The acceleration due to gravity on the surface of the Earth is maximum and it

1. Newton's Universal Law of Gravitation (basic)

Gravity is the invisible thread that binds the universe. For centuries, humans simply accepted that objects fall to the ground, but it was Isaac Newton who formalized this phenomenon as the Universal Law of Gravitation. This discovery marked a climax in the scientific revolution, moving us from mere observation to mathematical precision Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. Newton proposed that the same force pulling an apple to the ground is responsible for keeping the Moon in orbit around the Earth. He established that every object in the universe exerts an attractive force on every other object.

There are three defining characteristics of this gravitational force that you must master for basic mechanics:

• It is always attractive: Unlike magnetic or electrostatic forces, which can both attract and repel, gravity only pulls objects together Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.72.
• It is a non-contact force: It acts through empty space without needing physical contact between the two objects Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.72.
• It is measured in newtons (N): As with all forces in the International System of Units, the SI unit is the newton Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.65.

Mathematically, the law states that the force (F) is directly proportional to the product of the masses (m₁ and m₂) and inversely proportional to the square of the distance (r) between their centers. This is expressed as: F = G(m₁m₂/r²), where G is the Universal Gravitational Constant. Because of this relationship, even small changes in mass distribution — such as the loss of material in deep oceanic trenches — can lead to measurable differences in gravitational pull Physical Geography by PMF IAS, Tectonics, p.108.

Factor	Relationship with Gravity	Effect
Mass	Directly Proportional	If mass increases, gravitational pull increases.
Distance	Inversely Proportional (Square)	If distance increases, gravitational pull decreases rapidly.

Sources: Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.72; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.65; Physical Geography by PMF IAS, Tectonics, p.108

2. Mass vs. Weight: Understanding the Difference (basic)

In everyday conversation, we often use the terms mass and weight interchangeably, but in the realm of physics and for the UPSC syllabus, distinguishing between them is fundamental. Mass is the measure of the actual quantity of matter present in an object Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142. It is an intrinsic property, meaning it does not change regardless of where the object is located in the universe. If you have a mass of 60 kg on Earth, your mass remains exactly 60 kg on the Moon, in deep space, or at the Earth's core. Weight, conversely, is not an inherent property but a force. Specifically, it is the force with which a celestial body (like Earth) attracts an object towards itself Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142. Because weight is a force, its SI unit is the Newton (N), whereas the unit for mass is the kilogram (kg). We calculate weight using the formula W = mg, where 'm' is mass and 'g' is the acceleration due to gravity. Since gravity varies depending on your location—decreasing as you move to higher altitudes or deeper into the Earth—your weight will change even though your mass stays constant Science, Class VIII NCERT, Exploring Forces, p.77.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Gravitational force acting on an object.
Nature	Constant everywhere.	Variable; changes with gravity (g).
SI Unit	Kilogram (kg).	Newton (N).
Measurement	Measured using a physical/two-pan balance.	Measured using a spring balance.

It is fascinating to note that at the very center of the Earth, the gravitational pull from all directions cancels out, making the value of 'g' zero. Consequently, your weight at the center of the Earth would be zero Newtons, but your mass would remain entirely unchanged Physical Geography by PMF IAS, Earths Interior, p.58.

Sources: Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII NCERT, Exploring Forces, p.77; Physical Geography by PMF IAS, Earths Interior, p.58

3. Acceleration due to Gravity (g) on Earth (intermediate)

When we talk about acceleration due to gravity (g), we are referring to the rate at which an object speeds up as it falls freely toward the Earth. On average, this value is approximately 9.8 m/s² at the Earth's surface Physical Geography by PMF IAS, The Solar System, p.23. However, it is a mistake to think of 'g' as a universal constant; in reality, its value shifts depending on where you are located on the planet and how far you are from its center.

The first major variation occurs due to the shape of the Earth. Because our planet is an oblate spheroid (bulging at the equator and flattened at the poles), a person standing at the North or South Pole is actually closer to the Earth's center of mass than someone standing at the Equator. Consequently, gravity is greater at the poles and less at the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, The Origin and Evolution of the Earth, p.19. Additionally, the density of materials beneath your feet isn't uniform. Variations in the mass of the crustal material lead to gravity anomalies, where the measured gravity differs from the expected theoretical value, giving scientists clues about the Earth's internal structure FUNDAMENTALS OF PHYSICAL GEOGRAPHY, The Origin and Evolution of the Earth, p.19.

