Acceleration Due to Gravity: Principle, Measurement, Applications

Table of Contents

Introduction to Acceleration Due to Gravity

We have studied that every object falls down to earth when thrown upward. This is certainly because of gravity. These objects also fall at a definite rate. This falling of an object under the influence of gravity is known as free fall and the rate at which the object experiences the free fall is known as acceleration due to gravity. It is widely known as ‘g’ having the SI unit m/s². This value acceleration is constant within a limited boundary but varies for different regions accordingly.

The massive objects have greater gravitational pull and the objects tend to fall in their periphery at greater rate compared to smaller objects. Thus, the concept of this acceleration must be understood for every practical implication. In physics, it is an important value to crack classical mechanics. In various topics of engineering and structural designs also this value has a great significance.

Understanding the Concept of Gravitational Acceleration

The falling of an object is fixed and directed to a certain point. The falling object is pointed towards the earth and always attracted towards the center of the earth. In case of vacuum, all the objects of any mass fall at the same rate.

Gravity is a force that pulls an object while gravitational acceleration is the rate at which the object comes towards the object pulling it. We can say, this acceleration is the cause of gravity. If we disregard air resistance, every object whatever is its mass feels the same acceleration when dropped from a certain height. This principle was first illustrated by Galileo by dropping two different spheres from the Leaning Tower of Pisa. The two spheres reach the ground at the same time.

The Standard Value of g: 9.8 m/s² Explained

The standard value of the acceleration due to gravity on the surface of Earth is approximately 9.8 m/s². This means that when an object is falling, it experiences a free fall whose rate of change in velocity every second is 9.8 m/s. This value is not a randomly chosen value but derived from experimental observations and calculations including the mass and radius of Earth. The accurate value obtained after calculation is 9.80665 m/s² that is rounded off and approximated to 9.8 m/s². It meets the international standard and is accepted globally.

A feather and coin experiment in a vacuum tube also demonstrates the rate of falling objects which is unaffected by their mass in the absence of air resistance. We also got an answer to the question of a ball falling from a height with constant increase in its velocity. However, certain factors like latitude and altitude of earth may slightly affect the value of ‘g’.

Calculating Gravitational Acceleration Using Newton’s Law

Calculation of acceleration due to gravity depends upon Newton’s Universal Law of Gravitation. According to this law, the gravitational force between two objects is given by,

F=Gm₁m₂/r² [Equation 1]

Where:

F is the gravitational force between two masses
G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
m₁ and m₂ are the masses of the two objects
r is the distance between the centers of the two masses

If one object in equation [1] is the earth and another is a small object having tiny mass as compared to earth, then the mass of that tiny object can be neglected, which gives the acceleration due to gravity.

Mathematically,

g = GM/R² [Equation 2]

Where:

M is the mass of the Earth ≈ 5.972 × 10²⁴ kg
R is the radius of the Earth ≈ 6.371 × 10⁶ m

Substituting these values in equation [2] we get,

g = 6.674×10⁻¹¹× 5.972×10²⁴/ (6.371×10⁶)²

≈9.8m/s²

Factors Influencing Variations in g

We can see from equation [2] that the larger distance of the object can affect the value of ‘g’ as they are inversely proportional to each other. Therefore some of the factors affecting the acceleration due to gravity on earth may be the altitude, latitude, local geological formations or earth’s shape and its rotation.
A small variation in ‘g’ occurs due to these reasons. The variations can be ignored while viewing the rate of fall in ordinary cases while these variations must be counted in many physical and engineering calculations.

Altitude and Its Effect on g

When a person moves to higher regions from the earth’s surface, the distance between the surface and the person increases. Since, the distance and acceleration due to gravity are inversely related; ‘g’ may decrease slightly. Similar case applies when an object is inside an aircraft.

‘g’ is measured on earth from the sea level which is 9.8 m/s². If an object raises 5 km above the sea level, g decreases by approximately 0.01 m/s². In contrast, the value of ‘g’ slightly increases on going to the depth of earth.

Latitude and Earth’s Rotation Impact

The Earth’s shape is an oblate spheroid. It slightly flattened at the poles and bulged at the equator. Thus the poles are at a shorter distance than the equator.

Also, the rotation of earth gives rise to a centrifugal force which is maximum at the equator and zero at the poles. This force slightly decreases the value of g at the equator. Observations have obtained the value of g at poles to be approximately 9.83 m/s^2 and that at equator is 9.78 m/s^2.
Thus, the effect of gravity is slightly greater at the poles than at the equator.

Gravitational Acceleration on Other Celestial Bodies

The acceleration due to gravity differs according to mass and size of that object. Therefore, its value can’t be a constant value throughout the space. Some of the celestial bodies and their value of ‘g’ are tabulated below.

	Celestial Body	g (m/s²)
	Earth	9.8
	Moon	1.62
	Mars	3.71
	Jupiter	24.79
	Venus	8.87
	Mercury	3.7

From the above table we can see that the Moon’s gravity is about one-sixth of Earth’s because of which an object appears to be floating on the moon’s surface. Jupiter is the largest and heaviest planet thus has a strong value of gravitational acceleration.

