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# Gravitational Force

Gravitational force is explained by the Newton's universal law of gravitation. This law tells about the attractive force between two masses. This attractive force is nothing but the gravitational force. It a fundamental force in nature and also it is a non contact force. Which means that there is no contact between the two masses. The gravitational force on earth is same as that of it exerts the force on us. More concepts related to this specific topic is explained in detail in the following paragraphs. Related Calculators Gravitational Force Calculator Gravitation Calculator Calculate Gravitational Acceleration Gravitational Potential Energy Calculator

## What is Gravitational Force?

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Gravitational force is defined using the Newton's universal law of gravitation. It is defined as the attractive force between any massive objects is directly proportional to the product of the masses and inversely proportional to the the square of the distance between them. The proportionality constant is known as the gravitational constant.

## Gravitational Force Equation

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The mathematical representation of the gravitational force can be F = $\frac{Gm_{1}m_{2}}{d^{2}}$
Where F is the gravitational force
G is the gravitational constant
$m_{1}$ is the mass of the first body
$m_{2}$ is the mass of the second body
d is the distance between two masses

## Gravitational Force Units

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The SI unit of the Gravitational force is Newton and is denoted as N.

## Gravitational Force is Affected by

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From the equation, it is clear that gravitational force is affected by the masses of the bodies and the distance between these bodies. The product of the masses is directly proportional and the square of the distance is inversely proportional to the force of attraction.

## Gravitational Force on Earth

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The gravitational force on earth means that the the force of attraction between the earth and the object. So the equation becomes
F = $\frac{GMm}{r^{2}}$
Where M is the mass of the earth
m is the mass of the object on the earth
We know that, F = mg

Equating these two equations

Then g = $\frac{GM}{r^{2}}$
Substitute values of G, M and r we get g=9.81m/s2

## Net Gravitational Force

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When we consider the force between more than two objects, then the net gravitational force is the sum of the gravitational force of the each object.

That is, F = F12 + F23 + F34 +..........

## Gravitational Force on Mars

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From the above equation substitute the vales of mass of the Mars, radius and the value of G. The the value of g is given as

g = $\frac{GM}{r^{2}}$ = 3.91m/s2

## Gravitational Force on the Moon

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When we substitute the values of the mass and radius of the Moon in the above equation, the gravity is 1.6 m/s2.

## Gravitational Force of the Sun

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The sun and the earth

Sun: mass M= 1.99×1030Kg
Earth: mass n=5.97×1024 Kg
G = 6.673×10-11 Nm2/Kg2

Distance Between Sun &Earth: r = 1.5 × 1011 m

F = $\frac{GMm}{r^{2}}$

Substitute these values in the above equation we get the value of the gravitational force between earth and sun.

## Magnitude of Gravitational Force

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Magnitude of the gravitational force means that the value of the resultant force without considering any direction. Only the numerical value is considering as the magnitude.

## Newton's Law of Gravitational Force

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Newton's law of gravitation is also known as the universal law. It is given as the force of attraction between two objects is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
The equation related to this law is mentioned above.

## Work Done by Gravitational Force

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Using this equation F = $\frac{GMm}{r^{2}}$ we can calculate the work done by the gravitational force. Work done is depending up on the situation how the object is placed. According to that we can calculate the work done by the gravitational force.

## Gravitational Force vs Electric Force

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Gravitational force is the attraction between the two objects whereas the electric force is the force between two charges. Both forces are inversely proportional to the distance and directly proportional to the product of the masses in the first case product of the charges in the second case.

## Examples of Gravitational Force

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• Falling of apple from the tree
• Jumping from a height
• The movement of earth in its orbit

## Gravitational Force Problems

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Some of the problems related to the gravitational forces are given below:

### Solved Examples

Question 1: The mass of the electron and proton in a Hydrogen atom is given by 9×10-31 Kg and 1.9×10-27 Kg respectively which is separated by a distance 6×10-11m. Calculate the gravitational force of attraction between them?
Solution:

The given parameters are:
Me=9×10-31 Kg and Mp=1.9×10-27 Kg, G=6.673×10-11Nm2/Kg2, r=6×10-11m
F=$\frac{GM_{e}M_{p}}{r^{2}}$
F=$\frac{6.673\times 10^{-11}\times 9\times 10^{-31}\times 1.9\times 10^{-27}}{(6\times 10^{-11})^{2}}$
F=3.16×10-47N

Question 2: Let m1 and m2 be the masses of two bodies. Calculate the changes in the masses if the distance between them is doubled but the gravitational force remains same?

Solution:

We know that,
F=$\frac{Gm_{1}m_{2}}{r^{2}}$......................1
F'=$\frac{G(m_{1}m_{2})'}{2d^{2}}$...............2

From the question it is given that F=F'
So, $\frac{Gm_{1}m_{2}}{r^{2}}=\frac{G(m_{1}m_{2})'}{2d^{2}}$
4$m_{1}m_{2}$=$(m_{1}m_{2})'$
The product of mass is increased by a factor of 4.

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