Gravitation

Why This Chapter Matters

Gravitation puts 2 to 4 questions in almost every SSC and RRB physics paper, and it comes back year after year because the concepts are few but the confusions are many. Ask a hundred aspirants the difference between mass and weight, or why an astronaut floats despite gravity still acting on them up there, and most will fumble. Get this chapter right and you convert easy marks that most of your competition drops.

The single biggest mistake aspirants make here is mixing up mass and weight, and a close second is confusing g variation with altitude and g variation with depth — one uses the square of distance, the other uses a simple fraction, and exam-setters love swapping them in options. This chapter fixes both, along with escape velocity, satellites, and Kepler's laws, all kept to the fact level SSC and RRB actually test.

Newton's Law of Gravitation

Every object with mass pulls every other object with mass toward it. Isaac Newton, in 1687, gave this idea a precise number. Newton's law of gravitation states that the force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

In simple words: F = G × (m1 × m2) / r²

Here m1 and m2 are the masses of the two bodies, r is the distance between their centres, and G is the universal gravitational constant, with an accepted value of approximately 6.674 × 10⁻¹¹ N m²/kg². G was first measured experimentally by Henry Cavendish in 1798, using a torsion balance, decades after Newton proposed the law itself.

Notice the word "universal." This is not a force that only works on Earth. The Moon pulls Earth, Earth pulls the Sun, and even you pull your study table, though the force is too tiny to notice because G itself is such a small number. Gravitation is the weakest of the four fundamental forces of nature, but it wins over long distances because it never cancels out the way electric forces can.

Analogy: think of gravitation like the pull between two magnets made of cotton wool. It is real and it is always there, but you only feel a magnet's pull strongly when one magnet is huge (like a fridge magnet) or very close. Between two ordinary objects, both masses are too small for the pull to be noticeable. Between Earth and you, one mass — Earth's — is gigantic, so the pull becomes obvious as your weight.

Exam trap: the force in Newton's law depends on the square of the distance, not the distance itself. If distance doubles, force does not halve, it becomes one-fourth. Options in MCQs often test this exact substitution.

Kepler's Laws of Planetary Motion

Before Newton explained why planets orbit the Sun, Johannes Kepler, using data painstakingly collected by his teacher Tycho Brahe, worked out how they move. Kepler gave three laws around 1609–1619, and SSC exams expect you to know all three by name and idea, not by formula.

1. Law of Orbits: every planet moves around the Sun in an elliptical path, with the Sun at one of the two foci of the ellipse, not at the centre.
2. Law of Areas: the line joining a planet to the Sun sweeps out equal areas in equal time intervals. This means a planet moves faster when it is closer to the Sun (called perihelion) and slower when it is farther away (called aphelion).
3. Law of Periods (Harmonic Law): the square of a planet's orbital time period is directly proportional to the cube of the semi-major axis of its orbit. Planets farther from the Sun take disproportionately longer to complete one revolution.

Memory hook: remember the order as "Oval, Odd-speed, Overall-time" — Orbits are oval (elliptical), speed is Odd (uneven, faster near the Sun), and the third law links the Overall orbital time to distance. Three O-words, three laws, in the order SSC usually lists them.

Exam trap: students often say a planet moves in a "circular" orbit. It is elliptical. A circle is only a special case of an ellipse, and exam options frequently plant "circular" as the wrong answer to catch students who oversimplify.

Acceleration Due to Gravity (g)

When gravity acts on a falling object near Earth's surface, it produces an acceleration. This is called acceleration due to gravity, written as g, and its standard value is 9.8 m/s², often rounded to 9.81 m/s² in more precise contexts, or approximated as 10 m/s² in quick calculations.

The value of g is not the same everywhere. It depends on Earth's shape and rotation.

• Earth is not a perfect sphere. It bulges slightly at the equator and is flatter at the poles, meaning the poles are closer to Earth's centre. Since gravity weakens with distance, g is highest at the poles and lowest at the equator.
• Earth's rotation also reduces g slightly at the equator because of the centrifugal effect working against gravity there.

Variation of g with Altitude and Depth

This is the pairing SSC loves to test, so learn the shape of each formula, not just the words.

With altitude (going up, away from Earth's centre): g decreases as you move away from Earth's surface, following an inverse-square relationship, similar to Newton's original law. The higher you go, the weaker gravity gets, and it keeps weakening in proportion to the square of your distance from Earth's centre.

