# Applications of the Newton’s Law of Gravitation

Gravity Isn’t Just a Name, the Moon, the Apple, and the Inverse Square Law. Isaac Newton compared the moon’s acceleration to the acceleration of objects on Earth. Newton was able to draw an important conclusion about the dependence of gravity on distance by believing that gravitational forces were responsible for each. This comparison led him to the conclusion that the gravitational attraction between the Earth and other objects is inversely proportional to the distance between the center of Earth and the center of the object. However, distance is not the only variable that influences the magnitude of a gravitational force. In this article, we will have a deep look on the Newton’s law of gravitation and its applications.

## History of Law of Universal Gravitation

Sir Isaac Newton was the first scientist to express the concept of gravitational force explicitly, and his writings detailed how gravitational attraction affects both falling objects and celestial body motions. Newton, on the other hand, relied on the observations and theories of other mathematicians and physicists such as Max Kepler, Robert Hooke, Edmund Halley, and Christopher Wren. The English physicist Henry Cavendish articulated the concept of the gravitational constant G more than 100 years after Newton published his work. Cavendish’s work, among other things, helped establish an accurate value for Earth’s total mass. (When using Newton’s equation to calculate the gravitational effects of the Earth on an earthbound object, M represents the mass of the Earth and m represents the mass of the earthbound object.)

## Newton’s law of gravitation

Consider Newton’s well-known equation.

**F = m a**

This is also known as Newton’s second law of motion. Newton recognized that the force causing the apple’s acceleration (gravity) had to be proportional to the apple’s mass. And, because the force that causes the apple’s downward acceleration also causes the earth’s upward acceleration (Newton’s third law), that force must be proportional to the earth’s mass. According to Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of Earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance between the earth’s and the object’s centers.

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However, Newton’s law of gravitation extends gravity beyond Earth. The universality of gravity is addressed by Newton’s law of universal gravitation. Newton’s induction into the Gravity Hall of Fame is due to his discovery that gravitation is universal, not his discovery of gravity. All objects have a gravitational attraction to one another. Gravity is a universal force. This gravitational attraction force is directly proportional to the masses of both objects and inversely proportional to the square of the distance between their centers. Newton’s conclusion about the magnitude of gravitational forces is symbolically expressed as

**F = (G m _{1} m_{2}) / r^{2}**

Here G is gravitational constant, m_{1} and m_{2} are the masses of the two objects considered and r is the distance between the centers of those objects. Because gravitational force is directly proportional to the mass of both interacting objects, larger objects will attract each other with greater gravitational force. As a result, as the mass of either object increases, so does the force of gravitational attraction between them. If one of the objects’ mass is doubled, the force of gravity between them is also doubled. If one of the objects’ mass is tripled, so is the force of gravity between them. If the mass of both objects is doubled, the gravitational force between them is quadrupled, and so on.

Because gravitational force is inversely proportional to the square of the separation distance between two interacting objects, the greater the separation distance, the weaker the gravitational force. As two objects are separated from one another, the gravitational attraction between them weakens. When the separation distance between two objects is doubled (increased by a factor of 2), the gravitational attraction force is reduced by a factor of four (2 raised to the second power).

When NASA launches rockets into space, they must contend with much more than astronaut training, fuel loads, and a mission objective. Astrophysicists who plan space travel must also deal with fundamental physical laws. The most important of these is Sir Isaac Newton’s law of gravitation.

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According to Newton’s law of universal gravitation, two bodies in space pull on each other with a force proportional to their masses and the distance between them. This means that large objects orbiting each other, such as the moon and Earth, exert noticeable force on one another. Although it appears that the moon is orbiting a relatively stationary Earth, the moon and Earth are actually rotating around a third point between them. The barycenter is the name given to this point. Newton’s law states that every object in the universe attracts every other object with a measurable force (however slight).

## Applications of the Newton’s Law of Gravitation

The universal gravitational law applies to many topics in modern science. Among these topics are:

- Tides (due to the gravitational pull of the moon on Earth)
- Interaction of two earthbound objects
- It explains the gravitational force acting between two bodies.
- It describes the phenomenon of heavenly body revolution.
- The interaction of one earthbound object with the Earth herself
- Astrophysics is the study of how celestial bodies exert force on one another and on much smaller objects like spacecraft.
- It determines the downward force on the earth’s surface.

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Because the mass of a spaceship relative to Earth is so small, the ship does not exert much force on Earth when orbiting or leaving Earth. The primary implication for spaceflight is that as the distance between the spaceships and Earth increases, so does the force of gravity on the spaceship. In fact, as the force is divided by the distance squared, it decreases rapidly.