Question

What is the importance of the universal law of gravitation?

Answer 1

Hint: Try to form an equation for the gravitational force, then infer its dependency on different parameters.

Formulae used: Essentially, the formula for the gravitational force between two objects is used. The formula is,

$F=G\dfrac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$

Complete step-by-step answer:
The universal law of gravitation or Newton's law of gravitation states that any object of mass in the universe attracts any other with a force varying directly as the product of the masses of the objects and inversely as the square of the distance between them.

The important observations deduced from the law are as follows:

1. The gravitational force or gravity between two masses becomes stronger with increasing the mass of an object.
2. Similarly, if the masses of the two objects are fixed, the gravity between them weakens if they are further distanced, as the distance between them increases.

- This law has been successful in explaining many phenomena especially concerning celestial bodies such as:
Revolution of planets and moons around the sun and the planets respectively.
Existence of gravity, an attractive force, on Earth.
Origination of tidal waves.

And many more…

Additional Information:
Now, we will try to write an equation from the above statement. The law shows that the gravitational force only depends on the masses of the objects and the distance between them. So, let the mass of the first object be ${{m}_{1}}$ , mass of the second object be ${{m}_{2}}$ and the distance between them be $d$ .

Now, according to the first sentence of the law, the gravitational force, let us take $F$ , is proportional to the product of the mass of the objects. Therefore, in mathematical terms it can be written as

$F\propto {{m}_{1}}{{m}_{2}}$

Second line states that the force is inversely proportional to the square of the distance between the two objects. Which gives,

$F\propto \dfrac{1}{{{d}^{2}}}$

Combining the two proportionalities, we get

$F\propto \dfrac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$

When the experiments were performed to verify this law, it was found that to get the accurate value of the gravitational force, a proportionality constant had to be multiplied. The constant was then named the Gravitational constant $G$ . Its value is

$G=6.673\times {{10}^{-11}}N{{m}^{2}}k{{g}^{-2}}$

Therefore, the final equation for gravitational force is

$F=G\dfrac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$

Note: The law assumes the objects to be point sized. When considering celestial objects, since the distances are very large and the masses are huge, the bodies are approximated as point sized. All the theories proposed for the celestial bodies are some assumed approximations.