With depth (going down, into a mine or borehole): g also decreases, but through a different, gentler relationship, roughly proportional to how much of Earth's mass still lies below you. At Earth's exact centre, gravity from every direction cancels out and g becomes zero.

Exam trap: many students assume g decreases the same way with both altitude and depth. It does not. Altitude follows an inverse-square style decrease, so g falls off relatively fast as you go up. Depth follows a straight-line style decrease down to zero at the centre. If a question says "at the centre of the Earth, g is..." the answer is always zero, not "maximum."

Analogy: picture Earth like a giant onion. As you climb a tower (going up, away from the onion), you are simply getting farther from all its mass, and the pull fades fast, squared-distance fast. As you dig into a mine (going down, into the onion), you are removing layers of onion from above you that used to pull you upward too, cancelling part of the downward pull, so gravity fades more gently, all the way to nothing at the very core.

Mass vs Weight

This is the pair that decides whether you get gravitation questions right or wrong under exam pressure, so slow down here.

Mass is the amount of matter in a body. It is measured in kilograms (kg), it is a scalar quantity, and it never changes regardless of where the object is, whether on Earth, the Moon, or floating in space.

Weight is the force with which gravity pulls that mass toward the centre of a planet. It is measured in newtons (N), it is a vector quantity, and it changes depending on the local value of g. Weight equals mass multiplied by g (W = m × g).

Property	Mass	Weight
What it measures	Amount of matter	Force of gravity's pull on that matter
SI unit	kilogram (kg)	newton (N)
Type of quantity	Scalar	Vector
Changes with location?	No, always constant	Yes, changes with g
Value on the Moon	Same as on Earth	About one-sixth of Earth weight
Measuring instrument	Beam balance	Spring balance

Exam trap: a common wrong answer choice claims "an astronaut's mass becomes zero in space, that is why they float." False. Their mass is unchanged. They float because they and their spacecraft are both in continuous free fall around Earth, so there is no supporting surface pushing back on them, not because gravity or mass has vanished. This exact misconception shows up as a distractor option repeatedly.

Real-world grounding: think of a 60 kg person. On Earth, their weight is roughly 588 N (60 × 9.8). On the Moon, where g is about one-sixth of Earth's, the same 60 kg person would weigh only about 98 N, they could jump much higher with the same effort, exactly what you have seen in footage of astronauts bounding across the lunar surface. Their mass, the 60 kg, never changed.

Escape Velocity

To leave a planet's gravitational pull permanently, without additional propulsion, an object needs a certain minimum launch speed. This is called escape velocity, the minimum speed required for an object to break free of a planet's gravitational field without falling back.

For Earth, escape velocity is approximately 11.2 km/s, or roughly 40,000 km/h. This number does not depend on the mass of the object being launched, a feather and a rocket both need the same escape velocity from Earth in theory, only air resistance makes the practical picture different.

Escape velocity depends on the mass and radius of the planet. A more massive planet, or a smaller, denser one, has a stronger gravitational pull at its surface and therefore needs a higher escape velocity. This is exactly why the Moon, with far less mass than Earth, has an escape velocity of only about 2.4 km/s, and why it was realistic for the Apollo missions to launch back off the Moon's surface using a comparatively small ascent module.

Analogy: think of escape velocity like the exact speed needed to throw a ball out of a deep well in one throw, hard enough that it never falls back down. Throw softer, it falls back. Throw at exactly this speed or faster, it clears the rim and keeps going. A bigger, deeper well (a more massive planet) needs a harder throw.

Satellites: Natural and Artificial

A satellite is any object that revolves around a larger body under its gravitational pull. The Moon is Earth's only natural satellite. Beyond that, thousands of artificial satellites, human-made objects launched into orbit, circle Earth today for communication, weather monitoring, navigation, and scientific research.

Artificial satellites are broadly classified by their orbit type, and SSC exams focus on two:

Geostationary satellites orbit directly above the equator at an altitude of roughly 36,000 km, and they take exactly 24 hours to complete one orbit, matching Earth's own rotation period. Because their orbital speed matches Earth's spin, they appear to stay fixed over the same point on Earth at all times. This makes them ideal for communication and broadcasting, since a satellite dish on the ground can stay pointed at one fixed spot in the sky. India's own communication satellites, launched under the INSAT series, use this orbit.

Polar satellites orbit at a much lower altitude, typically 500 to 800 km, passing over or near both poles on each revolution while Earth rotates beneath them. Because Earth spins underneath a polar satellite's fixed orbital path, the satellite eventually scans the entire surface of the planet over repeated passes. This makes polar orbits ideal for remote sensing, weather observation, and mapping. India's IRS (Indian Remote Sensing) satellites and many weather satellites use polar orbits.

