How can you experimentally verify Newton's law of gravitation?

You can experimentally verify Newton's law of gravitation through the Cavendish experiment or by observing planetary motion.

The Cavendish experiment, conducted by Henry Cavendish in 1798, is a classic method to verify Newton's law of gravitation. Cavendish used a torsion balance, a horizontal bar suspended from a thin wire, with two small lead spheres attached to either end. He then brought two larger lead spheres close to the smaller ones, and observed the tiny twisting motion caused by the gravitational attraction between the spheres. By carefully measuring this twist and knowing the properties of the torsion wire, Cavendish was able to calculate the gravitational constant (G) and thus verify Newton's law.

The experiment requires extreme precision and careful control of environmental factors. Any air currents, temperature changes, or even slight vibrations can affect the results. Therefore, it's often conducted in a sealed room with temperature control and vibration isolation. Modern versions of the Cavendish experiment use laser interferometry to measure the tiny twisting motion with even greater precision.

Another way to verify Newton's law of gravitation is by observing the motion of planets. According to the law, the force of gravity decreases with the square of the distance between two objects. This means that planets further from the sun should move more slowly in their orbits, which is indeed what we observe. For example, Mars, which is about 1.5 times further from the sun than Earth, takes about 1.9 Earth years to complete an orbit. This observation matches the predictions of Newton's law of gravitation.

Moreover, the law also predicts that the force of gravity should cause planets to move in elliptical orbits, with the sun at one focus of the ellipse. This prediction has been confirmed by centuries of careful astronomical observations. The precise shapes and timings of planetary orbits provide strong evidence for Newton's law of gravitation.

In conclusion, both the Cavendish experiment and observations of planetary motion provide experimental verification of Newton's law of gravitation. These experiments demonstrate the law's predictions about the strength of gravity and the motion of objects under its influence.