Exercise 4 : Numerical Data Pertaining to the Earth

All of you have had algebra and should be able to manipulate numbers and manage conversion from one set of units to another. For this exercise you may use a calculator.

Read through Appendix A in your text for some background.

1. The equitorial radius of the Earth is 6,378 kilometers (km):

   1. convert this to centimeters (cm)

   2. one km = 1,000 meters = 100,000 cm = 10⁵ cm

   3. Therefore, 6,378 km = 637,800,000 cm

   4. or 6.378 * 10⁸ cm

   5. always check the units: (6.378 * 10³ km) * (10⁵ cm/km) = 6.738 * 10⁸ km (cm/km) and the km's cancel leaving the answer in cm.

2. Convert the equitorial radius from km to miles:

   1. one meter = 3.2808 feet

   2. = 6,378 km * 1,000 m/km * 3.2808 ft/m * 0.0001894 mi/ft

   3. = 3,963 miles

      Note that the units are in miles. Write this problem down for yourself and make sure you understand how the units cancel out.

   Question 1 -- Where does the term 0.0001894 come from? That is, how would you get this conversion factor?

3. The volume of the Earth is 1.083 * 10²⁷ cubic centimeters.

   Question 2 -- How many cubic cm are in one cubic inch? [there are 2.54 cm in one inch]

   Question 3 -- Therefore, one cubic centimeter equals ___________ cubic inches.

   Question 4 -- What is the volume of the Earth in cubic inches _____________.

4. The volume of a sphere equals (4/3)pr³ where p is "pi", the ratio of the circumference to the diameter of a sphere (use the value of 3.1416) and r is the radius of the sphere.

   Question 5 -- Compute the volume of the earth in cubic centimeters using the equitorial radius given above (6,378 km).

   Question 6 -- Why do you think your answer does not agree with the volume given above? What if the Earth is not a perfect sphere -- that is, what if the radius at the pole is not equal to the radius at the equator?

5. The mass of the Earth is 5.976 * 10²⁷ grams.

   Question 7 -- Compute the density of the Earth (using the volume given at the start of the problem) - the ratio of mass to volume - usually given as grams/cubic centimeters.

   The density of the crust is about 2.6 and that of the mantle is about 3.2.

   Question 8 -- What does your calculation tell you about the density of the core?

Answer all of the questions given above and submit at the proper time. _________________________________________________________________________________________________

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Copyright by John C. Butler, July 29, 1995