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The law of gravity was developed by Isaac Newton, following his discovery of gravity and gravitational force. Gravitational force is one of nature’s greatest forces that create attraction between all objects in the universe. Gravity causes the attraction between masses near the surface of the earth. Several factors influence gravitational force, including the mass of an object and the distance between objects.

The force of gravity was discovered by the famous scholar, Isaac Newton, who formulated the law of gravity. Newton’s law of gravity implies that the force of gravity between two objects is directly proportional to the product of the objects’ masses and is inversely proportional to the distance between the objects. This law of gravity can be further divided into three separate laws. The first law of gravity states that an object will remain in its state of rest unless it is acted upon by and external force. The second law of gravity states that the gravitational acceleration of an object is proportional to the applied force divided by the objects mass. The third law of gravity, which is a modification of Kepler’s law, states that the there is an equal and opposite reaction force to every action force (Gondhalekar, 2013).

These three laws of gravitational force are important because they provide an understanding of theuniversee. They also form a foundation for several other laws in physics. The relationship between gravity and distance is of great significance in physics considering that objects in nature exist in varying distances. In addition, the relationship between mass and gravitational force implies that larger objects will exert more gravitational pull on others than smaller objects.

It has been established that gravity plays a role in the motion of planets. It keeps the planets orbiting the sun in their paths. The revolution of the moons of various planets is also because of gravity. The beautiful Saturn ring contains particles that orbit the planet because of gravity. The free fall of objects is also as a result of gravity. This essay provides a detailed analysis of the law of gravity, the equations of the law of gravity, and the applications of gravitational force.

## Deriving the formula for the law of gravity

The relationship between the gravitational force and their distances can be linearly represented in a graph. It is possible to calculate the force between two objects using the newton’s law of gravity given their masses and the distance between them.

F=M1M2/r^{2} where m1 & m2 can be assumed to be the masses of the two objects respectively. r^{2} is the distance between the two objects. The formula is derived from the centripetal acceleration.

Acceleration (a) = v2/r where V is the velocity and r is the orbital radius.

For universal law of gravity, the masses considered are the mass of the moon and that of the earth. The distance between them is denoted by r V =2pr/T. T refers to the moons period of revolution and its usually 27.3 days or 2.36*10^{6} s.

Therefore, a =v ^{2} /r = 4p^{2} r/ T^{2}.

Depending on the distances of the object, the action and reaction force are equal but opposite. I.e. F(m1)= -F(m2). This can be simplified to be F=(M+M)^{n} and since mass of the object is independent of its acceleration. Hence, the value of n can be considered to be 1. In this case, the gravitational force F,

F -M1M2/since gravitational force depends on the distance between the objects, it is very smaller when considering two close objects. The gravitational force between two atoms in a molecule exists but is almost negligible. The force also varies between different attitudes being lowest in high attitudes and lowest in low attitudes (Schultz, 2003).

Fig 1: The relationship between gravitational force and mass

Fig 2: the relationship between gravitational force and distance

From the relationship between force with mass and distance, newton introduced a constant G known as the universal gravitational constant.

F=Gm1m2/r^{2}

The universal gravitational constant G does not vary between places. It is the same between various places and time. The value is very small and makes gravitational force weakest among the other forces of nature. The value of G=6.6741*10^{11} NM^{2}/Kg^{2} and is referred to as the Newton constant. The universal law of gravity extends behold the earth (Gondhalekar,2013).

The intensity of Gravity gives the mass and weight of an object the difference. That is the reason why the weight of an object varies between different places depending on the gravity. The weight of an object will change relative to gravity while the mass remains constant. For instance, an object on the moon will have less weight because the gravity is different. However, the mass will remain unchanged. Several experiments can be used to determine the value of the gravity intensity.

### Determining the intensity of gravity: The pendulum experiment

The pendulum experiment is one of the many experiments that can be used to determine the intensity of gravity g. the pendulum experiment is the most common way of establishing gravity intensity, as it is easy and simple to use. The experiment is also accurate and easy to control. Using a pendulum and a threat that is at least ammeter long, the pendulum is fixed in a specific location. It is swung a number of times oscillations. The pendulum weight, the length of the chord that is attached to the pendulum and the angle at which it is released can be adjusted. While recording the time taken to make the specified oscillations, the intensity of the gravity can be determined experimentally. The number of oscillation divided by the time taken for the oscillation gives period (Raymond & Vuile 2007).

T =2π (L/g)^{1/2}

Making g the subject, where T is the period, g is the gravity intensity and L is the length of the pendulum

g= 4 π^{2}L/T^{2}

#### Effects of the law of gravity

There are various where the law of gravity of applies. Gravity plays a role in various daily activity like walking, driving and standing upright. The medium orbit satellites orbiting and the planetary bodies in the space are maintained in their planetary orbits by the force of gravity. The tidal waves experienced in large water bodies like the oceans are because of gravity. The tides result from the attraction of the earth relative to the moon and the sun.

The sun is several times larger in mass that the earth and the other planets. It exerts a greater gravitational force on all the planets and interplanetary bodies to keep them orbiting around it. Similarly, the moon orbits the earth as a result in affixed orbit because of gravity. The beautiful ring around the planet Saturn is a because of uncountable particles of ice that orbit the planet because of gravity. Although newton discovered the law of gravity, he further discovered that gravity was universal. He joined the hall of fame because of this discovery. The law of gravity has been modified by several scientists like the Einstein. Einstein proposed the use of newton’s law s of gravity in quantum physics through his general theory of relativity.

The universal law of gravity formulated by newton is applicable while designing the space ships and lockets in the technology of today. For a rocket to launch from the earth’s surface, it must have the sufficient power to overcome the gravitational pull towards the surface of the earth. Once in the orbits, scientists apply the gravitational force and the acceleration force to keep the satellite balanced in tits orbits path around the earth (Wald, 1997).

#### Conclusion

The law of gravity explains one of the greatest forces of nature. The law was invented by Isaac newton who studied the concept of free fall from a simple illustration of the fall of an apple and its acceleration towards the ground. According the law of gravity, the force between the two objects is directly proportional to the distance between them. Newton also modified Kepler’s law of action and reaction to apply to gravity. All the objects maintain their free state unless acted by an external force. These laws combined formed the universal law of gravity that can be summarized as the force between two objects is directly proportion to their masses and inversely proportional to the distances between them. The law of gravity has various effects that include the pulling of all objects towards the surface of the earth, maintaining satellites and planetary objects in their orbits and tidal waves. To measure the intensity of the gravity in various areas, several experiments that can be used, one of the experiments are the pendulum experiment. In conclusion, gravity is not constant but changes depending on various factors like attitude.

#### References

Gondhalekar,P(2013). The Grip of gravity: The quest to understand the laws of motion and gravitational. New York: Cambridge University Press

Schutz,B(2003). An introduction to guide on gravity and general relativity. Max Planck institute for gravitational physics. New York: Cambridge university press

Wald, R(1997). Space, time and gravity. (2^{nd} ed). Chicago and London: the University of Chicago press.

Raymond a & Vuile C(2007). The essentials of college physics. Australia: Thomson bookstore