JEE/NEET Physics · Gravitation series · Part 1 of 8 · All parts →

As a result, throw a ball at 40,320 km/h and it never comes back. That speed — 11.2 km/s — is Earth’s escape velocity. Most students can quote it; far fewer can answer the follow-ups examiners actually ask: 11.2 km/s from where? Does it depend on the ball’s mass? Why does a force as relentless as gravity have a speed limit at all? This card is Part 1 of the Gravitation series for JEE Main, JEE Advanced and NEET — eight parts, one chapter, exam-ready. By the end, you will not just recall the number; you will be able to derive it, apply it to any planet, and sidestep the three traps that cost candidates marks every year.

The Concept: Arrive at Infinity With Zero Speed.

Notably, gravity weakens with height, so a projectile does not need speed to spare at infinity — it needs to arrive at infinity with exactly zero speed. That is the definition of escape velocity: the minimum launch speed for which the projectile just barely breaks free, arriving infinitely far away with nothing left in the tank. Any faster and it escapes with speed to spare; any slower and it turns back.

Meanwhile, apply energy conservation between the surface and infinity (where gravitational potential energy is conventionally defined as zero):

Walk through the derivation once so it sticks. At the surface, the total mechanical energy is the kinetic energy ½mv² plus the potential energy −GMm/R. At infinity, for the minimum case, both kinetic and potential energy are zero. Setting total energy equal:

½mv² − GMm/R = 0 ⟹ ½mv² = GMm/R ⟹ v² = 2GM/R ⟹ vₑ = √(2GM/R).

Indeed, the launched object’s mass m cancels from both sides: a coin and a truck escape at the same speed. And since g = GM/R² at the surface, you can substitute GM = gR² to get the second form, vₑ = √(2gR), which is often the faster route in problems. Finally, state the conditions in your solution — no air resistance, launch from the surface — because examiners award steps for them.

The Formula Table.

A quick comparison worth memorising: Earth’s vₑ ≈ 11.2 km/s, the Moon’s ≈ 2.4 km/s, Mars ≈ 5.0 km/s, Jupiter ≈ 59.5 km/s. Heavier and larger bodies demand dramatically higher escape speeds — a pattern examiners love to test through ratio problems rather than raw calculation.

Solved Numerical (NEET Pattern).

Notice the problem-solving rhythm: write the formula, substitute with consistent SI units, take the square root, then sanity-check the order of magnitude against a known value. That last step takes two seconds and catches sign errors, unit slips and misplaced powers of ten before they cost you.

Real-World Physics.

The black-hole connection deserves a pause. The radius at which vₑ = c is called the Schwarzschild radius, r_s = 2GM/c². For Earth that works out to roughly 9 millimetres; for the Sun, about 3 km. The same energy-conservation argument you just learnt, pushed to its limit, predicts the most extreme objects in the universe — a satisfying reminder that exam-level physics and frontier physics share one toolbox.

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In fact, JEE/NEET Physics · Gravitation series · Part 2 of 9 · All parts →

Notably, the International Space Station has been falling for 25 years — and it has never hit the ground. not because gravity is missing up there (it’s still 89% as strong). it’s because the ISS moves sideways so fast that as it falls, the curved Earth keeps dropping away beneath it. Part 2 of the Gravitation series — and this one you can understand with a thrown ball.

The Simple Idea: Newton’s Cannonball

Specifically, throw a ball sideways — it lands a few metres away. Meanwhile, throw harder — it lands farther. now imagine throwing extremely hard, from a very high mountain.

Similarly, here’s the key: the Earth is round, so its surface curves downward. Meanwhile, as the ball flies farther, the ground beneath it drops away. If the ball flies fast enough, its falling matches the Earth’s curving — the ball falls forever and never touches ground. That’s an orbit.

So an astronaut isn’t floating because there’s no gravity. Overall, the astronaut and the whole station are falling together — like being in a lift whose cable snapped. Indeed, everything falls together = everything floats together.

What Each Letter Means

Why Higher Satellites Move SLOWER

Feels wrong, right? In fact, higher = farther from Earth = fighting more gravity? No — it’s the opposite. As a result, farther from Earth, gravity is weaker. Meanwhile, the satellite needs less speed to keep circling. vₒ shrinks as r grows: doubling the orbit distance cuts the speed by √2.

