Consider Newton's famous equation. Newton knew that the force that caused the apple's acceleration gravity must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration Newton's third law , that force must also depend upon the mass of the earth.
So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.
But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal.
ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as. Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force.
So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled.
If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.
So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled increased by a factor of 2 , then the force of gravitational attraction is decreased by a factor of 4 2 raised to the second power. If the separation distance between any two objects is tripled increased by a factor of 3 , then the force of gravitational attraction is decreased by a factor of 9 3 raised to the second power.
The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation. Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality.
This equation is shown below. The constant of proportionality G in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. This experiment will be discussed later in Lesson 3. The value of G is found to be. The units on G may seem rather odd; nonetheless they are sensible. Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance.
As a first example, consider the following problem. The solution of the problem involves substituting known values of G 6. The solution is as follows:. This would place the student a distance of 6. Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student a. This illustrates the inverse relationship between separation distance and the force of gravity or in this case, the weight of the student.
The student weighs less at the higher altitude. However, a mere change of 40 feet further from the center of the Earth is virtually negligible. A distance of 40 feet from the earth's surface to a high altitude airplane is not very far when compared to a distance of 6.
This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made. Then, after deviant measurements have been weeded out, they average the values obtained at different times, and subject the final value to a series of corrections.
Finally, in arriving at the latest "best values", international committees of experts then select, adjust and average the data from an international selection of laboratories. Despite these variations, most scientists take it for granted that the constants themselves are really constant; the variations in their values are simply the result of experimental errors.
The oldest of the constants, Newton's Universal Gravitational Constant, known to physicists as Big G, shows the largest variations. As methods of measurement became more precise, the disparity in measurements of G by different laboratories increased, rather than decreased.
Between and , the lowest average value of G was 6. These published values are given to at least 3 places of decimals, and sometimes to 5, with estimated errors of a few parts per million.
Either this appearance of precision is illusory, or G really does change. The difference between recent high and low values is more than 40 times greater than the estimated errors expressed as standard deviations. What if G really does change? Maybe its measured value is affected by changes in the earth's astronomical environment, as the earth moves around the sun and as the solar system moves within the galaxy.
Or maybe there are inherent fluctuations in G. Such changes would never be noticed as long as measurements are averaged over time and averaged across laboratories. In , the US National Institute of Standards and Technology published values of G taken on different days, revealing a remarkable range. On one day the value was 6. In , a team lead by Mikhail Gershteyn, of the Massachusetts Institute of Technology, published the first systematic attempt to study changes in G at different times of day and night.
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The two outliers are a quantum measurement and a measurement known to suffer from drift. The green dot is an estimate of the mean value of G after the 5. Credit: J. Anderson, et al. The solar cycle monthly mean of the total sunspot number black curve does not consistently align with the data on G. More information: J. Anderson, G. Schubert, V. Trimble and M. Citation : Why do measurements of the gravitational constant vary so much?
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