# Newton’s Law of Gravitation

## The legendary myth that an apple falls on the head of Newton opened a new page in the development of physics.

Newton’s Law of General Gravitation

The legendary myth that an apple falls on the head of Newton opened a new page in the development of physics. Although we are not sure whether it happened or not, we get the result from this story. Newton starts thinking about why the apple falls down on the earth in a straight line without moving to any other direction. He thought perhaps the earth has the attraction to the apple. For many years, he experiments about this subject and we get the law of general gravitation from his efforts.

Newton alone was not concerned about the term ‘gravitation.’ Scientists before Newton and his contemporaries had the same question in their minds. They used their own processes to make new experiments. They collected information and kept records of them. Before starting his broad research on gravitation, Newton took deeper attention to the previously available works. Some mentionable scientists who had much influence on him are-

Ismael Bullialdus

He was a French astronomer and mathematician. He got many scholars of his time as companions. He was a supporter of Galileo Galilei and Nicolaus Copernicus. His ‘Astronomia Philolaica’ is the most famous work by him. Though he supported Kepler’s law regarding planets’ elliptical orbitals around the sun, he argued with him at one point. As per as Kepler, the force that the sun exerts into the planets lessens in inverse proportion to their distance. But Bullialdus mentioned it has to follow inverse-square law for the first time. He could not prove it and that’s why he is known as the ‘finder but not keeper of the Inverse Square Law of Gravitation.’

Giovanni Alfonso Borelli

The Renaissance Italian physiologist, physicist, and mathematician; Borelli demonstrated the moons orbital of the Jupiter. His study finds out elliptical orbitals of them. He also studied the trajectory of a comet for one year. He describes the pathway of that comet is parabolic. There is some virtue acting between celestial bodies. It attracts and unites them. He was the first to relate gravity with the human body. It is known as biomechanics and he is considered as the father of modern biomechanics. Newton uses his idea in his research. Borelli’s view that the sun attracts all other planets was appreciated by him.

René Descartes

He was an influential scientist to Newton. He contributed to the development of modern physics although he is known as one of the founders of modern philosophy. He formulated the law of nature. Newton studied his conservation principle of motion while doing research on the laws of general gravitation. Newton was surely indebted to the works of Descartes as it helped him to express the concept of linear inertia.

Johannes Kepler

He is famous for his invention of the laws that we know as ‘Keplar’s Law’ today. He established the laws from the astronomical observations by Tycho Brahe. Nicolaus Copernicus’s cosmology terms were in his consideration and Kepler re-interpreted the observations according to those terms. The laws by Kepler are-

• The orbit of a planet is an ellipse, with the Sun at one of the two foci.
• A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Newton later re-interpreted the laws of Kepler in keeping Copernicus’s cosmology terms in his mind.

Edmund Halley

He had something extraordinary to tell Newton about the celestial mechanics. Halley wanted to know about the shape of the orbitals of the planets moving around the sun and the force that is in the form inverse-square law with the distance between them (planet and the sun). Newton told that the orbital is an ellipse and also showed the proof of his view. Then Halley took initiatives to publish the works by Newton. He proposed the Royal Society and did not hesitate to spend his money on the publication of Newton’s book “Principia”.

Newton’s law on general gravitation

The modern language states the law in the following way:

Every point mass attracts every single other point mass by a force acting 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.

the distance between the centers of the two masses.

F = G{(m1*m2)/r^2}

where:

F = force between the two masses;

G = the gravitational constant (6.674×10−11 N·(m/kg)2)

m1 = the first mass;

m2 = the second mass;

r = the distance between the centers of the two masses.

After the publication of the law, there arose a dispute between Newton and Hooke. Robert Hooke accused Newton of copying his ideas on that "the rule of the decrease of Gravity, being reciprocal as the squares of the distances from the Center". For defending himself, Newton agreed that Hooke is the author of this idea. But he did not have enough researches to prove the ideas. Newton credited Hooke by acknowledging him for his individual efforts for the inverse-square law. He also acknowledged Wren and Halley for their endeavor.

The value of G

Although Newton proposed a gravitational constant ‘G’ in his inverse square law, he was unable to grab the value of this constant. Henry Cavendish is credited for his determining the value. In 1798, after completing a series of experiments, he was able to measure it. The value is 6.674×10−11 N·(m/kg)2

Shell Theorem

According to the law, if we want to calculate ‘g’ we have to consider the radius of the earth as the distance between the masses. The attraction between the earth and any other object depends on its radius. We assume the earth’s mass is concentrated on its’ center. It may be true when we compare its’ force to other planets. But difficulty arouses when we measure the force on an object on its surface. To make more precise assumptions from the law, Newton brings his “Shell Theorem”.  They are-

• A spherically symmetric object affects other objects gravitationally as if all of its mass were concentrated at its center.
• If the object is a spherically symmetric shell (i.e., a hollow ball) then the net gravitational force on a body inside of it is zero.

Limitations of the law

Newton’s law of general gravitation is a great discovery. It helps physics in many ways. But it has some limitations too. The law cannot explain the orbits of the planets as it cannot find out the precession of the perihelion of the orbits. It is apparent in the case of planet Mercury. In detecting the angular deflection of light rays by gravity, Newton’s law can only go halfway through. But general relativity is more helpful in doing so. The orbiting stars in spiral galaxies strongly disobey this law.

Einstein’s law of general relativity

As per the limitations that are considered by scientists, they need a unique theory to solve their problems. Here comes the law of general relativity by Einstein. In his law, gravity is not showed as a force propagated between bodies. Rather it is an attribute of curved spacetime. The curved nature of his proposed model has a unique geometry of its own. It influences the energy and momentum in this system.

There are many practical instances that work by maintaining Newton’s law of general gravitation. Some of them are-

• Motion of the Moon: When the apple stuck him, Newton understood that a force is behind this. He then thought of the Moon and the force may be the reason that causes its motion. For the general theory of gravitation, the moon is supposed to fall towards the earth. But it does not. The curvature of the spacetime created by the earth keeps the moon away from us moving in its orbital in a systematic way.

• Submarines: Submarines are a part of modern warfare. They are built to stay and move underwater. To avoid collision and function in a proper way, it needs to follow Newton’s gravitation law besides the Archimedes principle. Scientists have invented gravity gradiometers to detect anomalous mass in a trajectory quickly. The collected data by this tool ensures a safe underwater journey.

• Ocean’s tide: The tides in the oceans swell up because of gravitation. The moon is the only satellite of our planet. The force between the two is the cause of tide. Some places on the earth are pretty close to the moon and they get more attraction from it. So, we find massive tides there. The tides occur about an hour later each day because the moon passes in the same way. The sun is also able to cause tides. The spring tides and the leap tides happen for the sun’s gravitational force on the earth.

• The seasons: We can see the variations of seasons in both the Northern Hemisphere and the Southern Hemisphere. The law of general gravitation is mainly responsible for this. We have a misconception about seasons that they happen because of varying distances of the Earth from the Sun on its elliptical orbit.