Everything, or every law, was made with an accusation. Similarly, Newton asked himself why everything was falling on the ground with the same acceleration, and he spent years until he found the reason and named it gravity. You may think when was gravity discovered? In 1687, Isaac Newton published a text called "Philosophiae Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), where he presented his three laws of motion and his law of universal gravitation, thus providing a mathematical explanation for Kepler's laws.
What is the law of universal gravitation?
Newton's law of universal gravitation "Every particle attracts every other particle with force inversely proportional to the square of any distance between them and directly proportional to the product of their masses." In fact, now, when you are reading, you are in the force of gravity. Newton explained this gravity as F = Gm1m2/r 2; here, gravitational force 'F' is always attractive, So now we are going to explain this formula briefly
Significance of Mass
Now, we are going to explore how Newton derived the formula. Newton said that force is dependent on Mass, and F is directly proportional to Mass. Let's suppose that two objects, A and B, both have different masses, so according to Newton's law of gravitation, the force should act according to their Mass; if the Mass of A will become two times, then the force will be two times as strong as it is on object b because of this the acceleration due to gravity to all objects will remain same. This is why an apple and a watermelon fall at the same acceleration. Newton proved this phenomenon and used it in his formula of gravitation. Newton also concluded that it is not only the Mass of A or B that is in the effect of gravity; these both also affect the Mass of Earth, amazingly because of the reason that comparatively Earth's Mass is too much higher than these objects; Mass of these is negligible. In the same way, this law implies the universe.
How distance effect Gravitation
Now we know what is the significance of Mass (m1 m2) in the equation, but still, there is something on which gravity depends, and that is distance denoted by r2. Let's suppose you are blowing a candle now; the farther you are, the less chance that candle could blow. And the nearer you are, the higher the chance that candle could blow; why is this happening? The reason is simple candle flame will blow or not is directly dependent on air pressure, and the pressure of air is higher at less distance and vice-versa. In the same manner force of gravity works: at a short distance; force is more elevated, and at a long distance, force is less; with this, Newton concluded that F is inversely proportional to the distance (r2) between the two masses. We had covered the essential part of the formula, but Newton had to put a constant denoted with G to remove the sign of proportion.
What is the formula of the Gravitational constant?
The gravitational force between two masses is inversely proportional to the square of any distance between them and directly proportional to the product of their masses. The strength of this force is independent of whether or not they are isolated from other masses. The gravitational constant G is a physical constant that appears in both Newton's law of universal gravitation and the Einstein field equation (i.e., general relativity). The value of G is 6.674×10-11m3kg-1s-2.
Dimension formula of the Gravitational Constant?
Where F is the magnitude of the force (N), m1 and m2 are the two masses (kg), G is a constant called Newton's constant (N·m2/kg2), and r is the distance between them (m). So the dimension of the constant is: G is (N·m2/kg2)
= dimension of N - [M1L1T-2]
= dimension of m2 - [L2]
= dimension of kg2 - [M2]
dimension of G =Fr2/m1m2
= [MLT-2] * [L2] * [M-2]
= [ M-1L3T-2]
The gravitational potential energy associated with this force changes by an amount equal to twice this negative change in potential energy when they are separated by x meters:
What is the Gravitational field?
The gravitational field is a mathematical description of the gravitational force on a particle from other particles. It consists of a scalar field and a vector field, where the vector field represents the gravitational force between two particles, such as two electrons or two protons, whereas the scalar field represents mass density.
The gravitational constant is one of the most important constants in physics, and its value can be used to describe the gravitational force between two objects. Directly measuring this value with high precision is crucial for understanding many phenomena on Earth and throughout space. Now we know how gravity is dependent on Mass and distance and how every particle is in the effect of gravity you can see this in the figure given below. Today we have covered What is the law of universal gravitation, What is Gravitational Formula, When was gravity discovered, and how mass and distance affect gravity & Gravitational Field.
If you want deeper about these so that you may read "The Ascent of Gravity". And if you want me to cover your favourite topic, please give me your suggestions in the comment section and support us.