These values must be noted before launching any missions in space.

Experimental Methods for Measuring g

Over the years, scientists have developed various methods to measure the acceleration due to gravity. Some of the most notable include:

Pendulum Method

The time period determination of a simple pendulum relies on the length of the pendulum (L) and the value of ‘g’ i.e.

T=2π√L/g

Therefore for a known value of L and T, we can find the value of g.

Free-Fall Method

As a simple experiment one can drop a ball from a certain height (h) and record the time of fall using a stopwatch. Using the equation, g = 2h/t², we can calculate the value of g.

Drop Tower and Laser Interferometry

In modern laboratories, scientists use highly advanced laser systems that give precise measurement to record the rate of free fall of objects in vacuum. This gives an accurate measurement of g.

Gravimeters

Gravimeters are specially designed instruments to measure gravitational force. They are very sensitive which detect very small changes in the acceleration. They are used in geological surveys and mineral exploration.

Applications of Gravitational Acceleration in Science and Engineering

Gravitational acceleration plays a foundational role in various scientific and engineering fields:

Aerospace Engineering: With the help of g engineers determine the escape velocity required to launch a satellite and to calculate their orbital parameters. Hence, they are able to propel rockets or launch any spacecraft outside earth.
GPS Technology: Highly precise time signals are required for GPS to provide the information about locations. To maintain the accuracy of data, time dilation factor due to the effect of gravity must be included. Thus, the calculation of g is very important for GPS technology.
Geophysics: In geophysics, g is used to check the earth vibration during earthquakes and its effect on objects. It is also used in weather forecasting, to provide accurate weather signal data, temperature data and climate change information.
Physics Education: It is a basic concept of a class to determine parameters like force, mass, distance etc. using g.

Medical Sciences: Medical science also studies gravitational acceleration to lower the effect of microgravity on a human body. This is important for an astronaut in an outer-space mission.
Scientific Research: The Hubble Space Telescope, which is in low Earth orbit, implies consistency in its orbital path to study distant galaxies, stars, and planets with unusual detail which is free from Earth’s atmospheric disturbance.
Telecommunications: Satellites in geostationary orbit give steady communication channels because they remain fixed with respect to a specific place on Earth. This fixed position is very essential for television broadcasting, internet services, and emergency communications.

Common Misconceptions About Acceleration Due to Gravity

Gravitational acceleration is also misunderstood sometimes. If not explained clearly, confusion arises. Common misconceptions about this acceleration are as follows:

Heavier Objects Fall Faster

Yes, gravity depends on the mass of an object but it is different for regions without air resistance. In those regions like vacuum, objects fall regardless of their mass. A hair and a stone fall at the same rate in vacuum.

Gravity Is the Same Everywhere

As already mentioned, gravity is affected by altitude, latitude, depth, rotation of earth. Therefore, the acceleration varies from place to place.

Zero Gravity Means No Gravity

Microgravity doesn’t mean zero gravity but means the constant falling rate which gives the sensation of weightlessness.

The Moon Has No Gravity

The Moon also has a small gravity which is about 1/6th that of Earth. Because of the gravity of the moon, tides occur on earth.

The Significance of g in Understanding Gravity

The calculation of g is very important in the analysis of gravity at certain points. It also allows scientists to research gravitational behavior at certain regions by creating a virtual environment. Prediction of planetary motion and various missions in space is also possible by the accurate calculation of g. Einstein’s theory of general relativity looks with a different perspective and declares it as an effect but not a cause. However, relativity also requires gravitational acceleration in its mathematical measurement. The study of the effect of g also helps astronauts to live in a better way in outer space.

Conclusion

Gravitational pull is a universal factor. To study any properties regarding gravity, first we need to learn about the acceleration due to gravity. It is just a simple value, constant for a specific area, but has a profound impact in physical study. Its study is used from Galileo’s era of experiments to Einstein’s ideas of relativity and leaves its major prints in physics.

A falling ball to the moon’s revolution, all is bound by earth’s gravity. A mission on a moon or any other planet is completed on the basis of gravity. This push and pull is continuing more vigorously in some other regions where even light has no entry. Anybody is simply attracted when the gossip is about beyond earth. Thus, acceleration due to gravity is a major topic in describing gravity.

References

Irani, A. (2022). Gravity, Density, Acceleration, and the Constants of Nature. Journal of High Energy Physics, Gravitation and Cosmology, 9(1), 210-215.

Brown, B. (1969). The Acceleration Due to Gravity. In General Properties of Matter (pp. 54-81). Boston, MA: Springer US.

Cook, A. H. (1965). The absolute determination of the acceleration due to gravity. Metrologia, 1(3), 84.

Sani, H. M., Baraya, T. J., Mu’awuya, M. S., & Abdulkarim, A. (2016). Comparison of Theoretical and Measured Acceleration Due to Gravity. International Journal of Innovative Research in Science, Engineering and Technolog (IJIRSET), 5(3), 3787-3797.

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Acceleration due to Gravity