1797–1798: The Henry Cavendish Experiment : Measuring Earth's Density and Revolutionizing Gravitational Physics
The Cavendish experiment, conducted between 1797 and 1798 by British scientist Henry Cavendish, was a groundbreaking endeavor that measured the force of gravitational attraction between masses in a laboratory setting. This experiment provided the first accurate determination of the Earth's density and, by extension, allowed for the calculation of the gravitational constant (G), a fundamental constant in physics.
Background and Motivation
Prior to Cavendish's work, Sir Isaac Newton's law of universal gravitation had established that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. However, the gravitational constant (G) in Newton's equation was not known with precision, making it challenging to calculate the exact force of attraction between two known masses. Determining G was essential for quantifying gravitational forces and understanding the mass and density of celestial bodies, including Earth.
Apparatus and Experimental Setup
Cavendish utilized a torsion balance apparatus, initially designed by geologist John Michell but left unused due to Michell's death. The apparatus consisted of a horizontal bar suspended from its center by a thin wire or rod. At each end of the bar, small lead spheres were attached. Larger stationary lead spheres were positioned near the smaller ones, arranged so that gravitational attraction between the large and small spheres would cause the bar to rotate, twisting the suspending wire.
To ensure the accuracy of his measurements, Cavendish placed the entire apparatus in a wooden shed to shield it from air currents and temperature variations. He observed the experiment from a distance using telescopes, minimizing any potential disturbances.
Experimental Procedure
Calibration: Cavendish first calibrated the torsion balance to determine the relationship between the angle of rotation and the torsional force exerted by the wire. This step was crucial for quantifying the gravitational force based on the observed deflection.
Measurement: With the apparatus calibrated, Cavendish brought the large lead spheres into proximity with the smaller ones, causing a gravitational attraction that led to the rotation of the horizontal bar. He meticulously measured the angle of deflection and the time it took for the system to oscillate, providing data on the gravitational force between the masses.
Calculations: Using the measured deflection angles and oscillation periods, Cavendish calculated the torque exerted on the wire. From this torque, he determined the force of attraction between the masses. Knowing the masses and distances involved, he could then compute the Earth's density.
Results
Cavendish's meticulous experimentation led him to conclude that the Earth's average density was approximately 5.48 times that of water. This value is remarkably close to the modern accepted value of about 5.52. While Cavendish did not explicitly calculate the gravitational constant (G) as it is known today, his findings allowed later scientists to derive G with precision.
Implications for Physics
Determination of Earth's Mass and Density: By establishing the Earth's density, Cavendish's experiment enabled the calculation of the planet's total mass, enhancing the understanding of Earth's composition and informing geological and geophysical studies.
Measurement of the Gravitational Constant (G): Although Cavendish did not directly compute G, his data provided the means for its calculation. The gravitational constant is fundamental in physics, appearing in Newton's law of universal gravitation and Einstein's general theory of relativity.
Validation of Newtonian Gravity: The experiment offered empirical evidence supporting Newton's law of universal gravitation by quantifying the gravitational attraction between known masses. This validation was crucial for the acceptance and further development of gravitational theory.
Advancement of Experimental Physics: Cavendish's use of the torsion balance and his attention to experimental detail set new standards for precision in scientific experimentation, influencing future experimental methodologies in physics.
Conclusion
The Cavendish experiment stands as a landmark achievement in the history of physics. By measuring the tiny gravitational forces between masses in a controlled laboratory setting, Henry Cavendish provided critical insights into the Earth's density and laid the groundwork for the determination of the gravitational constant. His work exemplifies the power of precise measurement and experimentation in uncovering the fundamental laws of nature.
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