Gravitation

Newton's Universal Law of Gravitation

The British mathematician and scientist Sir Isaac Newton was curious as to why a fruit was falling vertically rather than horizontally from a tree to the ground. He came to the conclusion—after much research and consideration—that the fruit fell into the earth's center due to the attraction between the apple and the planet. In a similar vein, he questioned how the sun, moon, stars, planets, etc. are fixed in the sky.

Following extensive research, Newton came to the conclusion that all bodies are attracted to one another. Gravitation is the term he gave this force. He proposed the Universal Law of Gravitation in 1687.

The gravitational force between two bodies is calculated and displayed. The PhET Interactiv Simulations available on the Internet were used to get these results.Open your web browser and enter https://phet. colorado.edu/sims html/gravity-force-la latest/gravity-force-lab_en.html to begin this activity on your PC within the search field. The slider in the simulation allows you to adjust the sphere's mass and distance. The table below shows the two scenarios when the mass and distance are changed. Examine and make appropriate inferences from the provided information.

(a) Doubling the mass of the first sphere initially while maintaining the same mass of the second sphere and their distance from one another; after this, doubling the mass of both spheres while maintaining their distance from one another.

(b) Doubling the distance between two spheres keeps the mass constant.

This exercise demonstrates that when the mass of one sphere and the mass of both spheres double, the gravitational force is two times and four times the initial force, respectively. In this instance, a four-fold increase in the product of two masses results in a four-fold increase in gravitational force. Put another way, as long as the distance is constant, the gravitational force is directly proportional to the product of the masses of the two objects. In a similar vein, it is demonstrated that for every two spheres' doubling distance, the gravitational force is lowered four times. Stated differently, the mass of two objects remains constant, but the gravitational force is inversely proportional to the square of their distance.

All of the results are incorporated into Newton's universal law of gravity. According to this law, the gravitational force that exists between any two objects in the universe is directly related to the product of their masses and is inversely proportionate to the square of their separation.

As shown in figure, let the masses of the objects 10 kg and 20 kg be m₁ and m₂ respectively, and the gravitational force produced between them be F. According to Newton's law of gravity, the gravitational force (F) is directly proportional to the product of the masses of these objects, m₁ and m₂,

that is,  F \(\infty\) m₁ m₂.............(i)

and inversely proprtional to the square of the distance d,

that is,  F \(\infty\) \(\frac{1}{d^{2}}\) ..............(ii)

combining (i) and (ii),

F  \(\infty\)  \(\frac{m_{1}m_{2}}{d^{2}}\)

F= G \(\frac{m_{1}m_{2}}{d^{2}}\) ..............(iii)

G, sometimes referred to as the universal gravitational constant, is the proportionality constant in this instance. The gravitational force between any two objects may be computed using equation (iii).

The gravitational constant G is the gravitational force that results from two unit masses separated by a unit distance.

Henry Cavendish used the Cavendish balance to measure the gravitational constant for the first time in 1798. G's value was determined from the experiment to be 6.67 x 10-11. Its value is constant across all materials and media between the bodies, which is why it is known as the universal gravitational constant. N m² / kg² is its SI unit.

Variation in Gravitational Force with Mass and Distance

The gravitational force formula may be used to quantitatively describe the change in gravitational force seen in the activity. Assume that A and B are two objects with corresponding masses of m1 and m2. If the gravitational force in the initial condition is F1 and the distance d between those objects is d.

then, F₁ = \(\frac{Gm_{1}m_{2}}{d^{2}}\) ................(i)

Upon When an object's mass doubles while maintaining the same distance between them, the gravitational force correspondingly rises by twice as much. In a similar vein, the gravitational force increases by a factor of 4 when the mass of both objects is doubled.

Upon When an object's mass doubles while maintaining the same distance between them, the gravitational force correspondingly rises by twice as much. In a similar vein, the gravitational force increases by a factor of 4 when the mass of both objects is doubled.

Consequences of Gravitational Force

The following list includes a few effects of gravitational forces:

• The solar system and the rest of the cosmos are conceivable because of gravity. The planets rotate around the sun due to the gravitational pull between them.
• Despite having far less mass than the Sun, the Moon is nevertheless significant since it is closer to Earth than the Sun is. Tidal effects are produced because the moon's gravitational pull is more apparent in the ocean than on land.
• Items on the surface adhere to the earth due to gravitational forces between the earth and the items. In addition, if anything is hurled vertically upward, it will return to the surface.