### Gravitational Force

Attraction or gravitation is a phenomenon, Gives an idea about the existence of a force between any two objects. Gravity is always attractive and a natural and vital phenomenon. There force pulls objects toward the center of a planet or other system.

When it is thrown up all objects land on the ground. Gravitational force is one of the fundamental forces that attract any two bodies with mass.

For example , Isaac Newton’s statement is a proof of this Fruits on a tree fall down. The reason for this is that all objects above are attracted by the earth and fall down due to the force of gravity.

### Gravitational force formula

Gravitational force between two objects F_{g(kg.m/s2)} in kilogram meter per second2 is equal to the product of gravitational constant G_{(Nm2)} in Newton per meter2 and multiply the mass of first and second object m_{1(kg)} * m_{2(kg) } in kilogram and divided by square of the distance between the objects r^{2 }_{(m)} in meter.Hence the gravitational force can be written as

F_{g(kg.m/s2)} =G_{(Nm2)}* m_{1(kg)} * m_{2(kg)} /r^{2 }_{(m)}

The gravitation formula is also known as Newton’s law of gravitation. Also, it defines the magnitude of force between two objects. Also, the gravity formula includes its value as the gravitational constant=6.67 *10^{-11} N.m2/kg2.

Gravitational force=(gravitational constant)(mass of object1)(mass of object2)/(distance between objects)^{2}

F_{g} =G m_{1}* m_{2} /r^{2}

F_{g} = refers to the gravitational force between two objects (N=kg.m/s^{2})

G=refers to the gravitational constant (G=6.67*10^{-11} N.m^{2}/kg^{2})

M_{1}= refers to the mass of the first object in kilogram

M_{2}= refers to the mass of the second object also in kilogram

R=refers to the distance between the object in meters

### Gravitational Force Calculation:1

Suppose two satellites that orbit the earth passes close to each other. Also, for a moment they are 100 m apart. Furthermore, the masses of the satellites are 500 kg and 30 kg. So, calculate the magnitude of the force of gravity between these satellites?

### Answer:

F_{g} =G m_{1}* m_{2} /r^{2}

F_{g}=(6.67*10^{-11 }N.m^{2}/kg^{2})*(500kg)(30kg)/(100m^{2})

F_{g}=(6.67*10^{-11 }N.m^{2 }/kg^{2})*(15000)/10000m^{2}

F_{g}=(6.67*10^{-11} N.m^{2}/kg^{2})*(15000kg^{2}/10000 m^{2})

F_{g}=(6.67*10^{-11} N.m^{2}/kg^{2}) *(1.5000 kg^{2} /m^{2})

Fg=(6.67*10^{-11} N)*(1.500)

F_{g}≅1.0005*10^{-10}

### Example:2

Suppose two satellites that orbit the earth passes close to each other. Also, for a moment they are 200m apart. Furthermore, the masses of the satellites are 4500 kg and 800 kg. So, calculate the magnitude of the force of gravity between these satellites?

### Answer:

F_{g} =G m_{1}* m_{2} /r^{2}

F_{g}=(6.67*10^{-11 }N.m^{2}/kg^{2})*(4500kg)(800kg)/(200m^{2})

F_{g}=(6.67*10^{-11 }N.m^{2 }/kg^{2})*( 3600000)/40000m^{2}

F_{g}=(6.67*10^{-11} N.m^{2}/kg^{2})*(3600000kg^{2})/40000 m^{2})

F_{g}=(6.67*10^{-11} N.m^{2}/kg^{2}) *( 144000kg^{2} /m^{2})

Fg=(6.67*10^{-11} N)*(144000)

F_{g}≅0.96048*10^{-11}