Gravitational Force: Principle, Law, Factors, Waves, Examples

Table of Contents

Introduction to Gravitational Force

There are four universal forces in nature. Among those forces gravitational force is considered to be the weakest one but has significant effects when the topic is about large-scale structures. It exists between any two objects having a certain mass, either very small or very large. The whole universe is driven by gravitational force. The motion of planets around the sun, the motion of satellites around the planets, all are in the discipline of gravity. The concept of gravity was brought for the first time by Aristotle. However, no full evidence was found on his hypothesis. Later, deeper studies and research was carried on. Now we already have gravitational waves on our way, which were predicted by Einstein in the 19th century.

The actual credit for the discovery of gravitational force goes to Sir Isaac Newton. His theory clearly explains the nature of force and quantifies the amount of force on a body with his formula. Lately, particle physics introduces gravitons as the matter responsible for carrying gravitational force. However, because of their very weak nature, the particles are only predictions. Advanced studies are being carried out for the detection.

Newton’s Law of Universal Gravitation

According to this law, any object having a certain mass also attracts another object of some mass with a force. This force of attraction is called the gravitational force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The mathematical form of Newton’s law is:

F = G Mm/r² [Equation 1]

Where:

F is the gravitational force between two objects,
G is the gravitational constant with value 6.67 ✕ 10^-11 Nm²/kg²
M and m are the masses of the two objects,
r is the distance between the centers of the two masses.

This law has become the greatest discovery in the history of physics. Any problems related to gravity are solved by this law. Although opposed by other theories, it is applicable in the normal cases. Only in relativistic cases it has been proven wrong.

Gravitational Constant (G): Its Value and Significance

The gravitational constant appears in Newton’s law of gravitation as proportionality constant. It is denoted by G whose value is very small (6.67 ✕ 10^-11 Nm²/kg²). Looking at this small value, we can conclude that gravitational force is extremely small. Hence, it has a significant role in quantifying gravitational force, in our calculation. It allows us to measure the strength of gravity between two masses.

G was calculated for the first time by Henry Cavendish but the experiment was not specifically for G. He used a torsion balance to calculate G directly. It helped the scientists to find the density of earth. Not only in classical mechanics but it has an important application in astrophysics and cosmology. Scientists apply G in the study of motion of the planets, to study the orbits of stars and also in the predictions of compact objects.

Similarly, beyond celestial objects, it helps to calculate the amount of gravity in smaller objects. In engineering too, it is used to study the forces between objects while constructing huge structures. Gravitational constant can also be used for the precise measurement of GPS systems and modern technologies like atom interferometers. It can also help to find the potential of dark matters in future.

Factors Affecting Gravitational Force: Mass and Distance

Gravitational force primarily depends on two major aspects: Masses of two bodies and the separation between them.

Mass: From equation [1] we can see that masses of two bodies and gravitational force are directly proportional quantities. If the masses are heavier, we can see a larger effect of gravitational force while the effect is smaller if the product of their masses is a small value. Therefore, very common objects have negligible gravitational force and large scale structures have massive impacts of gravitational force.
Distance: Again recalling equation [1] we see that the force of gravitation has an inverse relation with the square of the distance between two bodies. Thus. bodies at larger distances have lesser impact of gravitation than those being closer apart. On doubling the separation, the force is reduced by factor four.

Gravitational Force Between Celestial Bodies: Earth, Moon, and Planets

As we studied, gravitational force is massively larger for celestial bodies; it controls everything in outer space. Some effects of this force in celestial bodies are given below:

Gravitational waves: The merging of galaxies leads to an event like black hole merger and neutron star merger that result in gravitational waves. These waves periodically keep expanding and compressing space-time.
Earth and Moon: The gravitational force between Earth and the Moon holds the Moon in its orbit around the Earth. This attraction is the cause of tidal effects on the oceans.
Planets and Sun: Solar system is in existence due to the massive gravitational pull of the sun.
Planetary Interactions: The interplanetary force of attraction can change the motion of planets and expel them from their orbits. The phenomena like orbital resonances and perturbations can occur due to the pull for a prolonged time period.

Gravitational Fields and Potential Energy

Gravitational field is a certain area around which one object can show its effect of gravitation to another object. Although the range of gravity is infinite, its effect can be negligible and an observer can detect no force of attraction between two objects, beyond the gravitational field. The formula for gravitational field strength is,

g = GM/r² [Equation 2]

Where

g is the gravitational field strength,
M is the mass producing that field and
R is the distance from the center of that mass.

Thus, by calculating gravitational field strength, we can find the effect of gravity on a body around the surface of another massive body.

Potential energy refers to the energy by a certain position of an object. Here, gravitational potential energy means the amount of energy contained by the object, inside the gravitational field. It is given by the formula,

U = -GMm/r

The negative sign indicates that gravitational potential energy decreases as the object approaches closer to the mass having that field.

