Every CDS Science paper carries a question or two on gravitation. The favourite traps are the difference between G and g and the way g varies with height, depth, latitude and Earth's spin. This page builds the idea from Newton's law to numerical shortcuts, so you can answer these quickly and never confuse the universal constant with acceleration due to gravity.
Why Gravity is a Sure-Shot CDS Topic
Gravitation links almost every mechanics chapter — free fall, weight, satellites, projectile motion and even tides. Because the rules are short and the numbers are clean, the UPSC examiners use this topic to test whether you truly understand a concept or have only memorised a formula.
The questions are rarely heavy calculation. Instead they ask conceptual one-liners: where is g maximum, why does a body weigh less at the equator, or what happens to weight at the centre of the Earth. If your basics are firm, these become free marks.
Historically, gravitation gives a steady share of marks in the General Knowledge paper, and the same handful of ideas reappear year after year in slightly reworded forms. Because the options are designed to tempt the unprepared, learning the reasoning behind each rule — not just the rule itself — is what separates a confident answer from a guess. The sections that follow take you from the basic law to the variation rules in a logical chain so that each fact reinforces the next.
Mass is the amount of matter in a body and never changes. Weight is the gravitational pull on that mass and changes wherever g changes. Most CDS traps exploit this single distinction.
Newton's Universal Law of Gravitation
Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
F = G × (m1 × m2) ÷ r2
Here F is the force of attraction, m1 and m2 are the masses, r is the distance between centres, and G is the universal gravitational constant.
This force always acts along the line joining the two centres and is always attractive, never repulsive. It is also a mutual pair — the Earth pulls the apple and the apple pulls the Earth with an equal and opposite force, obeying Newton's third law. The reason the apple falls and the Earth does not visibly move is the apple's tiny mass compared to the Earth.
The inverse-square nature is worth dwelling on. If you double the distance between two bodies, the force does not halve — it drops to one-quarter, because the square of two is four. Triple the distance and the force falls to one-ninth. This rapid weakening with distance explains why the Moon, though massive, exerts only a gentle pull on us, and why deep-space probes feel almost no gravity once they are far from any planet.
The Universal Constant G
The gravitational constant G was first measured experimentally by Henry Cavendish. Its value is the same everywhere in the universe, which is why it is called universal.
G = 6.674 × 10−11 N·m2/kg2
It does NOT depend on the masses, the medium between them, temperature, or location.
Because G is extremely small, gravitation is the weakest of the four fundamental forces. We only notice it when at least one body is astronomically large, like a planet or star.
Do not write the unit of G as m/s2 — that is the unit of g. The unit of G is N·m2/kg2.
Acceleration Due to Gravity (g)
When the Earth pulls a body towards its centre, the body accelerates. This acceleration is called the acceleration due to gravity, g. By equating the gravitational force on a body of mass m with mg, we get a neat formula.
g = G × M ÷ R2
where M is the mass of the Earth and R is the radius of the Earth. Notice the mass of the falling body cancels out — so all bodies fall with the same g (ignoring air resistance).
The standard value on Earth's surface is g ≈ 9.8 m/s2 (often rounded to 9.81 or 10 in problems). At the surface g depends only on Earth's mass and radius, not on the falling object.
A feather and a coin fall together in a vacuum because g is independent of mass. In air the feather falls slower only because of air resistance, not gravity.
G versus g — Never Confuse Them
This pair is the single most repeated trap in defence exams. Keep the contrasts crystal clear.
- G is the universal gravitational constant; g is the acceleration due to gravity.
- G is constant everywhere; g changes with location.
- G has unit N·m2/kg2; g has unit m/s2.
- G is a scalar; g is a vector pointing towards the Earth's centre.
- G ≈ 6.674 × 10−11; g ≈ 9.8 at the surface.
One-line memory hook: big G is the same in the whole galaxy; small g is small-minded and changes from place to place.
Variation of g With Altitude (Height)
As you move above the Earth's surface, the distance from the centre increases, so g decreases. For a small height h compared to the radius R, the value of g falls off.
At height h: gh = g × (1 − 2h÷R), valid when h is small compared with R.
For large heights use the full form gh = g × R2 ÷ (R + h)2.
This is exactly why a body weighs slightly less on a high mountain than at sea level, and why satellites high above experience weaker gravity. g decreases as altitude increases. The effect is small for everyday heights but becomes large for spacecraft. At an altitude equal to one Earth radius above the surface, the distance from the centre doubles, so by the inverse-square rule g falls to one-quarter of its surface value.
If a question gives a large altitude such as “at a height equal to the radius of the Earth,” do not use the (1 − 2h/R) shortcut — that approximation only works for small heights. Use the full inverse-square form instead.
Variation of g With Depth
Going below the surface, into a mine or a deep well, g also decreases — but for a different reason. Only the mass of the sphere below you pulls you inward; the outer shell of Earth cancels its own pull.
