Question

State Newton’s law of universal gravitation.

Answer 1

Hint: In order to answer the above question, we will be discussing the history of Newton's Law of universal gravitation. We will look upon the history when Newton discovered this law and we will also be writing the equation defining this law.

Complete step by step solution:
First of all, we will shine some light on the history behind this law:
As we all know that the falling of an apple from a tree provided Sir Isaac Newton with the inspiration for his Law of Universal Gravitation.
While an apple may not have fallen on Sir Isaac Newton's head as history is certain, it did inspire him to make one of the most important discoveries in mechanics: the Law of Universal Gravitation. Newton discovered that the Earth must be responsible for the apple's downward motion after questioning why the apple never falls downwards, sideways, or in any other direction and it only falls in the direction perpendicular to the ground.
Newton was able to formulate a general physical law by induction after theorising that this force would be equal to the masses of the two objects concerned and using previous intuition regarding the inverse-square relationship of the force between the earth and the moon
Now, we can define the law of universal gravitation as:
According to the Law of Universal Gravitation, every point mass in the universe is attracted to every other point mass in the universe by a force pointing in a straight line between their centers-of-mass, and this force is proportional to the masses of the objects and inversely proportional to their separation. This attractive force is often drawn inward, from one point to the next.
Although Newton was able to express and experimentally validate his Law of Universal Gravitation, he was only able to measure the relative gravitational force in relation to another force. The Law of Universal Gravitation did not obtain its final algebraic form until Henry Cavendish checked the gravitational constant:
$F=G\dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}$
Where $F$ is the force, $G$ is the gravitational constant $\left( G=6.674\times {{10}^{-11}}N\dfrac{{{m}^{2}}}{k{{g}^{2}}} \right)$, ${{m}_{1}}$ and ${{m}_{2}}$ are the masses and $r$ is the separation.

Note:
 It is very important to note here that this Law extends to all objects with masses, no matter how large or small they are. If the distance between two large objects is very large in comparison to their sizes or if they are spherically symmetric, they may be regarded as point-like masses. In these cases, each object's mass can be measured by a point mass at its center of mass.