Moreover, real numbers: ISS at 400 km flies at 7.7 km/s. TV satellites at 36,000 km crawl at 3.1 km/s. In other words, the Moon at 384,000 km strolls at 1 km/s. Indeed, low orbits are the fast lane; high orbits are the slow lane.

The √2 Memory Trick

Therefore, from Part 1 : escape velocity 11.2 km/s, orbit velocity 7.9 km/s. Notably, the ratio is always √2, for any planet, at any height. Meanwhile, memorise the pair, and any question about either one hands you the other.

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In fact, JEE/NEET Physics · Gravitation series · Part 3 of 9 · All parts →

Notably, in 1609, a man with no telescope predicted the motion of every planet using three simple rules. NASA still uses them to plan missions today. In fact, kepler's laws look like boring history — they're actually three of the easiest marks in NEET and JEE Main. Meanwhile, part 3 of the Gravitation series , told simply.

Rule 1: The Squashed Circle

Overall, everyone pictures orbits as perfect circles. Meanwhile, they're not — they're ellipses : circles gently squashed, like a slightly oval roti. And the Sun doesn't sit in the middle — it sits slightly off-centre, at a point called a focus .

Consequently, what this means: a planet's distance from the Sun keeps changing through the year. Meanwhile, earth is closest in January (147 million km) and farthest in July (152 million km). Moreover, a perfect circle is just the special case where the squash is zero.

Rule 2: Faster Near the Sun

Furthermore, picture a ball rolling in a large round bowl. Indeed, near the edges (high up) it rolls slowly. Therefore, near the centre it whizzes fast. Planets do the same: closer to the Sun = faster; farther = slower.

Likewise, earth runs at 30.3 km/s in January and 29.3 km/s in July. As a result, the reason (angular momentum) is Part 4 's story.

Rule 3: Farther = Much Longer Year

Therefore, why does distance matter SO much? Meanwhile, two reasons stack up: a bigger orbit is a longer track AND the planet moves slower on it (Part 2's rule). Meanwhile, longer track + slower speed = much, much more time. That's why the r is raised to the power 1.5.

The 15-Second Exam Trick

Meanwhile, almost every exam question on Rule 3 is a comparison. Meanwhile, don't compute full years — compare: year ratio = (distance ratio)^1.5.

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In fact, JEE/NEET Physics · Gravitation series · Part 4 of 9 · All parts →

In other words, watch an ice skater spin: arms stretched out — slow. Meanwhile, arms pulled in — suddenly whirling fast. No push, no engine. In fact, where did the extra spin come from? That’s the secret — a rule so strict the whole universe obeys it. Part 4 of the Gravitation series , the rule behind planets, skaters and pulsars.

The Simple Idea: You Can’t Beat the Rule

Similarly, some things in physics can be changed by pushing harder. But a few are locked. Moreover, one locked thing: if no outside ‘twist’ (torque) acts on a spinning system, its turning quantity — angular momentum — cannot change. Meanwhile, not by pulling arms in, not by exploding, not by any internal trick.

Overall, why can’t gravity change it for a planet? Meanwhile, because gravity pulls the planet straight toward the Sun — along the string connecting them. Therefore, a pull aimed straight at the centre can speed you up or slow you down, but it can never twist you around. In one line: gravity can pull, but it cannot twist. So a planet’s turning quantity is locked for eternity.

What Each Letter Means

Subsequently, read it as a see-saw: v × r must stay constant (m doesn’t change). Indeed, shrink r, and v must grow to pay for it. Grow r, and v must drop. That’s the entire rule.

The Skater, Step by Step

In fact, arms out: her hands are far from the spin axis (big r), moving at modest speed (v). Meanwhile, she pulls her arms in: r shrinks — and since v × r is locked, v rises automatically. She spins faster without doing any rotational work. Her muscles worked to pull the arms in, but the spin-up is pure rule, not push.

