affect the overall density very much.

(b) The center of the Sun is 110 times denser than water.  That's
over five times denser than the densest material on Earth!  Let's do
some reasoning: if just one percent (1%) of the volume of the Sun has
that density, then the mass of that one percent would be

   0.01 * (1.43 * 10^27 m^3) * (110 * 1000 kg/m^3) = 1.57 * 10^30 kg

which is over three-quarters the total mass of the Sun.  The rest of
the matter in the Sun would have an average density of

   (0.43 * 10^30 kg) / (0.99 * 1.43 * 10^27 m^3) = 304 kg/m^3

which is less than one-third the density of water.  Suddenly the idea
of the Sun being primarily liquid is not so certain; if water occupies
even 40% of the Sun's volume in this scenario, then over 50% of the
Sun's volume must be completely empty, and this doesn't make sense.  

There must be some sort of change from super-dense in the Sun's center 
to very un-dense at the Sun's surface.  We can jump to a few conclusions, 
but two come to mind.

   The Sun could differentiated, like the planets, into layers of
      different-density materials.  In this case, most of the volume
      must be sparse gas.
  The Sun is primarily one phase of matter.  In this case, the only
      phase that can be squeezed to super-density (at super-high pressure)
      AND exist at very low densities (at low pressure) is gas.

In both cases, the Sun's volume should be mostly gaseous.  This turns out
to be true; almost the Sun's entire volume is gas permeated with magnetic
fields - a state we call plasma.