As you move away from the surface, the behavior of gravity follows two distinct paths:

• Going Up (Altitude): As you climb a mountain or fly in a plane, your distance from the Earth's center increases. Since the gravitational pull weakens with distance, the value of g decreases.
• Going Down (Depth): Interestingly, if you were to travel into a deep mine, gravity also decreases. This is because the mass of the Earth "above" you is no longer pulling you downward; only the mass within the sphere below your current depth counts. At the very center of the Earth, g becomes zero.

Change in Position	Effect on 'g'	Primary Reason
Moving from Equator to Pole	Increases	Decreased distance to Earth's center.
Increasing Altitude (Going Up)	Decreases	Increased distance from Earth's center.
Increasing Depth (Going Down)	Decreases	Effective mass of Earth pulling you down reduces.

Beyond physics, this force is the engine of our landscape. Without gravity, there would be no gradients, and without gradients, the movement of air (wind), water (rivers), and soil (erosion) would cease to exist FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geomorphic Processes, p.38.

Sources: Physical Geography by PMF IAS, The Solar System, p.23; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, The Origin and Evolution of the Earth, p.19; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geomorphic Processes, p.38

4. Earth's Shape and Gravity (Polar vs. Equator) (intermediate)

To understand why gravity varies across the Earth, we must first look at the Earth's actual shape. While we often imagine a perfect sphere, the Earth is technically a Geoid (or an oblate spheroid). Because the Earth rotates on its axis, a centrifugal force is generated that is strongest at the equator. Over millions of years, this force has caused the Earth to bulge outward at the center and flatten slightly at the top and bottom. Consequently, the distance from the Earth's center to the surface (the radius) is about 21 kilometers longer at the equator than at the poles Physical Geography by PMF IAS, Latitudes and Longitudes, p.241.

This difference in shape has a direct impact on the acceleration due to gravity (g). According to the laws of physics, gravitational pull is inversely proportional to the square of the distance from the center of mass. Because you are physically closer to the Earth's center when standing at the North or South Pole, the pull of gravity is strongest at the poles. Conversely, because you are further from the center when standing at the equator, gravity is weakest at the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.

Interestingly, gravity isn't perfectly uniform even at the same latitude. The local mass distribution of materials within the Earth's crust—such as dense ore deposits or lighter sedimentary basins—can cause the measured gravity to differ from the theoretically expected value. These variations are known as gravity anomalies. By studying these anomalies, geologists can map out the internal composition of the Earth's crust without having to dig deep into the ground Physical Geography by PMF IAS, Earths Interior, p.58.

Feature	At the Equator	At the Poles
Distance from Center	Greater (Equatorial Bulge)	Smaller (Flattened)
Gravitational Pull	Lower	Higher

Sources: Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Earths Interior, p.58

5. Kepler's Laws and Planetary Motion (intermediate)

To understand how the planets dance around the Sun, we must move beyond the simple idea of perfect circles. Johannes Kepler, through meticulous observation, gave us three fundamental laws that describe planetary motion. The First Law (Law of Orbits) states that every planet moves in an elliptical orbit, with the Sun situated at one of the two 'foci' (singular: focus) of the ellipse Physical Geography by PMF IAS, The Solar System, p.21. This means the distance between a planet and the Sun is constantly changing as it completes its journey. When a planet is at its closest point to the Sun, we call it perihelion (or perigee in general orbital terms), and when it is farthest, it is at aphelion (or apogee) Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257.

The Second Law (Law of Equal Areas) is perhaps the most fascinating for understanding orbital speed. It dictates that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. For this to be true, the planet cannot move at a constant speed. Instead, it must travel faster when it is closer to the Sun and slower when it is farther away. A practical consequence of this is seen in our seasons: in the Northern Hemisphere, summer occurs when Earth is near its aphelion. Because Earth moves slower at this distance, it takes about 92 days to travel from the summer solstice to the autumnal equinox, making our summers slightly longer than our winters (~89 days) Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256.