The Comet: The Same Trick in Space

Moreover, a comet on its long oval orbit is a skater with invisible arms. Meanwhile, far from the Sun: big r, slow crawl. Falling closer: r shrinks — v must rise. The comet whips around the Sun at maximum speed at closest approach, then slows again on the way out. This IS Kepler’s Rule 2 from Part 3 — ‘faster near the Sun’ was this locked quantity all along. Kepler saw the pattern; this rule explains it.

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In fact, JEE/NEET Physics · Gravitation series · Part 5 of 9 · All parts →

Notably, there’s a minus sign in gravity’s energy formula, and it decides marks. Meanwhile, remove it and every answer goes wrong. But the minus isn’t there to torture you — it has a beautifully simple meaning: negative energy = trapped. In fact, part 5 of the Gravitation series , explained like a bank account.

The Bank Account Picture

Similarly, potential energy always needs a ‘zero’ chosen by us. Meanwhile, near the ground, you choose the ground as zero — that’s why mgh is positive when you climb. But for planets, ‘the ground’ is a bad choice (every planet has different ground!). So physics chooses the only universal zero: infinite distance apart = zero energy.

Overall, now think like a bank account. Meanwhile, far away (at infinity): balance zero. Moreover, bring a satellite closer to Earth — gravity pulls it in. Doing work for free — like receiving free money, your balance goes below zero (into debt). Closer = deeper debt. That debt is the minus sign:

And here’s the elegant connection: to escape. Consequently, your throwing energy must exactly pay off the debt: ½mv² = GMm/R — which rearranges to v = √(2GM/R) . Indeed, part 1’s escape velocity was a debt repayment all along!

What Each Letter Means

Why the Minus Sign Is Forced, Not Chosen

In fact, follow the steps: (1) We declared U = 0 at infinite distance. Meanwhile, (2) Gravity is attractive — it pulls masses together for free , doing positive work as r shrinks. Therefore, (3) Energy conservation then forces stored energy to drop below its zero mark as they come together. Result: at any finite distance, U is negative. The minus sign is bookkeeping for ‘gravity already paid. You’re in debt.’ Closer = more negative = deeper trap.

mgh: The Honest Small-Distance Shadow

Is mgh wrong? Moreover, no — it’s a local approximation. Meanwhile, near the surface, the big formula expands to: U ≈ (a big negative constant) + mgh. Meanwhile, the ‘big constant’ is invisible to us (we only measure changes ), so we see just mgh. That’s why mgh works for a shelf and fails for a satellite: for a 400-km orbit, the full −GMm/r must be used.

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In fact, JEE/NEET Physics · Gravitation series · Part 6 of 9 · All parts →

Notably, every satellite in orbit is in debt — and the size of that debt follows one fixed pattern that solves nearly every exam question on this topic. If Part 5 was the bank account, this card is the repayment schedule. In fact, part 6 of the Gravitation series .

The 2:1:1 Pattern (Memorise This, Not Three Formulas).

Similarly, a satellite in a circular orbit has two energies: speed-energy (positive — it’s moving) and gravity-debt (negative — it’s trapped). Meanwhile, using the orbit speed from Part 2 , the maths gives a fixed pattern:

Furthermore, read the pattern as a sentence: ‘the debt is always exactly twice the speed-energy. Meanwhile, the account is negative by exactly the amount of the speed-energy.’ Escape means paying off exactly the speed-energy you have. That single sentence answers most questions.

The Drag Paradox, Explained.

Likewise, here’s the strangest fact in this chapter: when a satellite loses energy (to air drag), it speeds up. Indeed, losing energy deepens the debt → deeper debt = smaller orbit r → smaller orbit = faster orbit speed (Part 2’s rule). So the satellite descends and speeds up while its account gets worse. As a result, space stations fight this constantly — drag bleeds them downward, and re-supply craft re-pay the debt.

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Therefore, JEE/NEET Physics · Gravitation series · Part 7 of 9 · All parts →

Consequently, Stand on a spring balance at the equator, then at the North Pole — the same you weighs about 350 grams more at the Pole. Meanwhile, Not an instrument trick: g itself genuinely changes with height , depth , and latitude . NEET asks all three as direct formula questions. Part 7 of the Gravitation series — with one recipe behind all three.

The One Recipe Behind Everything.

