Gravitational Force Formula, Definition, Equation with Examples

Gravitational Force: Newton’s universal gravitation law describes gravity’s force. This law states that every massive particle in the universe attracts every other massive particle with some additional force; it is ad directly proportional to the product of its masses. It is inversely proportional to the square of the distance between them. This simple, physical law is derived from observations made by induction.

For Gravitational Force, gravity is all around us. It determines how much and how far our weight travels when the basketball is thrown before returning to the surface. The force of gravity on the Earth is equal to the force the Earth exerts on you. At rest, near the Earth’s surface, the force of gravity is equal to your weight. On another celestial body, such as Venus or the Moon, the acceleration of gravity is different than on Earth, so if you stand on a scale, it tells you that you weigh differently than on Earth.

Gravitational Force

When two objects are locked in, their gravitational force is concentrated at the system’s barycenter rather than at the center of either object. The formula is similar to a see-saw. If two people are very different weights sit opposite the balance point, the heavier person should sit closer to the balance point so they balance each other’s masses. For example, if a heavy man weighs twice as much, he should sit only half as far from the fulcrum, and the balance point is the center of mass of the see-saw, and the barycenter is the balance point of the Earth-Moon system. This point moves around the Sun in Earth’s orbit, while the Earth and Moon each move around the barycenter in their orbits.

Gravitational Force Formula

Newton proposed the theory of universal gravitation in the late 1600s, which he derived through inductive reasoning. This means that some empirical evidence supports his theory, and mathematical formalism supports his arguments. As he did, many of Newton’s contemporaries worked to understand the nature of the laws that govern the fundamental nature of how things fall toward Earth. The basic concept here is that mass is attracted to Earth.

A conceptual move is to extend this idea to the idea that the Earth is attracted to the Sun. The other significant contribution to the development of the nature of gravity was the understanding that the distance objects fall toward Earth is proportional to the time they fall. However, Newton could not verify his hypothesis with the equipment and data.

Universal Law of Gravitation by Newton

Newton’s concept of universal gravitation was not confirmed until experiments conducted by British scientist Henry Cavendish confirmed the basic properties of the principle of universal gravitation. With Cavendish’s torsion balance experiment, he determined a numerical value for the proportionality constant G and verified the fundamental nature of the inverse square law.

Gravitational Force Equation

Newton’s Universal Law of Gravitation equation is stated as follows and tells us how to calculate the force of gravity:                

The unit of gravitational force is the newton (N), the same unit for all forces. 1 N = 1 Kg * m/s2 (N) in SI units. Looking at the right-hand side of the above equation, both masses are in units of Kg and distance is measured in m. Adding the units of those terms, we get Kg2/m2. Therefore, G must have m3 /(kg*s2) units to give the correct energy units (as indicated in the accepted value for G listed above) on the right-hand side.

Note that r is squared and is in the denominator. Therefore, the force is inversely proportional to the square of the distance between the two masses, so it can be considered an inverse square law. Many inverse square laws describe phenomena in many natural philosophical disciplines, such as Coulomb’s law in electrostatics, so it is good to be familiar with the terminology and its geometric implications. Similarly, it is clear from the numerator of the above equation that the force (F) between 2 masses is directly proportional to the product of the masses.

Gravitational Force Examples

Let’s see how the above ratios play out with some simple sample calculations, then look at Cavendish’s approach and do some more realistic calculations. Since G is a constant of proportionality, we leave it out of the equation for now. As our first example, we consider two masses, one of which is twice as large as the other. Thus, if we separate two masses by a distance of M = 2m and 1 m, we can say that the force of attraction b/n the masses is proportional to

What if we were to double M? Then our proportionality would look like this:

Note that by doubling one of the masses in the law of gravity, the force increases by the same amount. So, the law of gravitation is proportional to the product of mass. Now, let’s go back to the original masses, but double the distance between them.

Note that by doubling the distance, the force (F) decreases by 4. Therefore, the law of gravitation is inversely proportional to the square of the distance between the masses.

We use Newton’s Universal Law of Gravitation and the power law for circular motion to calculate the mass of the Sun. We assume that we already know the mass of the Earth, the distance between the Sun and the Earth, and the value of G.

Conclusion

In physics, gravity is the pulling of two masses together. Every single particle of matter in the whole universe has a gravitational pull on every other particle. The terms gravity and gravity are often used interchangeably for the attraction between something with force or mass.