### What Is the Third Law of Gravitational Force

So you know that the gravitational force between two objects can be described as \$\$vec{F_{12}}=G*frac{m_1*m_2}{{r}_{12}^2}has{r_{12}}\$\$ and according to Newton`s 3rd law, the force that the rock exerts on earth is the same and opposite to that of the Earth on the rock. They attract each other (not in a strange way, mind you). However, since the mass of the rock is negligible compared to the Earth, the Earth does not really move (\$vec{F}=mvec{a}\$). If he were to move, then anyone who drops a stone somewhere would cause major disasters. Plus, you`re drawn to the farthest star man knows, but because the term \$vec{r}\$ is so large (even more square), you barely feel the connection (which makes the star sad). That is an answer to the question. If you want to know more, I recommend University Physics or Berkeley`s Mechanics (www.astrosen.unam.mx/~posgrado/libros/1_Mechanics_Kittel_BPC.pdf) Figure 1. According to early reports, Newton was inspired to make the connection between falling bodies and astronomical movements when he saw an apple fall from a tree and realized that if gravitational force could extend through the ground on a tree, it could also reach the sun. The inspiration for Newton`s apple is part of world folklore and may even be based on the act. Great importance is attached to this because Newton`s universal law of gravity and his laws of motion answered very old questions about nature and greatly supported the idea of underlying simplicity and unity in nature. Scientists still expect the underlying simplicity to emerge from their ongoing studies of nature.

1. Suppose 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 attraction between the two objects? Gravitational constant, G: proportionality factor used in Newton`s universal law of gravity equation; it is a universal constant – that is, it is thought to be the same everywhere in the universe Figure 7. A black hole is an object with such a strong gravity that even light cannot escape it. This black hole was created by the supernova of a star in a two-star system. The tidal forces generated by the black hole are so great that it tears material from the companion star. This material is compressed and heated when sucked into the black hole, producing light and X-rays observable from Earth. where F is the amplitude of the gravitational force and G is a proportionality factor called the gravitational constant. G is a universal gravitational constant – that is, it is thought to be the same everywhere in the universe. It was measured experimentally, to be Newton`s law of universal gravity, is usually declared to attract other particles into the universe with a force that is directly proportional to the product of its masses and inversely proportional to the square of the distance between its centers. [Note 1] The publication of the theory became known as the „first great union” because it marked the union of previously described gravity phenomena on Earth with known astronomical behaviors.

   As discussed in Lesson 3, Isaac Newton compared the acceleration of the moon to the acceleration of objects on Earth. Newton believed that gravitational forces were responsible for each of them and was able to draw an important conclusion about gravity`s dependence on distance. This comparison led him to conclude that the force of attraction between the Earth and other objects is inversely proportional to the distance between the center of the Earth and the center of the object. But distance is not the only variable that affects the magnitude of a gravitational force. Although there may be two equal and opposing forces acting on a single body, it is important to remember that for each of the forces, a pair of the Third Law acts on a separate body. This can sometimes be confusing when several pairs of the Third Law are at work. Below are some examples of situations where several pairs of the Third Law occur. In this way, it can be shown that an object with a spherically symmetrical mass distribution exerts the same gravitational attraction on the external bodies as if all the mass of the object were concentrated at a point at its center.  (This generally does not apply to non-spherical-symmetrical bodies.) Attempts are still being made to understand the gravitational force. As we will see in particle physics, modern physics explores the links of gravity with other forces, space and time. The theory of general relativity changes our view of gravity and leads us to think of gravity as a curvature of space and time. Tides are not only found on Earth, but occur in many astronomical systems.

The most extreme tides occur where the gravitational force is strongest and varies the fastest, such as near black holes. B (see Figure 7). Some likely candidates for black holes have been observed in our galaxy. These have masses larger than the Sun, but have diameters of only a few kilometers in diameter. The tidal forces in their vicinity are so great that they can actually tear the material of a companion star. While Newton was able to formulate his law of gravity in his monumental work, he felt deeply uncomfortable with the idea of „remote action” implied by his equations. In 1692, he wrote in his third letter to Bentley: „That one body can act on another at a distance through a void, without the mediation of anything else, through and through which its work and power can be transferred from each other, is such an absurdity to me that I believe that no man who has a competent ability to think in philosophical matters, could never fall into it. Newton`s description of gravity is accurate enough for many practical purposes and therefore widely used. Deviations from this are small if the dimensionless quantities φ/c 2 {displaystyle phi /c^{2}} and ( v/c ) 2 {displaystyle (v/c)^{2}} are both much smaller than one, where φ {displaystyle phi } is the gravitational potential, v {displaystyle v} is the speed of the objects examined and c {displaystyle c} is the speed of light in a vacuum.

 For example, Newtonian gravity provides an accurate description of the Earth/Sun system, because Newton knew that the force that caused the acceleration of the apple (gravity) had to depend on the mass of the apple. And since the force that causes the apple to accelerate downwards also causes the earth to accelerate upwards (Newton`s third law), this force must also depend on the mass of the earth. For Newton, the 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 separating the centers of gravity of the Earth and the object. Gravitational fields are also conservative; That is, the work done by gravity from one position to another is independent of the path. As a result, a gravitational potential field V(r) exists, so the amplitude of the force on each object (one has a mass greater than the other) is the same, according to Newton`s third law. If the distance is increased by a factor of 2, the force decreases by a factor of 4 (22). .