gravitational attraction between objects, for it gave a mathematical relation between the length of each planet’s year—the time it takes for it to go around the sun and its distance from the sun. From this law, one could easily derive that the velocity of the planets around the sun falls in a fixed way with their distance from the sun. Specifically, Kepler’s laws showed that their velocity falls inversely with the square root of their distance from the sun.
Armed with this knowledge, and his own generalization from the results of Galileo that the acceleration of moving bodies must be proportional to the force exerted on them, Newton was able to show that if planets were attracted toward the sun with a force proportional to the product of their mass and the sun’s mass, divided by the square of the distance between them, Kepler’s velocity law would naturally result. Moreover, he was able to show that the constant of proportionality would be precisely equal to the mass of the sun times the strength of the gravitational force. If the strength of the gravitational force between all objects is universal, this could be represented by a constant, which we now label G.
Even though it was beyond the measuring abilities of his time to determine the constant G directly, Newton did not need this to prove that his law was correct. Reasoning that the same force that held the planets around the sun must hold the moon in orbit around the Earth, he compared the predicted motion of the moon around the Earth—based on extrapolating the measured downward acceleration of bodies at the earth’s surface with the actual measured motion: namely, that it takes about 28 days for
the moon to orbit the Earth. The predictions and the observations agreed perfectly. Finally, the fact that the moons of Jupiter, which Galileo had first discovered with his telescope, also obeyed Kepler’s law of orbital motion, this time vis-à-vis their orbit around Jupiter, made the universality of Newton’s Law difficult to question.
Now, I mention this story not just to reiterate how the mere observation of how things move—in this case, the planets—led to an understanding of why they move. Rather, it is to show you how we have been able to exploit these results even in modern research. I begin with a wonderful precedent created by the British scientist Henry Cavendish, about 150 years after Newton discovered the Law of Gravity.
When I graduated and became a postdoctoral fellow at Harvard University, I quickly learned a valuable lesson there: Before writing a scientific paper, it is essential to come up with a catchy title. I thought at the time that this was a recent discovery in science, but I have since learned that it has a distinguished tradition, going back at least as far as Cavendish in 1798.
Cavendish is remembered for performing the first experiment that measured directly in the laboratory the gravitational attraction between two known masses, thus allowing him to measure, for the first time, the strength of gravity and determine the value of G. In reporting his results before the Royal Society he didn’t entitle his paper “On Measuring the Strength of Gravity” or “A Determination of Newton’s Constant G.” No, he called it “Weighing the Earth.”
There was a good reason for this sexy title. By this time Newton’s Law of Gravity was universally accepted, and so was the premise that this force of gravity was responsible for the observed motion of the moon around the Earth. By measuring the distance
to the moon (which was easily done, even in the seventeenth century, by observing the change in the angle of the moon with respect to the horizon when observed at the same time from two different locations—the same technique surveyors use when measuring distances on Earth), and knowing the period of the moon’s orbit—about 28 days—one could easily calculate the moon’s velocity around the Earth. Let me reiterate that Newton’s
Armed with this knowledge, and his own generalization from the results of Galileo that the acceleration of moving bodies must be proportional to the force exerted on them, Newton was able to show that if planets were attracted toward the sun with a force proportional to the product of their mass and the sun’s mass, divided by the square of the distance between them, Kepler’s velocity law would naturally result. Moreover, he was able to show that the constant of proportionality would be precisely equal to the mass of the sun times the strength of the gravitational force. If the strength of the gravitational force between all objects is universal, this could be represented by a constant, which we now label G.
Even though it was beyond the measuring abilities of his time to determine the constant G directly, Newton did not need this to prove that his law was correct. Reasoning that the same force that held the planets around the sun must hold the moon in orbit around the Earth, he compared the predicted motion of the moon around the Earth—based on extrapolating the measured downward acceleration of bodies at the earth’s surface with the actual measured motion: namely, that it takes about 28 days for
the moon to orbit the Earth. The predictions and the observations agreed perfectly. Finally, the fact that the moons of Jupiter, which Galileo had first discovered with his telescope, also obeyed Kepler’s law of orbital motion, this time vis-à-vis their orbit around Jupiter, made the universality of Newton’s Law difficult to question.
Now, I mention this story not just to reiterate how the mere observation of how things move—in this case, the planets—led to an understanding of why they move. Rather, it is to show you how we have been able to exploit these results even in modern research. I begin with a wonderful precedent created by the British scientist Henry Cavendish, about 150 years after Newton discovered the Law of Gravity.
When I graduated and became a postdoctoral fellow at Harvard University, I quickly learned a valuable lesson there: Before writing a scientific paper, it is essential to come up with a catchy title. I thought at the time that this was a recent discovery in science, but I have since learned that it has a distinguished tradition, going back at least as far as Cavendish in 1798.
Cavendish is remembered for performing the first experiment that measured directly in the laboratory the gravitational attraction between two known masses, thus allowing him to measure, for the first time, the strength of gravity and determine the value of G. In reporting his results before the Royal Society he didn’t entitle his paper “On Measuring the Strength of Gravity” or “A Determination of Newton’s Constant G.” No, he called it “Weighing the Earth.”
There was a good reason for this sexy title. By this time Newton’s Law of Gravity was universally accepted, and so was the premise that this force of gravity was responsible for the observed motion of the moon around the Earth. By measuring the distance
to the moon (which was easily done, even in the seventeenth century, by observing the change in the angle of the moon with respect to the horizon when observed at the same time from two different locations—the same technique surveyors use when measuring distances on Earth), and knowing the period of the moon’s orbit—about 28 days—one could easily calculate the moon’s velocity around the Earth. Let me reiterate that Newton’s
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