Furthermore, Your gravity depends on only two things: how much planet is beneath you. Meanwhile, How far you are from its centre. Specifically, Climb: mass same, distance bigger → g falls. Dig: distance smaller BUT mass beneath you shrinks too → g still falls. Spin: some gravity gets ‘spent’ holding you on the circle → felt g falls. Three variations, one recipe.

Going Up: The Mountain Case.

However, Climbing to height h moves you farther from the centre: divide by (R+h)² instead of R². Meanwhile, Calibration: at Everest’s top, g drops only 0.03 m/s² — tiny, because 8.8 km is truly tiny next to 6,400 km. But at h = R (one full radius up), the exact formula gives g/4 — while the shortcut would absurdly give −g. If h isn’t tiny, use the exact form. A wrong-sign answer is your alarm bell.

Going Down: The Mine Case.

Moreover, Descend to depth d and something lovely happens: all the rock ABOVE your head cancels its own pull (a shell of uniform rock pulls you equally in all directions from inside — net zero). Only the ball of rock beneath you counts — and that ball shrinks as you descend. At the centre of the Earth: nothing beneath, pulls from every side cancel — g = 0. You would float at the centre of the Earth.

Spinning: The Equator Case.

In fact, The spinning Earth carries you around a circle (biggest circle at the equator, shrinking to nothing at the poles). Going in a circle needs some inward pull — part of gravity is ‘spent’ as that inward pull. The balance you stand on reads less. The discount is small (0.34% at the equator) but permanent — and combined with Earth’s slight equatorial bulge, real g runs 9.780 (equator) to 9.832 (poles).

What Each Letter Means.

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JEE/NEET Physics · Gravitation series · Part 8 of 8 · All parts →

In 2015, humanity “heard” two black holes collide — 1.3 billion years after the event actually happened. Every formula used in that detection is over a century old at most, and the core mathematics traces straight back to the gravitation you have revised across this series. This finale of the Gravitation series shows exactly how the syllabus connects to modern astrophysics — and then hands you the complete revision card.

Black Holes From Your Syllabus.

Start with escape velocity from Part 1: vₑ = √(2GM/R). Now imagine shrinking R while keeping M fixed. As the radius decreases, the escape velocity climbs. At some critical radius, vₑ equals c — the speed of light. Beyond that boundary, nothing escapes, not even light itself:

Here is the exam-relevant correction most students miss: at a distance, a black hole’s gravity is identical to that of any object of equal mass. If you swapped the Sun for a Sun-mass black hole tomorrow, Earth’s orbit would not change by a metre. Black holes do not “suck things in” — they simply have gravity, and their horror lies only in how close you can get to the mass.

LIGO: Energy Conservation at 22 Decimal Places.

In September 2015, two black holes — 36 and 29 solar masses — spiralled into each other and merged. In the final moments, three entire solar masses converted directly into pure energy as gravitational waves: E = mc², Part 5’s bookkeeping applied at cosmic scale. For a few hundredths of a second, that merger out-radiated all the stars in the observable universe combined.

LIGO — the Laser Interferometer Gravitational-Wave Observatory — caught the signal. Its two 4-km detector arms measured a length change of roughly one ten-thousandth of a proton’s width, a precision so extreme that engineers must account for quantum noise, thermal vibration of the mirrors, and even the rumble of trucks hundreds of kilometres away. This is energy and momentum conservation verified at 22 decimal places.

And the story is coming home: LIGO-India is under development as India’s flagship gravitational observatory, which will sharpen the sky-localisation of every future detection dramatically. Expect this in the “current science” flavour of exam questions.

Lagrange Points: Parking Spots in Space.

There are five special points in the Sun–Earth system where the Sun’s gravity, the Earth’s gravity and the orbital motion balance out. A satellite parked there holds station with almost no fuel — these are the Lagrange points.

• L1 (1.5 million km sunward of Earth) gives an uninterrupted view of the Sun. It hosts Aditya-L1, ISRO’s solar observatory — India’s first dedicated solar mission.
• L2, on the far side of Earth from the Sun, gives telescopes a permanently dark, cold sky. It hosts the James Webb Space Telescope.
• L3 sits behind the Sun — useful only for fiction, since we can never see what’s there.
• L4 and L5 lead and trail Earth by 60° in its orbit; naturally captured asteroids (“Trojans”) collect at such points in other planetary systems.