At depth d: gd = g × (1 − d÷R)
At the centre of the Earth (d = R), g becomes zero, so a body's weight there is zero even though its mass is unchanged.
Students often think g keeps rising as you go deeper because you are closer to the centre. It does NOT — g falls with depth and reaches zero at the centre.
Variation With Latitude and Earth's Rotation
The Earth is not a perfect sphere; it bulges at the equator and is flattened at the poles. The equatorial radius is larger, so g is slightly smaller at the equator. On top of this, the Earth's rotation provides a centrifugal effect that further reduces the effective g away from the poles.
g is maximum at the poles and minimum at the equator. The difference is about 0.5%, roughly gpole ≈ 9.83 m/s2 and gequator ≈ 9.78 m/s2.
The rotation effect means that if the Earth spun much faster, the effective g at the equator could drop to zero and objects there would fly off. A body therefore weighs marginally more at the poles than at the equator.
For latitude questions, remember the order from heaviest to lightest weight: poles > mid-latitudes > equator.
Weightlessness and Free Fall
An astronaut in an orbiting space station feels weightless not because gravity is absent, but because the station and the astronaut are in continuous free fall around the Earth together. With no surface pushing back, the sensation of weight disappears.
The same happens in a freely falling lift — for the duration of the fall, the apparent weight is zero. True zero weight also occurs at the exact centre of the Earth, where g itself is zero. Apparent weight is best understood through the reading on a weighing scale: it is the normal force the surface pushes back with. In free fall there is no such push, so the scale would read zero, even though gravity is pulling the body down at the full value of g.
This idea ties the whole topic together. Wherever the supporting force is removed — an orbiting station, a falling lift, a jumping diver mid-air — the body feels weightless. Wherever g itself drops — high altitude, deep mine, the equator — the body genuinely weighs less. Keeping these two causes separate prevents most exam errors on this chapter.
Weightlessness means apparent weight = 0, not that gravity has vanished. Orbiting satellites are firmly held by gravity; that pull is what bends their path into an orbit.
Worked Example: Weight at Altitude
Let us apply the altitude formula to a clean exam-style number.
A body weighs 100 N on the surface of the Earth. Find its approximate weight at a height equal to one-hundredth of the Earth's radius (h = R/100). Take g constant otherwise.
So the body weighs about 98 N at that height — lighter than at the surface, as expected.
When a question gives a small height or depth as a fraction of R, plug straight into the (1 − 2h/R) or (1 − d/R) form. It is faster than the full inverse-square formula and accurate enough for the options given.
Previous-Year Style Question
Q. The acceleration due to gravity (g) at a place is maximum at which of the following locations?
Answer: At the poles. Because the Earth is flattened at the poles, the polar radius is smallest, and the rotation effect is least there. With g = GM/R2, a smaller R gives a larger g, so g is maximum at the poles and minimum at the equator.
Do not pick the equator thinking it is closer to the Sun or warmer. Distance from the Sun has nothing to do with g on Earth — only Earth's own mass and radius matter.
Quick Revision and Recap
Run through these one-liners the night before the exam to lock in the full topic.
- Gravitation: F = G m1m2/r2, always attractive, along the line of centres.
- G = 6.674 × 10−11 N·m2/kg2; universal and constant.
- g = GM/R2 ≈ 9.8 m/s2; independent of the falling body's mass.
- g decreases with altitude: gh = g(1 − 2h/R).
- g decreases with depth: gd = g(1 − d/R); g = 0 at the centre.
- g is maximum at the poles, minimum at the equator.
- Weightlessness = apparent weight zero in free fall, not absence of gravity.
Frequently asked questions
What is the difference between G and g?
G is the universal gravitational constant (6.674 × 10−11 N·m2/kg2) and is the same everywhere. g is the acceleration due to gravity (about 9.8 m/s2 at Earth's surface) and changes with location.
Where on Earth is g maximum and minimum?
g is maximum at the poles, where the radius is smallest and rotation has least effect, and minimum at the equator, where the equatorial bulge and rotation reduce it. The difference is roughly 0.5%.
Why does g become zero at the centre of the Earth?
Only the mass inside the radius at which you stand pulls you towards the centre. At the exact centre there is no mass below you, the surrounding shell pulls equally in all directions, and the net force becomes zero, so g = 0.
Does the mass of a falling object affect its acceleration due to gravity?
No. In the formula g = GM/R2, the falling body's mass cancels out, so all objects fall with the same g in the absence of air resistance. A feather and a coin fall together in a vacuum.
Why do astronauts feel weightless in orbit if gravity is still acting?
Gravity is still strong in orbit; it is what keeps the satellite circling the Earth. Astronauts feel weightless because they and the spacecraft are in continuous free fall together, so there is no supporting force to give a sensation of weight.
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