Gravitation — Class 11 Physics: quick revision, 15 bites

Every Mass Pulls Every Other Mass

Gravity is universal — not just Earth's.

Newton's law of gravitation states that **every particle of matter attracts every other particle** with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Takeaway. Gravitation is a universal, always-attractive, action-at-a-distance force between any two masses.

The Universal Gravitational Constant G

One number rules all gravity.

Takeaway. G is a universal constant — its tiny value explains why gravity feels weak between everyday objects.

G vs g — Don't Mix Them Up

G and g are NOT the same.

Takeaway. G is a fixed universal constant; g is a local value that changes with position.

Acceleration Due to Gravity on Earth

Why g equals 9.8 m/s².

Equating gravitational force to weight $mg$ gives the surface value of g.

Takeaway. g depends only on the mass and radius of the planet — not on the mass of the falling object.

Heavier Objects Do NOT Fall Faster

Feather vs coin — same g, different drag.

Takeaway. g is independent of the falling object's mass — heavier objects don't fall faster in vacuum.

Variation of g with Height and Depth

g shrinks as you climb or dig.

Takeaway. g decreases with height (≈ 1 − 2h/R) and decreases linearly with depth (1 − d/R), becoming zero at Earth's centre.

Kepler's Three Laws of Planetary Motion

Planets follow three elegant rules.

Takeaway. Kepler's laws are empirical; Newton's law of gravitation explains all three.

Gravitational Potential Energy

The minus sign matters here.

For two masses separated by distance r, gravitational potential energy is taken as zero at infinity.

Takeaway. U is always negative for a bound system — energy must be supplied to separate masses to infinity.

Escape Velocity — Break Free from Earth

11.2 km/s and you're gone.

Takeaway. Escape velocity is the minimum speed needed to leave a planet's gravity permanently — ~11.2 km/s for Earth.

Orbital Velocity of a Satellite

The speed that keeps you circling.

For a satellite in a circular orbit of radius r, gravitational force provides the centripetal force.

Takeaway. Orbital velocity decreases with orbital radius; near Earth it's about 7.9 km/s.

Why Astronauts Float in Orbit

They're falling — just missing Earth.

Takeaway. Weightlessness in orbit = free fall, not zero gravity.

Gravity in Everyday Life

Gravity runs the solar system and your GPS.

Takeaway. Gravitation is not abstract — it powers tides, satellites, and space exploration.

High-Yield Exam Formulas

Memorise these five — they cover most questions.

Takeaway. These five formulas solve the majority of numericals in this chapter.

Remember Escape vs Orbital

Escape is √2 times orbital.

Since $v_e = \sqrt{2GM/R}$ and $v_o = \sqrt{GM/R}$, we get **$v_e = \sqrt{2}\, v_o$** — escape velocity is always √2 (≈1.41) times the near-surface orbital velocity.

Takeaway. v_e = √2 · v_o — a quick ratio to remember for numericals.

Gravity Is the Weakest Fundamental Force

Yet it shapes the cosmos.

Gravitation is by far the **weakest** of the four fundamental forces — but because it is always attractive and has infinite range, it dominates at cosmic scales, shaping galaxies, stars, and planets.

Takeaway. Weak locally, dominant cosmically — gravity's range and universality make it the architect of the universe.