Finally, the Third Law (Law of Periods) establishes a mathematical harmony between a planet's distance from the Sun and its orbital period. It states that the square of the orbital period (T) of a planet is proportional to the cube of the semi-major axis (r) of its orbit (T² ∝ r³) Physical Geography by PMF IAS, The Solar System, p.21. Essentially, the further a planet is from the Sun, the significantly longer its 'year' becomes. This isn't just because the path is longer, but because the Sun's gravitational 'grip' is weaker, requiring a slower orbital velocity to maintain a stable path.

Sources: Physical Geography by PMF IAS, The Solar System, p.21; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256-257

6. Escape Velocity and Orbital Mechanics (exam-level)

To understand how we send satellites into space, we must first master the tug-of-war between gravity and velocity. Imagine throwing a ball upward; gravity eventually pulls it back. Escape Velocity is the theoretical minimum speed an object must reach to break free from a planet's gravitational pull permanently, without any further impulse. For Earth, this speed is approximately 11.2 km/s. To put that in perspective, while P-waves from earthquakes travel through the Earth's interior at speeds up to 13.5 km/s in the lower mantle, most seismic waves are much slower, ranging from 5 to 8 km/s Physical Geography by PMF IAS, Earths Interior, p.61. Only high-energy rockets can achieve the speeds necessary to allow artificial objects to leave our Solar System entirely Physical Geography by PMF IAS, The Solar System, p.39.

However, we don't always want to leave Earth; often, we want to stay nearby in a stable orbit. This requires Orbital Velocity. When a satellite is launched, it is given enough horizontal speed so that as it "falls" toward Earth due to gravity, the Earth's surface curves away beneath it at the exact same rate. This balance creates a circular or elliptical path. It is important to remember that gravity is not constant; it follows an inverse-square relationship with distance. As we move to higher altitudes, the distance from the Earth's center increases and the pull of gravity decreases Physical Geography by PMF IAS, Earths Interior, p.58. Consequently, satellites in higher orbits (like Geostationary satellites) actually require lower orbital velocities to stay in place than those in Low Earth Orbit (LEO).

In the Indian context, ISRO utilizes different launch vehicles depending on the required orbit and velocity. The Polar Satellite Launch Vehicle (PSLV) is a workhorse for placing Indian Remote Sensing (IRS) satellites into polar orbits, which are vital for monitoring natural resources INDIA PEOPLE AND ECONOMY, Transport and Communication, p.84. For heavier communication satellites like the GSAT series, which need to reach much higher Geosynchronous Transfer Orbits, the more powerful GSLV (Geosynchronous Satellite Launch Vehicle) is employed, often utilizing advanced cryogenic stages to achieve the necessary thrust Geography of India, Transport, Communications and Trade, p.58.

Concept	Definition	Outcome
Orbital Velocity	Speed needed to maintain a stable path around a body.	Satellite stays in orbit (e.g., PSLV launches).
Escape Velocity	Speed needed to overcome gravitational binding energy.	Object leaves the planet's influence (e.g., Voyager probes).

Sources: Physical Geography by PMF IAS, Earths Interior, p.61; Physical Geography by PMF IAS, The Solar System, p.39; Physical Geography by PMF IAS, Earths Interior, p.58; INDIA PEOPLE AND ECONOMY, Transport and Communication, p.84; Geography of India, Transport, Communications and Trade, p.58

7. Variation of 'g' with Altitude (intermediate)

To understand why the acceleration due to gravity (g) changes with altitude, we must go back to first principles. According to Newton's Law of Universal Gravitation, the force of gravity depends on the distance between the centers of two masses. At the Earth's surface, this distance is approximately the Earth's radius (R). However, as you climb a mountain or fly in an airplane, you are increasing your distance from the Earth's center. Because gravity follows an inverse-square relationship, even a small increase in distance results in a decrease in the gravitational pull.

Mathematically, the value of g at a height h above the surface is given by the formula: gₕ = GM / (R + h)². Since the denominator (the distance) is getting larger, the resulting value of gₕ must get smaller. For relatively small altitudes (like those within our atmosphere), this can be simplified to the approximation gₕ ≈ g(1 - 2h/R). This confirms that for every meter you move upward, the acceleration due to gravity drops slightly. This physical principle is a primary reason why g is considered maximum at the Earth's surface and diminishes as we move into outer space Physical Geography by PMF IAS, Earth's Interior, p.58.

