Gravitational Force
There are various forces at work in the universe, as well as numerous pushes and pulls.
Furthermore, even though it is just in the dirt, we are still dragging or pressing something. In physics, however, there are four basic forces from which all other forces are extracted. The weak force, positive force, gravity force, and electromagnetic force are all among these forces. In addition, this gravitational force attracts because it always tries to pull masses of an object together and it never pushes them apart. Furthermore, Newton's Universal Law of Gravitation states that any object, including you, pulls every other object in the universe.
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According to Newton's law of universal gravitation, every particle in the universe attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their masses. The gravitational theory is a publication that was dubbed the "first great convergence" because it brought together previously established gravity phenomena on Earth with known astronomical activities.
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Gravitational Force Formula
Newton's law of gravitation is another name for the gravitational force formula. It also specifies the degree of force that exists between two objects. The gravitational force formula also contains the gravitational constant, which has the magnitude of G. The formula for gravitational constant is \[G = 6.67\times 10^{-11} N.m^{2}/Kg^{2}\]
The universal law of gravitation formula is,
\[\text{Gravitational force}\] = \[\frac{(\textrm{Gravitational constant})(\textrm{mass of object 1})(\textrm{mass of object 2})}{\textrm{(distance between the objects)}}\]
\[F_{g}\] = \[\frac{G\times m_{1}\times m_{2}}{r^{2}}\]
Where,
\[F_{g}\]= gravitational force between two objects
G = gravitational constant
\[m_{1}\] = mass of the first object in kilogram
\[m_{2}\]= mass of the second object in kilogram
\[r^{2}\]= distance between the object in meters
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Gravitational Field Strength Formula
The gravitational field g, which is defined by the gravitational force per unit mass, is generated by all objects and attracts other objects.
By dividing our above equation by mass \[m_{2}\], we can determine the power of this gravitational field of mass \[m_{1}\] on any object with mass \[m_{2}\].
The gravity formula is,
g = \[\frac{F_{g}}{m_{2}}\]
Putting the gravitational force equation in gravity equation, we get,
g = \[\frac{\frac{G\times m_{1}\times m_{2}}{r^{2}}}{m_{2}}\]
g = \[\frac{G\times m_{1}\times m_{2}}{r^{2}m_{2}}\]
g = \[\frac{G\times m_{1} }{r^{2}}\]
Hence this is a gravitational field formula for \[m_{1}\].
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Solved Examples.
Ex.1. Consider two satellites that orbit the earth passes close to each other. Also, for a moment they are 80 m apart. Furthermore, the masses of the satellites are 30 kg and 20 kg. Calculate the magnitude of the gravitational force between these two satellites?
Answer:
Given,
Mass of first object, \[m_{1}\]= 30 kg
Mass of second object, \[m_{2}\]= 20 kg
Distance between two objects, r = 80 m
Gravitational constant, \[G = 6.67\times 10^{-11} N.m^{2}/Kg^{2}\]
The gravitational formula is,
\[F_{g} = \frac{G\times m_{1}\times m_{2}}{r^{2}}\]
\[F_{g}= \frac{6.67 \times 10^{-11}\times 30\times 20}{(80)^{2}}\]
\[F_{g} = \frac{4002\times 10^{-11}}{6400}\]
Fg = 0.6253 \[\times 10^{-11}\] N
Ex.2. What will be the force of gravity in between two balls of mass 4 kg and 7 kg separated by 6m distance?
Answer:
Given,
Mass of first object, \[m_{1}\]= 4 kg
Mass of second object, \[m_{2}\]= 7 kg
Distance between two objects, r = 6 m
Gravitational constant, \[G = 6.67\times 10^{-11} N.m^{2}/Kg^{2}\]
The gravitational formula is,
\[F_{g} = \frac{G\times m_{1}\times m_{2}}{r^{2}}\]
\[F_{g}= \frac{6.67 \times 10^{-11}\times 4\times 7}{(6)^{2}}\]
Fg = \[\frac{186.76\times 10^{-11}}{36}\]
Fg = 5.1878 \[\times 10^{-11}\] N
FAQs on Gravitational Force Formula
1. Why the value of G is constant?
The universal gravitational constant, denoted by G and measured in Nm2/kg2, is the force of attraction between any two unit masses separated by unit size. It is a scientific physical constant used in gravitational physics. Newton's Constant is another name for it. Anywhere in the universe, the gravitational constant has the same value. Gravitational constant (G) is not the same as g, which denotes the acceleration due to gravity.
2. Who discovered gravity?
Sir Isaac Newton.
Sir Isaac Newton was an English astronomer, physicist, and mathematician who lived between 1642 and 1727.
Newton is said to have observed Gravity while considering the forces of nature after seeing a falling apple.
