Name_______________
Date _____________
Earth Science
Measuring the Earth: Roundness and Smoothness
General Question: How round and smooth is the Earth?
Introduction: Astronauts observations and satellite pictures indicate that the Earth appears to be
perfectly round. From previous investigations we know that the Earth is not
perfectly round. From space, the Earth appears perfectly smooth but we know
that is not an accurate statement. We know that Mt. Everest rises 8.85 km above
the sea floor and that the Mariana Trench is 10.91 km below sea level in the
western Pacific Ocean.
Our problem is one of perspective or scale. From great distances the Earth really
does look very round and very smooth. Living on this planet, we can easily
visualize differences in the changing topography, but have some problems trying
to conceptualize the Earth’s shape due to its immense size. We can compare
relative roundness and smoothness of various objects by comparing ratios of
selected dimensions. The ratio of polar diameter:equatorial diameter, for a
perfectly round object would be 1.0. If we compare various objects the closer the
roundness ratio is to 1.0 the more round the object is. Similarly, an object that is
perfectly smooth when comparing the height (or depth) of a surface
irregularity:selected dimension would have a value of 0.0. As the irregularity
increases, the ratio becomes greater than zero indicating a less than smooth object.
Roundness Ratio = polar diameter / equatorial diameter
Note: Any pair of dimensions will work. (ex. Radii, circumferences)
Smoothness Ratio = height of irregularity / polar diameter
Note: Any spherical dimension may be used as long as it is consistent among the objects to be
compared.
Objectives: When you finish this investigation you should be able to:
 Determine whether the Earth or classroom globe is more perfectly round when given
appropriate dimensions.
 Determine whether the Earth or the classroom globe is the closest to perfectly smooth
when given irregularities and appropriate dimensions.
 Determine the height of a prominent feature (mountain, trench) on a properly scaled globe
given the height of the feature and the scale of the globe.
ethod: Method: (place all data in the data table provided.
1. Measure the polar and equatorial diameters of your classroom globe to the nearest tenth of
a centimeter. Calculate the polar and equatorial circumferences of your globe to the nearest
tenth of a centimeter. Determine the roundness ratio of the globe.
2. Using the polar diameter of the Earth (12,714km) and the equatorial diameter of the Earth
(12,756km), determine the roundness ratio of the Earth.
3. Measure the height of the highest imperfection on your classroom globe. This could be a
challenge. You may have to devise some indirect method to determine the height of the
irregularity. Using the equatorial diameter of your globe, calculate the roundness ratio for
the globe.
4. Using the height of Mt. Everest and the equatorial diameter of the Earth, calculate a
smoothness ratio for the Earth.
EARTH
Eq. Circumference
Polar Circumference
Eq. Diameter
Polar Diameter
High. Irregularity
Roundness Ratio
Smoothness Ratio
GLOBE
Introduction Questions
1. How does the Earth’s circumference measured around the poles compare to the
circumference measured around the equator?
2. The Earth’s shape is described as an oblate spheroid. What does this term
imply?
Observation Questions
1. Is the Earth or globe more nearly round? ______________
Explain your choice.
2. Is the Earth or globe more nearly smooth? _____________
Explain your choice.
3. How high would Mt. Everest appear on your globe if constructed to scale?
Show all work. ____________________
4. If a 2mm scratch were cut into a 30 cm diameter true scale globe, what would be
its depth on Earth? Show all work. ________________________
5. Some mountains on the moon are calculated to be 4.57 km high. Using the
Reference Tables, which is more smooth the Earth or the moon? Show all
work. (You will have to use equatorial diameter in the smoothness equation for
both)