Latitude and gravity
Measure the variation of g according to terrestrial latitude
Author:
Title 4
Learning objectives :
This activity allows students to verify that the acceleration of gravity varies depending on the Earth's latitude. It recreates an important historical discovery with modern tools.
Concepts covered
Acceleration of gravity; Shape of the Earth; Centrifugal force; Scientific collaboration; History of science
What students will do :
The student measures the acceleration of gravity using the FizziQ accelerometer in a static position on a table. By calculating the average of the recorded values and comparing this result with that of a class located near the equator, the student can verify experimentally that g is lower at the equator than at mid-latitudes in accordance with the historical observation of the astronomer Richer.
What is required :
Smartphone with the FizziQ application; A flat and stable surface; Contact with a class located near the equator (ideally); Internet access to check official g values; FizziQ experience notebook
Scientific background :
In 1672, the astronomer Jean Richer made a surprising discovery during an expedition to Cayenne (French Guiana): a pendulum clock, perfectly adjusted in Paris, was delayed by 2.5 minutes per day near the equator. This historical observation revealed that the acceleration of gravity g varies with latitude. This variation is explained by two main factors: 1) The ellipsoidal shape of the Earth (flattened at the poles): the Earth's radius is shorter at the poles (6357 km) than at the equator (6378 km), which brings the poles closer to the Earth's center of mass, thus increasing the gravitational force; 2) The centrifugal force due to the earth's rotation: maximum at the equator and zero at the poles, it partially opposes gravity. These two effects combined cause g to vary from approximately 9.78 m/s² at the equator to 9.83 m/s² at the poles, a difference of 0.5%. The accelerometer of a modern smartphone is sensitive enough to detect this variation, although individual instrumental errors may be of the same order of magnitude. This is why this experiment benefits from a collaborative approach: by averaging the measurements of several devices, random errors partially cancel each other out. Historically, this discovery helped confirm Newton's theory of the shape of the Earth and led to the first geodetic expeditions to precisely measure the shape of the Earth, notably that of Maupertuis in Lapland (1736) and that of La Condamine in Peru (1735-1744).