Memory hook: "Geo stays, Polar scans." A geostationary satellite stays fixed over one spot, useful for a phone call that must connect through the same relay point every time. A polar satellite scans the whole globe strip by strip, useful for a weather map that needs to cover the entire Earth.

Exam trap: students sometimes assume geostationary satellites orbit closer to Earth than polar satellites because "stationary" sounds passive or low-key. It is the opposite. Geostationary orbit, at about 36,000 km, is far higher than a typical polar orbit of 500 to 800 km. The higher an orbit, the longer it can take to match Earth's spin at exactly 24 hours.

Why We Do Not Feel Earth's Rotation or Pull Constantly

A quick, exam-relevant footnote: gravity is what keeps our atmosphere, oceans, and every loose object pinned to Earth's surface even though the planet is spinning and hurtling around the Sun at enormous speed. We do not feel this motion because we, the air, and everything around us move together at the same speed, the same reason you do not feel a smoothly moving train's speed unless it suddenly brakes or turns. Gravity is the reason there is no such sudden jolt, it holds everything to the surface as one moving system.

Quick Revision — One-Line Facts

• Newton's law of gravitation: force is proportional to m1 × m2, inversely proportional to r².
• The universal gravitational constant G is approximately 6.674 × 10⁻¹¹ N m²/kg².
• G was experimentally measured by Henry Cavendish in 1798.
• Gravitation is the weakest of the four fundamental forces but dominates over long distances.
• Kepler's first law: planetary orbits are elliptical, Sun at one focus.
• Kepler's second law: equal areas swept in equal time; planets move fastest near the Sun (perihelion).
• Kepler's third law: T² is proportional to r³ (orbital period squared vs semi-major axis cubed).
• Standard g on Earth's surface is 9.8 m/s² (approximated as 10 m/s² for quick math).
• g is greatest at the poles and least at the equator due to Earth's shape and rotation.
• g decreases with altitude following an inverse-square style relationship.
• g decreases with depth in a more gradual, straight-line style relationship.
• At the centre of the Earth, g = 0.
• Mass is constant everywhere; weight changes with local gravity.
• Mass is measured in kilograms, weight is measured in newtons.
• Mass is a scalar; weight is a vector.
• A person's weight on the Moon is roughly one-sixth of their weight on Earth.
• Astronauts float in orbit due to continuous free fall, not because gravity or mass disappears.
• Escape velocity from Earth is approximately 11.2 km/s.
• Escape velocity does not depend on the mass of the object being launched.
• The Moon's escape velocity, about 2.4 km/s, is far lower than Earth's.
• The Moon is Earth's only natural satellite.
• Geostationary satellites orbit at about 36,000 km, taking 24 hours per orbit, above the equator.
• Polar satellites orbit at roughly 500–800 km, passing near both poles each revolution.
• Geostationary satellites are used mainly for communication and broadcasting.
• Polar satellites are used mainly for remote sensing, weather monitoring, and mapping.
• India's communication satellites belong to the INSAT series.
• India's remote sensing satellites belong to the IRS series.
• Kepler built his laws using observational data from Tycho Brahe.
• The weight formula is W = m × g.
• Weight is measured with a spring balance; mass is measured with a beam balance.
• A geostationary orbit is higher in altitude than a typical polar orbit, not lower.

Memory Tables

Table 1: Gravitation Core Facts

Concept	Key Value / Fact
Newton's law	F = G(m1m2)/r²
Universal gravitational constant (G)	6.674 × 10⁻¹¹ N m²/kg²
Measured by	Henry Cavendish (1798)
Standard g on Earth	9.8 m/s² (approx. 10 m/s²)
g at Earth's centre	Zero
g variation	Highest at poles, lowest at equator
Escape velocity (Earth)	11.2 km/s
Escape velocity (Moon)	2.4 km/s

Table 2: Satellite Types Compared

Feature	Geostationary Satellite	Polar Satellite
Altitude	About 36,000 km	About 500–800 km
Orbital period	24 hours	Much shorter, several revolutions per day
Path	Fixed above equator	Passes near both poles
Appears from ground	Fixed in the sky	Moves across the sky, changes position
Main use	Communication, broadcasting	Remote sensing, weather, mapping
India's series	INSAT	IRS

