**What is Gravitational Force?**

The force of attraction between
any two or more objects in the universe is called the **gravitational force**. And
the process is called gravitation.

Newton gave a rule in 1887 for
the relation between the factor effect on the **gravitational force** and the
process of measuring such force, which is called Newton's universal law of
Gravitation.

According to the above rules
given by Newton, “*The gravitational force generated between any two objects in the
universe is directly proportional to the product of the mass of those objects
and is inversely proportional to the square of the distance between the centers
of those objects*.”

Gravitational force value of earth |

Before the 17th century, it was believed that the earth was at the center of the universe and the sun, moon and other planets are revolved around it. This is called geocentric theory. After then, according to heliocentric theory, the Sun is the center of the universe and all the planets and satellites revolve around it.

Soon after, Newton began researching it. According to Newton, not only does the earth attract ripe fruit or the moon, but all the objects in the universe attract each other. The process by which one massive particle attracts other massive particles is called gravitation.

For **gravitational force** examples,
the earth attracts the moon and the moon attracts the earth. The effects of
large bodies appear to have been felt in small bodies, but the effects of small
bodies appear to be relatively small in large bodies.

The Earth attracts its only one satellite, the Moon, other planets and stars. It is also called gravitationalforce of earth.

**What is Newton's universal Law
of Gravitation?**

“*The gravitational force generated
between any two objects in the universe is directly proportional to the product
of the mass of those objects and is inversely proportional to the square of the
distance between the centers of those objects.*”

law of gravitation |

Then according to **Newton's
universal Law of Gravitation**,

F µ
m_{1}xm_{2 }………………. (i) (If d is stable)

F µ
1/d^{2 }……………………. (ii) (If m1 and m2 are stable)

Writing both relationships together

F µ
(m_{1}xm_{2})/d^{2 }

or F = G(m_{1}xm_{2})/d^{2}
…………………. (iii)

The equation (ii) shows the **gravitational
force formula** where 'G' is a constant, which is also called Universal Gravitational
constant. The value of G is 6.67x10^{-11} Nm^{2}kg^{-2}.
The value of 'G' has been discovered by Henry Cavendish with the help of
sensitive balance.

**The gravitational force
formula**

F = G(m_{1}xm_{2})/d^{2}
is the **gravitational force formula**. In this formula, if we keep the values of
m1 = 1kg, m2 = 1kg and d = 1m, then F = G.

Therefore, the gravitational
force is the **Universal gravitational constant** when two objects weighing 1 kg are placed
at a distance of 1 meter.

It does not depend on mass, distance and medium (rare or denser) between bodies, so it is called universal gravitational constant.

**The gravitational force
generated between two objects differs in the following cases**

#### 1. 1. In case the distance is constant but the mass has changed

Suppose A and B are bodies, A has a mass of m1 and B has a mass of m2 and the central distance between them is d and the force of attraction is F.

According to Newton's universal Law of Gravitation

_{1}xm_{2})/d^{2} ………………….. (i)

Now keep the distance between A and B constant

And Keep the mass of B twice.

F_{1}
= G (m_{1}x2m_{2})/d^{2}

or F_{1} = 2G (m_{1}xm_{2})/d^{2}

F_{1} = 2F

Therefore, when mass of one of the two objects is doubled, their force also doubles.

#### 2. 2. In case the masses are constant but the distance has changed

Suppose A and B are bodies, A has a mass of m1 and B has a mass of m2 and the central distance between them is d and the force of attraction is F.

According to Newton's universal Law of Gravitation

F
= G (m_{1}xm_{2})/d^{2} ………………….. (i)

Now keep the masses of A and B constant

And half the distance between A and B.

F_{1}
= G (m_{1}xm_{2})/(d/2)^{2}

or F_{1} = 4G (m_{1}xm_{2})/d^{2}

F_{1} = 4F

Therefore, when the distance between two objects is halved, the gravitational force between them increases four times.

According to both conditions we
can say that the **gravitational force depends on** their mass and the distance
between the bodies.

**Gravitational force SI unit**

F = G (m_{1}xm_{2})/d^{2}

or F = Nm^{2}kg^{-2}(kg x kg)/m^{2} (SI unit of G is Nm^{2}kg^{-2},
unit of mass is kg and unit of distance M)

So that, F = N

This means the gravitational force SI unit N (N means Newton).

**Gravitational force value of
the earth for the moon**

The mass of the earth is 6x10^{24}kg,
the mass of the moon is 7.2x10^{22}kg and the distance between the
earth and the moon is 385,000.6 km.

Here, m1 = 6x10^{24}kg

m2
= 7.2x10^{22}kg

d
= 385,000.6 km = 385,000.6 x 1000m = 3.8x10^{8}m

And
the value of G is 6.67x10^{-11} Nm^{2}kg^{-2}

If we using the gravitational force formula

Then,

F = G (m_{1}xm_{2})/d^{2}

^{ }
= 6.67x10^{-11} (6x10^{24}x7.2x10^{22})/( 3.8x10^{8})^{2} (Units are not used to make calculations
easier)

= (288.114x10^{-11+24+22})/14.44x10^{16}

= (288.114x10^{35-16})/14.44

=
19.95x10^{19}N

Therefore gravitational
force between earth and moon is 19.95x10^{19}N.

**Gravitational force between
sun and earth**

The mass of the sun is 2x10^{30}kg,
the mass of the earth is 6x10^{24}kg and the distance between earth and
sun is 1.5x10^{8}km. The **gravitational force** can be extracted from the
above process using the gravitational force formula.

The Gravitational force value of
the sun for the earth is 3.56x10^{22}N

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