Gravitational Force in Everyday Life: Examples and Applications

We are so much familiar with gravitation as we are experiencing it in all stuff. Each matter of a certain mass has its own gravitational strength. Some of its examples and applications are given below:

Stability of objects: The objects in space do not move randomly. A certain amount of gravitational force holds them in a manner. For example, we are able to walk on land and not hover in air, because of the gravity of earth.
Tidal forces: Tides are the periodic waves seen in ocean foe every short period of time. This is because of the gravitational force of the moon and sun on water.
Everyday activities: All the daily activities like walking, jumping, running, playing etc. are possible due to the gravitational force of earth. In a place where gravity is zero, the object keeps floating and no activities can be performed.
Revolution of massive bodies: All planets are in the proper alignment with the sun and revolve in their orbits. The gravitational pull of the sun governs the revolution of those celestial bodies.
Falling objects: If we throw anything upward, after attaining a certain height, it falls down. A fruit also falls downward after getting released from the tree because of gravity.
Gases present in sun: Sun is the source of a tremendous amount of energy. These gases stay firmly in the sun, despite being distributed continuously, due to the gravity of the sun.
Precipitation: Water evaporates from the earth, forms water vapors and falls to the earth by some method of condensation. This precipitation usually falls to earth as rainfall or snow, which is possible due to the gravity of earth.

In addition, we may say, life has become possible and easier on earth due to this gravity. On other planets, this effect could be intolerable.

Gravitational Waves: Detection and Implications

Gravitational waves are the outcomes of two compact bodies swirling and merging together due to their gravitational force of attraction. These compact bodies may be black holes or neutron stars. A gravitational wave can also occur due to a neutron star and black hole merger. These waves expand and contract anything they pass through.

Gravitational waves travel at the speed of light creating plus and cross polarized waveforms. The advanced LIGO detector located in Livingston detected the 1st gravitational wave event in 2015. LIGO jointly operates two observatories: the LIGO Livingston Observatory in Livingston, Louisiana and the LIGO Observatory in Hanford located on the site of the Hanford Department of Energy near Richland, Washington. Another detector is the VIRGO interferometer located in Pisa, Italy and designed to increase the detection sensitivity of gravitational wave signals. LIGO and VIRGO together act as an international coordinate system. The raw data from interferometers is frequently non-stationary, including narrow band noise and broadband anomalies. The presence of glitches can substantially limit the effectiveness of astrophysical searches. These glitches are removed using several methods of signal processing and filtering to obtain a chirping nature of these waves indicating a detection of an event.

Gravitational Wave Open Science Center (GWOSC) has kept all the data of events till date on its website. There are also open data workshops including python codes to help us in obtaining the image of coalescence.

Comparing Newtonian Gravity and Einstein’s General Relativity

In Newtonian mechanics, gravity is regarded as a weak force whose calculation is accurate in non-relativistic cases, where the velocities of objects are ordinary. The mass described here is also ordinary mass. It plays a significant role when the topic is within the earth. However, it fails in relativistic cases where speed is as that of light and object is massive. Another concept known as Einstein’s Theory of General Relativity comes forward to describe the behavior of massive and super speedy objects.

Newtonian Gravity: Describes gravity as a force acting between two masses kept at some distance.
General Relativity: Describes gravity as the curvature of space-time caused by mass and energy of those massive objects. Massive objects wrap the space-time around it and objects move along these curved paths known as geodesics of space time.

General Relativity is an equally successful theory in describing gravity. Its hypotheses have been tested through several methods like the bending of light by gravity (gravitational lensing), time dilation near massive bodies, and the prediction of planetary motion. All these facts prove that gravity is a phenomenon that creates motion of everything.

The Ongoing Study of Gravitational Forces

Gravitational forces are a topic of huge interest today. All theoretical physicists, quantum researchers, astrophysicists and cosmologists are captivated by the concept of gravity. They are keeping their research at different levels and collaborating with each other for future prospects. Some of the ongoing research on gravitational forces is as follows:

Quantum Gravity: Quantum mechanics is being developed as a solely new idea of physics and trying to provide a new concept of gravity known as quantum gravity. Here gravity is also hypothesized as a small packet of force.
Dark Matter and Dark Energy: We know that more than 90% of the universe is composed of unknown objects known as dark matter and dark energy. The advanced study of gravitational force will make us able to know exactly what dark matter is and where the dark energy comes from.
Cosmology: Cosmology deals with the beginning of the universe. Whole cosmology depends on gravity and general theory of relativity. Thus the study of gravitational force can reveal information about the existence of the universe.
Advanced Detection Methods: On improving the sensitivity of gravitational wave detectors, we can study about the most powerful binary merger events.

Conclusion

Gravity influences every single incident of the universe. It existed with the existence of the universe. The ripples of massive gravitational interactions during the evolutionary period are still floating today. No physics is possible without the study of gravity. Not only physics, but every instrumental design to everyday actions is also governed by gravity. Predictions made 100 years ago are being proved today on the advancements of measuring devices. Same advancements can show some early pictures of the universe and set light on how we exist. It will not be wrong to say that we can predict what will happen next and where is the ending, on continuous study of gravitational forces.

References

Padmanabhan, T. (2010). Gravitation: foundations and frontiers. Cambridge University Press.

Carroll, S. M. (2019). Spacetime and geometry. Cambridge University Press.

Gravitational Force

https://byjus.com/physics/gravitational-force-escape-velocity/

https://www.geeksforgeeks.org/physics/gravitational-force/