Project I

 







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.

  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

    3. or, 637,800,000 cm

    4. or 6.378 * 108 km

  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 * 0.001894 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 0.001894 come from?

  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 radius of the Earth in centimeters using the volume given above. Check your units. Question 6 -- Convert to kilometers and compare with the equitorial radius given above. Why are the two numbers not the same?

  5. The mass of the Earth is 5.976 * 1027 grams. Question 7 -- Compute the density of the Earth - 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?