# Gravitational force: An overview

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### 1.0 Introduction

### 1.1 What is gravitational force?

Gravitational force is defined as a force of attraction which exerts between two objects with mass. It pulls two objects that have mass. (Gravitation and Gravity n.d.).

### 1.2 Background Information

### 1.2.1 The discovery of gravitational force

One day, Newton was sitting on his garden and observing the falling of an apple from a tree. A sudden inspiration appeared in his mind. There must be a force exerted on the apple since the apple accelerated while falling down from the tree with zero initial velocity. The force is then called “gravity” and the acceleration due to the force is called “acceleration due to gravity” (Sir Isaac Newton: The Universal Law of Gravitation n.d.).

### 1.2.2 Effects of gravitation on planets

If the force of gravity exerts at the top of the trees and mountains, then it must exerts all the way to the orbit of the moon. It is expected that the orbit of the moon around the earth results from the gravitational force as the acceleration due to the gravity can change the velocity of the moon in such a way it followed an orbit around the earth (Sir Isaac Newton: The Universal Law of Gravitation n.d.).

### 2.0 The Universal Law of Gravitation

### 2.1 Kepler's law of gravitation

Kepler's Third Law states that the ratio of the cubes of their mean distances from the Sun is same as the squares of the periods of any two planets orbit about the Sun. **P** represents the time taken for one revolution about the Sun and **R** represents the distance between the planet and the Sun. The equation indicates that the period for the planet to orbit the Sun is proportional to the radius of its orbit. (Johannes Kepler: The Law of Planetary Motion n.d.). However, the accurate measurements on the orbits of the planets showed that they do not precisely follow Kepler's laws. The validity of the Kepler's law is corrected by Newton. The mass of the Sun is extremely greater than any other planet. Thus, the force of attraction between planets will be small compared to the force due to the Sun (Sir Isaac Newton: The Universal Law of gravitation n.d.).

### 2.2 The law of universal gravitation

Law of universal gravitation states that every particle in the universe attracts each another with a force that is proportional to the product of their masses and inversely proportional to the distance apart squared. This force exerts along the line of centers joining the two particles. The magnitude of the gravitational force can be calculated using the formula:

**F**_{g}**= GMm F**** _{g}** is the magnitude of the gravitational force

**r² G** is universal gravitational constant

**M** and **m** are the masses of the two particles.

**r** is the distance between the two particles.

The universal gravitational force is also named universal constant as it is expected to be constant at any times and places. Therefore, it is universally characterized the intrinsic strength of gravitational force (Sir Isaac Newton: The Universal Law of gravitation n.d.). The gravitational constant is very small since we are unaware of the existence of the force of attraction between objects. The accepted value is G = 6.67 x 10^{-11} Nm²/kg^{2}. Based on the equation, the greater the distance between two masses, the smaller the gravitational force (Universal gravitation and weight n.d).

### 3.0 Gravitational fields

Gravitational field is defined as the gravitational force felt by a discrete particle in a particular area (Fowler 2006).

### 3.1 Field strength

Gravitational field strength is defined as force, **N** per unit mass, **kg**. The definition of gravitational field strength is derived from the Newton's second law, **ΣF=ma**. By making acceleration, **a**, as a subject and then substitute acceleration, **a** with gravitational field strength, **g**, and we would obtain a formula, **g = F/m**. **F** represents the gravitational force, **N** whereby **m** represents the mass of an object, **kg**. Gravitational field strength close to the earth's surface is the same as the gravitational acceleration, 9.8Nkg^{-1}. When the force is not given, gravitational field strength can be calculated by using the formula, **g = GM/r²**. This formula can be obtained by the substitution of the two equation, **F = mg** and **F = GMm/r²**. Hence, resulted in the formation of the equation, **g = GM/r²**. The greater the value of **g**, the greater the gravitational field strength (Universal Gravitation and Weight n.d.).

### 3.2 Principle of superposition

In terms of gravitation, principle of superposition refers to the total force of an object. Total force is the addition of all the vectors due to the gravitational fields of force acting on the object (Fowler, 2006). Superposition refers to the masses which interact with each other. To find the total force, we have to find the gravitational force for each mass by using the formula, F_{g} = GMm/r². Finally, add up all the forces by using vector addition method (Forces and Fields n.d.).

### 4.0 Future of Gravitation

Einstein theorized that gravity can be explained by the curvature of space time. Space time is warped by the mass and energy inside of it but not flat. Objects travel in straight line do not hold by mysterious force but follow the curves in space time. The objects move in straight lines along four-dimensional space time but move in elliptical circles in three-dimensional space. Light appears to travel in straight lines although it is actually bent, curved and changed by the fabric of space time. Although it looks like straight out in front of us, it is actually around the corner of the sun because the space time warp morphs the light. We see only the result of the light that is being bent around the sun. This can not be tested since the sun is shining us right in the eyes and we cannot see the stars. However, it is possible to test out this theory during a total solar eclipse. We are constantly orbiting the sun so we are able to observe the changes of the movement of the star in orbit (Space Time: The Fabric of the Universe n.d.).

### 5.0 Conclusion

In conclusion, based on the acceptable Newton's gravitational law of gravitation, gravitation is a mutual force. Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, gravitational force is depends on the masses of the bodies and the distance between the two bodies.

### Reference List

*Forces and Fields* n.d., viewed 29 July 2009, http://electron9.phys.utk.edu/phys136d/modules/m4/efield.htm

Fowler, M 2006*, Gravitational Field*, viewed 29 July 2009, http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm

*Gravitation and Gravity* n.d., viewed 29 July 2009, http://alex.edfac.usyd.edu.au/Methods/Science/studentwork/MassoftheEarth/gravitationandgravity.htm

*Johannes Kepler: The Laws of Planetary Motion* n.d., viewed 29 July 2009, http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

*Newton's Law of Gravitation* n.d., viewed 29 July 2009, http://theory.uwinnipeg.ca/physics/circ/node7.html

*Sir Isaac Newton: The Universal Law of Gravitation* n.d., viewed 6 June 2009, http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

*Space Time: The Fabric of the Universe* n.d., viewed 29 July 2009, http://www.astronomy.pomona.edu/Projects/moderncosmo/alex's%20page%201.html

*Universal Gravitation and Weight* n.d., viewed 29 July 2009, http://dev.physicslab.org/Document.aspx?doctype=3&filename=UniversalGravitation_UniversalGravitationWeight.xml

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