SOLUTIONS TO EXERCISE 19


(a) Density is given by D = M/V.  M = 2.0 * 10^30 kg, and V = volume of Earth,
which is a sphere with a radius of 6.38 * 10^6 m.

              2.0 * 10^30 kg
  D = ------------------------------ = 1.8 * 10^9 kg/m^3
      4/3 * 3.14 * (6.38 * 10^6 m)^3

One m^3 contains (100 cm)^3 = 10^6 cm^3; so one teaspoon is 5 * 10^(-6) m^3.
Thus, one teaspoon of white dwarf star material has a mass 

  M = DV = (1.8 * 10^9 kg/m^3) * (5 * 10^-6 m^3) = 9000 kg.
  This is nine tons!


(b) As above, Density is given by D = M/V.  M = 2 * 2.0 * 10^30 kg, and V = the 
volume of a sphere with a radius of 20/2 = 10 km.

            1.4 * 2.0 * 10^30 kg
  D = ------------------------------ = 6.7 * 10^17 kg/m^3
      4/3 * 3.14 * (10 * 10^3 m)^3

One m^3 contains (100 cm)^3 = 10^6 cm^3; so one teaspoon is 5 * 10^(-6) m^3.
Thus, one teaspoon of white dwarf star material has a mass 

  M = DV = (6.7 * 10^17 kg/m^3) * (5 * 10^-6 m^3) = 3.4 * 10^12 kg.
  This is over three billion tons!

(c) An adult elephant weighs about 6 tons, often more.  (This information
comes from numerous reputable sources, including the Oakland Zoo's African
Elephant information page at http://www.oaklandzoo.org/atoz/azeleph.html)
A small sewing thimble has a volume of about 0.5 cubic centimeter.  Thus,
a thimbleful of neutron star material has a mass

  M = DV = (6.7 * 10^17 kg/m^3) * (0.5 * 10^-6 m^3) = 3.35 * 10^11 kg.

 (3.35 * 10^11 kg) / (6 * 10^3 kg/elephant) = 5.6 * 10^7 elephants.

Thus, the number of elephants needed would be over 50 million!


There are about six billion (6 * 10^9) humans on Earth.  If we estimate that
the average mass of a human is about 40 kg (about 88 pounds) - a midpoint
between adults and children - then the mass of all of humanity put together is

  M = (6 * 10^9 persons) * (40 kg/person) = 2.4 * 10^11 kg.

Using the density of a neutron star, we find the volume of neutron star 
material needed to achieve this mass would be

  V = M/D = (2.4 * 10^11 kg) / (6.7 * 10^17 kg/m^3) = 0.36 * 10^(-6) m^3

Or about a third of a cubic centimeter - the size of a small sugar cube.