Why masses attract each other

Diagram used in the proof of the Shell Theorem : This diagram outlines the geometry considered when proving The Shell Theorem. The surface area of a thin slice of the sphere is shown in color. Note: The proof of the theorem is not presented here. Interested readers can explore further using the sources listed at the bottom of this article.

We can use the results and corollaries of the Shell Theorem to analyze this case. When the bodies have spatial extent, gravitational force is calculated by summing the contributions of point masses which constitute them. In modern language, the law states the following: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.

The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:. If the bodies in question have spatial extent rather than being theoretical point masses , then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies.

As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere. Furthermore, inside a uniform sphere the gravity increases linearly with the distance from the center; the increase due to the additional mass is 1. Gravitational Field of Earth : Diagram of the gravitational field strength within the Earth. Privacy Policy. 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.

The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity or weight yields the same result as when calculating it using the equation presented in Unit Gravitational interactions do not simply exist between the earth and other objects; and not simply between the sun and other planets.

Gravitational interactions exist between all objects with an intensity that is directly proportional to the product of their masses. So as you sit in your seat in the physics classroom, you are gravitationally attracted to your lab partner, to the desk you are working at, and even to your physics book.

Newton's revolutionary idea was that gravity is universal - ALL objects attract in proportion to the product of their masses. Of course, most gravitational forces are so minimal to be noticed. Gravitational forces are only recognizable as the masses of objects become large. To illustrate this, use Newton's universal gravitation equation to calculate the force of gravity between the following familiar objects.

Click the buttons to check answers. Today, Newton's law of universal gravitation is a widely accepted theory. It guides the efforts of scientists in their study of planetary orbits. Knowing that all objects exert gravitational influences on each other, the small perturbations in a planet's elliptical motion can be easily explained.

As the planet Jupiter approaches the planet Saturn in its orbit, it tends to deviate from its otherwise smooth path; this deviation, or perturbation , is easily explained when considering the effect of the gravitational pull between Saturn and Jupiter. Newton's comparison of the acceleration of the apple to that of the moon led to a surprisingly simple conclusion about the nature of gravity that is woven into the entire universe. All objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to their distance of separation.

Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects? If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 2 2. If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects? If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 2 2.

The new force is then 4 times the original 16 units. If the mass of both objects was doubled, and if the distance between the objects remained the same, then what would be the new force of attraction between the two objects? If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?

But this affect is offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 2 2 ; the result is that there is no net affect on force. If the mass of both objects was tripled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects? But this affect is partly offset by the doubling of the distance.

Doubling the distance would cause the force to be decreased by a factor of 4 2 2. If the mass of object 1 was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction between the two objects?

If the mass of one object is doubled. But this affect is more than offset by the tripling of the separation distance. Tripling the distance would cause the force to be decreased by a factor of 9 3 2. As a star ages, it is believed to undergo a variety of changes. Astronauts must tether themselves when doing work outside even the massive International Space Station ISS , as in Figure , because the gravitational attraction cannot save them from even the smallest push away from the station.

What happens to force and acceleration as the vehicles fall together? What will our estimate of the velocity at a collision higher or lower than the speed actually be? And finally, what would happen if the masses were not identical? Would the force on each be the same or different? How about their accelerations? The force of gravity on each object increases with the square of the inverse distance as they fall together, and hence so does the acceleration.

For example, if the distance is halved, the force and acceleration are quadrupled. Our average is accurate only for a linearly increasing acceleration, whereas the acceleration actually increases at a greater rate.

So our calculated speed is too small. But the accelerations will not be if they have different masses. The effect of gravity between two objects with masses on the order of these space vehicles is indeed small. Yet, the effect of gravity on you from Earth is significant enough that a fall into Earth of only a few feet can be dangerous. Find the acceleration of our galaxy, the Milky Way , due to the nearest comparably sized galaxy, the Andromeda galaxy Figure.

The approximate mass of each galaxy is billion solar masses a solar mass is the mass of our Sun , and they are separated by 2. Note that the mass of Andromeda is not so well known but is believed to be slightly larger than our galaxy. The Andromeda galaxy is the nearest spiral galaxy to the Milky Way, and they will eventually collide.

We can consider the galaxies to be point masses, since their sizes are about 25 times smaller than their separation. The mass of the Sun see Appendix D is [latex] 2. Does this value of acceleration seem astoundingly small? That is nine orders of magnitude smaller than the initial distance between them. In reality, such motions are rarely simple. These two galaxies, along with about 50 other smaller galaxies, are all gravitationally bound into our local cluster.

Our local cluster is gravitationally bound to other clusters in what is called a supercluster. All of this is part of the great cosmic dance that results from gravitation, as shown in Figure.

Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in science, and why was this action at a distance ultimately accepted? The ultimate truth is experimental verification.

Field theory was developed to help explain how force is exerted without objects being in contact for both gravity and electromagnetic forces that act at the speed of light. It has only been since the twentieth century that we have been able to measure that the force is not conveyed immediately. While all scientific conjectures must be experimentally verified, can you provide arguments as to why this must be? You may wish to consider simple examples in which any other form would lead to contradictory results.

Evaluate the magnitude of gravitational force between two 5-kg spherical steel balls separated by a center-to-center distance of 15 cm. Estimate the gravitational force between two sumo wrestlers, with masses kg and kg, when they are embraced and their centers are 1. The only known force a planet exerts on Earth is gravitational.