The placement math is Parts 2, 3 and 5 working together: gravitational force balance plus centripetal orbital conditions plus energy bookkeeping. If a question gives you the Sun–Earth distance and asks for the L1 distance, you are equating the net force toward the Sun with the required centripetal force for a 1-year orbital period — a beautiful synthesis problem.

Weighing the Invisible.

How do we know the black hole at our galaxy’s centre, Sgr A*, weighs about four million Suns? We watch a star orbit it. The star S2 completes a full 16-year loop around a point where nothing visible sits. Measure the orbital period T and the semi-major radius r, then apply Kepler’s third law from Part 3: M = 4π²r³/GT².

That is the astonishing part: a law published in 1619, derived from planetary observations by naked-eye-era astronomy, weighs a four-million-solar-mass monster. Kepler’s third law works equally for Mars and for black holes because gravity is gravity — the same inverse-square force everywhere in the universe. This technique, watching things orbit invisible masses, is also how astronomers first inferred dark matter in galaxies.

The Complete Gravitation Formula Card.

Revision tip: memorise the escape and orbital velocity pair together — the relation vₑ = √2·vₒ is tested far more often than either formula alone. The energy relations are the second-highest-yield row: remember that for a circular orbit, the total energy is negative and equal to half the potential energy in magnitude.

Where the Series Goes Next.

In short, the angular momentum conservation from Part 4 becomes the most powerful problem-solving tool in the next chapter — Rotational Motion: torque, moment of inertia and rolling bodies. The central-force argument (τ = 0 ⟹ L = constant) reappears everywhere in rotation, so the mental machinery you built here transfers directly. Gravitation, it turns out, was rotation’s rehearsal.

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In fact, JEE/NEET Physics · Gravitation series · Part 9 of 9 · All parts →

In other words, eight cards covered the main roads. Meanwhile, this bonus card completes the chapter’s side streets — gravity ‘field’, the hollow-shell surprise, true weightlessness. Why your TV satellite sits at exactly 36,000 km. All simple, all exam-tested. Moreover, part 9 (bonus) of the Gravitation series .

Gravity Field: The ‘Pull Per Kilogram’.

Similarly, you know g = 9.8 m/s². Therefore, generalise: the field at any point is the pull a 1-kg test mass would feel there: E = GM/r², direction: toward the planet. The subtle point: the field exists whether or not anything is there to feel it — it’s a property of space around a mass, an invisible arrow at every point. Meanwhile, (E and g are the same number; exams swap the names.)

The Hollow-Planet Surprise.

Overall, stand anywhere inside a hollow spherical shell of rock. Which way do you fall? As a result, nowhere — gravity is exactly zero, everywhere inside. Not approximately — exactly.

Consequently, look at a patch of shell on your right: close, so it pulls hard. Meanwhile, a cone of vision catches only a small patch. The same cone extended left catches a bigger but farther patch that pulls weakly. Small-near-strong exactly cancels big-far-weak. Every direction cancels. Notably, this is why, when you dig into the Earth ( Part 7 ). Only the rock BENEATH you counts — the shell above you cancels itself out.

At the Centre of a Planet.

Furthermore, combine the ideas: at the centre, pulls cancel from all sides (field = 0. Meanwhile, you’d float) — but the gravity trap is at its deepest (energy −1.5GMm/R). No pull ≠ shallow trap. Specifically, a favourite conceptual MCQ: zero field, deepest well — both at once.

Weightlessness, Properly Understood.

Likewise, astronauts float not because gravity is absent (at ISS height it’s 89% of surface value) but because they and their spacecraft fall together — nothing presses against anything. Meanwhile, same as a lift with a snapped cable: you’d float inside it, in full gravity. Weight is a contact force; weightlessness is absence of contact.

TV Satellites: The 36,000 km Story.

In short, for a satellite to hover over one fixed spot (so your dish never moves), it must circle exactly once per day. Meanwhile, part 3’s rule then FIXES its distance — no choice: r³ = GMT²/4π² gives r ≈ 42,300 km from Earth’s centre, i.e. Plus two more conditions: circle directly above the equator, moving eastward. All three together = ‘geostationary’.

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