how did cavendish measure the mass of the earth
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In 1798, Henry Cavendish performed an experiment to determine the density of the Earth, which would be useful in astronomical measurements. He used a torsion balance invented by geologist John Mitchell to accurately measure the force of attraction between two masses. From this measurement, he determined the mass of the Earth and then its density. In Cavendish's published paper on the experiment, he gave the value for the density and mass of the Earth but never mentioned the value forG.
It wasn't until 1873 that other scientists repeated the experiment and documented the value for G. The value for G implied from Cavendish's experiment was very accurate and within 1% of present-day measurements.
Because his experiment ultimately determined the value for G, Cavendish has been often incorrectly given credit for determining the gravitational constant.
Henry Cavendish performed an experiment to find the density of the Earth. Other scientists used his experimental setup to determine the value of G. The setup consisted of a torsion balance to attract lead balls together, measuring the torque on a wire and then equating it to the gravitational force between the balls. Then by a complex derivation, G = 2π2LθRe2/T2M was determined.
where The derived equation for G is:
G = 2π2LθRe2/T2M
where
G is the Universal Gravitation Constantπ is the Greek letter pi = 3.14...L is the length of the torsion barθ is the angle the bar turnsRe is the equilibrium point distance between Mand mT is the oscillation frequencyM is the mass of the larger object
The calculated value of G from this experiment is:
G = 6.674*10−11 m3/kg-s2
Since a newton is equivalent to kg-m/s2, G is also defined as:
G = 6.674*10−11 N-m2/kg2
It wasn't until 1873 that other scientists repeated the experiment and documented the value for G. The value for G implied from Cavendish's experiment was very accurate and within 1% of present-day measurements.
Because his experiment ultimately determined the value for G, Cavendish has been often incorrectly given credit for determining the gravitational constant.
Henry Cavendish performed an experiment to find the density of the Earth. Other scientists used his experimental setup to determine the value of G. The setup consisted of a torsion balance to attract lead balls together, measuring the torque on a wire and then equating it to the gravitational force between the balls. Then by a complex derivation, G = 2π2LθRe2/T2M was determined.
where The derived equation for G is:
G = 2π2LθRe2/T2M
where
G is the Universal Gravitation Constantπ is the Greek letter pi = 3.14...L is the length of the torsion barθ is the angle the bar turnsRe is the equilibrium point distance between Mand mT is the oscillation frequencyM is the mass of the larger object
The calculated value of G from this experiment is:
G = 6.674*10−11 m3/kg-s2
Since a newton is equivalent to kg-m/s2, G is also defined as:
G = 6.674*10−11 N-m2/kg2
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