Table 3: Kepler's Three Laws

Law	Name	Core Idea
First	Law of Orbits	Orbits are elliptical, Sun at one focus
Second	Law of Areas	Equal areas swept in equal time; faster near the Sun
Third	Law of Periods	T² is proportional to r³

Practice MCQs

Q1. Who proposed the law of universal gravitation? (a) Galileo Galilei (b) Isaac Newton (c) Albert Einstein (d) Johannes Kepler

Q2. What is the SI unit of weight? (a) Kilogram (b) Newton (c) Joule (d) Pascal

Q3. The value of acceleration due to gravity at the centre of the Earth is: (a) Maximum (b) Minimum but not zero (c) Zero (d) Same as at the surface

Q4. Which quantity remains constant regardless of an object's location in the universe? (a) Weight (b) Mass (c) Both weight and mass (d) Neither

Q5. Geostationary satellites are mainly used for: (a) Remote sensing (b) Weather mapping only (c) Communication and broadcasting (d) Measuring ocean depth

Q6. Approximately how long does a geostationary satellite take to complete one orbit of Earth? (a) 12 hours (b) 24 hours (c) 90 minutes (d) 30 days

Q7. Who experimentally determined the value of the universal gravitational constant G? (a) Johannes Kepler (b) Tycho Brahe (c) Henry Cavendish (d) Edmund Halley

Q8. According to Kepler's first law, a planet's orbit around the Sun is: (a) Perfectly circular (b) Elliptical, with the Sun at one focus (c) Parabolic (d) A straight line

Q9. The escape velocity of Earth is approximately: (a) 2.4 km/s (b) 7.9 km/s (c) 11.2 km/s (d) 15.6 km/s

Q10. Compared to the equator, the value of g at the poles is: (a) Lower (b) Higher (c) Exactly the same (d) Zero

Q11. A person weighing 600 N on Earth would weigh approximately how much on the Moon? (a) 600 N (b) 300 N (c) 100 N (d) 6000 N

Q12. Which instrument is used to measure mass, as opposed to weight? (a) Spring balance (b) Beam balance (c) Barometer (d) Thermometer

Q13. As per Kepler's second law, a planet moves fastest in its orbit when it is: (a) Farthest from the Sun (aphelion) (b) Closest to the Sun (perihelion) (c) At either focus equally (d) At the midpoint of its orbit

Q14. Why do astronauts appear weightless while orbiting Earth in the International Space Station? (a) Gravity does not exist at that altitude (b) Their mass becomes zero in space (c) They and the station are in continuous free fall around Earth (d) The station blocks Earth's gravitational pull

Q15. Polar satellites are typically placed at an altitude of about: (a) 36,000 km (b) 500–800 km (c) 100,000 km (d) 10 km

Answer Key

Q	Answer	Reason
Q1	(b)	Isaac Newton formulated the law of universal gravitation in 1687, connecting force, mass, and distance.
Q2	(b)	Weight is a force, so it is measured in newtons, unlike mass which is measured in kilograms.
Q3	(c)	Gravity from all directions cancels out exactly at Earth's centre, making g zero there.
Q4	(b)	Mass measures the amount of matter and stays constant everywhere; weight changes because it depends on local gravity.
Q5	(c)	Geostationary satellites stay fixed over one point on Earth, ideal for consistent communication and broadcast links.
Q6	(b)	A geostationary satellite's 24-hour orbit matches Earth's own rotation, which is what keeps it fixed overhead.
Q7	(c)	Henry Cavendish measured G experimentally in 1798 using a torsion balance, over a century after Newton's law was published.
Q8	(b)	Kepler's first law states planetary orbits are ellipses, not circles, with the Sun positioned at one focus.
Q9	(c)	Earth's escape velocity is approximately 11.2 km/s, the minimum speed to break free of Earth's gravity permanently.
Q10	(b)	Poles are closer to Earth's centre due to its equatorial bulge, so gravity, and hence g, is stronger there.
Q11	(c)	The Moon's gravity is about one-sixth of Earth's, so weight there is roughly one-sixth of the Earth weight.
Q12	(b)	A beam balance compares mass against known masses, unaffected by local gravity, unlike a spring balance which measures weight.
Q13	(b)	Kepler's second law (equal areas in equal time) means a planet speeds up when closest to the Sun, at perihelion.
Q14	(c)	Astronauts float because they and their spacecraft fall continuously around Earth together, not because gravity or mass vanishes.
Q15	(b)	Polar satellites orbit much lower than geostationary ones, typically 500 to 800 km, to scan the Earth's surface closely.