It is interesting to note how this interacts with our environment. We often associate high altitudes with lower atmospheric pressure and thinner air Exploring Society: India and Beyond - Social Science Class VII, Climates of India, p.50. While the drop in air pressure is due to the weight of the air columns above you, the underlying gravitational pull is also weakening. While the change in g at the top of Mt. Everest is only about 0.28% less than at sea level, in precision physics and satellite mechanics, this variation is critical for accurate calculations.

Sources: Physical Geography by PMF IAS, Earth's Interior, p.58; Exploring Society: India and Beyond - Social Science Class VII, Climates of India, p.50

8. Variation of 'g' with Depth (exam-level)

To understand the variation of 'g' with depth, we must first recognize that the Earth's gravitational pull is not a constant value everywhere. While we often use 9.8 m/s² for calculations, the actual value of acceleration due to gravity (g) reaches its maximum at the Earth's surface and decreases whether you go up into the atmosphere or down into a mine. This might seem counter-intuitive—usually, getting closer to the center of a mass increases gravity—but depth introduces a unique physical phenomenon.

When you descend to a depth 'd' below the surface, the mass of the Earth that is "above" you (the outer shell) no longer exerts a net downward gravitational force on you; its pull cancels out in all directions. Consequently, only the inner sphere of the Earth (the part below your current depth) contributes to the gravitational pull. As you go deeper, the mass of this effective inner sphere shrinks significantly. Mathematically, this is expressed as g' = g(1 - d/R), where R is the radius of the Earth. This indicates a linear decrease in gravity as depth increases. Ultimately, at the very center of the Earth (where d = R), the value of 'g' becomes zero because you are being pulled equally in every direction by the surrounding mass.

In the real world, this transition isn't perfectly smooth because the Earth's interior is not uniform. Differences in the density of materials (like heavy ores or lighter crustal rocks) cause slight variations known as gravity anomalies. These anomalies are crucial for geologists as they provide clues about the distribution of mass within the Earth's crust FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Chapter 2, p.19. Scientists use these readings to map the Earth's interior and identify different layers or resource deposits Physical Geography by PMF IAS, Earths Interior, p.58.

Location	Value of 'g'	Reasoning
Surface	Maximum (~9.8 m/s²)	Full mass of Earth pulls from a distance 'R'.
Altitude (Height)	Decreases	Distance from center increases (Inverse-square law).
Depth	Decreases	Effective mass pulling you down decreases.
Center of Earth	Zero	Net gravitational force cancels out.

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Chapter 2: The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Manjunath Thamminidi, Chapter 4: Earths Interior, p.58

9. Solving the Original PYQ (exam-level)

Great job mastering the fundamental principles of gravity! This question effectively tests your ability to synthesize the inverse-square law with the concept of effective mass. You have learned that Earth's gravitational pull is a result of its total mass acting from its center. At the surface, you are at the optimal point where you are closest to the entirety of Earth's mass. This question asks you to predict the behavior of acceleration due to gravity (g) when you move away from this specific equilibrium point, either toward the sky or toward the core.

Let’s walk through the logic like we’re in the exam hall. When you move upward (altitude), the distance from the Earth's center increases; since gravity follows an inverse-square relationship, the pull must decrease. When you move downward (depth), you are indeed closer to the center, but as noted in Physical Geography by PMF IAS, the mass of the Earth 'above' you no longer contributes to pulling you down. This reduction in effective mass causes the value of g to decrease linearly until it reaches zero at the center. Therefore, the correct reasoning leads us to (B) decreases as we go up or down.

UPSC designed the other options to catch students who only remember half of the rule. Option (A) and (C) are common traps that suggest gravity might increase in one direction—often exploiting the misconception that 'getting closer to the core' always increases pull. However, as FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT) explains, the mass distribution is key. Option (D) is a distractor for those who might confuse the local acceleration (g) with the Universal Gravitational Constant (G), which remains the same everywhere. By remembering that g is at its peak at the surface, you can easily dismiss any option suggesting an increase from that point.