Gravitation is the universal force of attraction acting between all bodies with mass, keeping objects grounded and governing planetary motion.

What is the universal law of gravitation?

Every particle in the universe 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: \( F = G \frac{m_1 m_2}{r^2} \), where \( G = 6.67 \times 10^{-11} \, \mathrm{N \, m^2 \, kg^{-2}} \).

What are Kepler's laws of planetary motion?

(1) Law of Orbits: Planets move in elliptical orbits with the Sun at one focus. (2) Law of Areas: The line from Sun to planet sweeps equal areas in equal times. (3) Law of Periods: \( T^2 \propto a^3 \), where \( T \) is orbital period and \( a \) is semi-major axis.

What is acceleration due to gravity (\( g \))?

\( g = \frac{GM_E}{R_E^2} \approx 9.8 \, \mathrm{m/s^2} \), where \( M_E \) is Earth's mass and \( R_E \) is Earth's radius.

How does \( g \) vary with height \( h \) above Earth's surface?

\( g_h = g \left(1 - \frac{2h}{R_E}\right) \) for \( h \ll R_E \); more generally \( g_h = \frac{GM_E}{(R_E + h)^2} \).

How does \( g \) vary with depth \( d \) below Earth's surface?

\( g_d = g \left(1 - \frac{d}{R_E}\right) \).

What is gravitational potential energy?

For two masses, \( U = -\frac{G m_1 m_2}{r} \) (zero at infinity).

What is escape speed?

Minimum speed to escape Earth's gravity: \( v_e = \sqrt{\frac{2GM_E}{R_E}} = \sqrt{2g R_E} \approx 11.2 \, \mathrm{km/s} \).

What is orbital velocity for a satellite?

\( v_o = \sqrt{\frac{GM_E}{r}} \), where \( r = R_E + h \); relates to escape speed by \( v_e = \sqrt{2} v_o \).

Why is gravitational force conservative?

Work done by gravity is path-independent, allowing definition of potential energy and conservation of mechanical energy in the gravitational field.

What is gravitational field?

Force per unit mass: \( \vec{g} = -\frac{GM}{r^2} \hat{r} \); scalar potential \( V = -\frac{GM}{r} \).

Why do satellites appear weightless?

Both satellite and occupants are in free fall toward Earth with the same acceleration, so no normal reaction is exerted on the body.

What is a geostationary satellite?

A satellite in circular equatorial orbit with time period \( T = 24 \,\text{h} \) at height \( h \approx 36{,}000 \,\text{km} \) that appears fixed over one point on Earth.

Calculate orbital period for low Earth orbit satellite.

For a satellite very close to Earth’s surface, \( T_0 = 2\pi \sqrt{\frac{R_E}{g}} \approx 85 \,\text{min} \).

If distance between two masses triples, what happens to force?

The gravitational force becomes \( \frac{1}{9} \) of the original, because \( F \propto \frac{1}{r^2} \).

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🪐 Master Gravitation
NCERT Class 11 · Chapter 8

Real PYQs from top competitive exams — filter by exam, attempt each question, track your progress and submit to see your full score report.

Attempt PYQs Study Strategy

Kepler's LawsOrbital VelocityEscape VelocityGravitational PESatellites

Real PYQs

Exam Bodies

15+

Years Covered

~8%

Exam Weightage

PYQs Overview

🌍

Universal Law of Gravitation

F = Gm₁m₂/r²; G = 6.67×10⁻¹¹; superposition principle.

★★★★★

92% Frequency

🛸

Orbital & Escape Velocity

v_o = √(GM/R); v_e = √(2GM/R) = √2 × v_o.

★★★★★

94% Frequency

🪐

Kepler's Laws of Planetary Motion

Law of orbits, areas, periods — T² ∝ r³.

★★★★★

88% Frequency

📡

Satellites — Geostationary

Height, orbital period, synchronous orbit conditions.

★★★★☆

78% Frequency

⚡

Gravitational PE & Field

U = –GMm/r; g at height h and depth d.

★★★★☆

82% Frequency

🌊

Variation of g

With altitude, depth, latitude, rotation of Earth.

★★★★☆

75% Frequency

Topic Frequency

Orbital & Escape Velocity 94%

Universal Gravitation 92%

Kepler's Laws 88%

Gravitational PE 82%

Satellites 78%

Variation of g 75%

Binding Energy 58%

💡 Did You Know?

v_escape = √2 v_orbital — asked every exam
Kepler's third law T² ∝ r³ — zero skips in JEE
g at height h — asked 11× in NEET
Geostationary orbit height ≈ 36,000 km
Chapter 8 = gateway to astrophysics

Key Takeaways

🔑

Escape velocity = √2 × orbital velocity

v_e = √(2GM/R); v_o = √(GM/R). Ratio is fixed at √2.

⚡

Kepler's third law: T² ∝ a³

a = semi-major axis. True for all planets around same star.

📐

g decreases both above and below surface

Above: g ∝ 1/r². Below: g ∝ r (g = 0 at centre).

🌊

Gravitational PE = –GMm/r (negative)

PE increases (becomes less negative) as r increases. PE = 0 at r = ∞.

🧮

Geostationary satellite: T = 24 h

Orbits in equatorial plane, west to east, h ≈ 36,000 km.

🎯

Binding Energy = –(Total ME) = GMm/2r

Energy required to remove satellite from orbit.

Study Strategy

Newton's Law of GravitationDay 1–2

F = Gm₁m₂/r²; superposition; shell theorem.

Gravitational Field & PEDay 3

g at h, d, latitude; gravitational PE = –GMm/r.

Orbital & Escape VelocityDay 4

Derive both; relationship between them; 20 numerical problems.

Kepler's LawsDay 5

All three laws; apply T² ∝ r³ to problems — 15 problems.

SatellitesDay 6

Geostationary, polar, energy of satellite — 15 problems.

Attempt All PYQsDay 7

Orbital velocity, escape velocity, Kepler's laws = top priority.

Mock TestDay 8

30-Q timed. Ratio problems (v_e/v_o) are classic favourites.

🗓️ 8-Day Chapter Plan

Day 1–2	Newton's Law of Gravitation
Day 3	Gravitational Field & PE
Day 4	Orbital & Escape Velocity
Day 5	Kepler's Laws
Day 6	Satellites
Day 7	Attempt All PYQs
Day 8	Mock Test

🧠 Pro Tip: v_e = √2 × v_o is the most-asked single fact in this chapter. Derive it once, memorise it forever.

🚀

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NCERT Class 11 Physics Gravitation PYQs – JEE, NEET & Entrance Exam Questions

NCERT Class 11 Physics Gravitation PYQs – JEE, NEET & Entrance Exam Questions — Complete Notes & Solutions · academia-aeternum.com

Gravitation is one of the most fundamental interactions in nature, governing the motion of planets, satellites, stars, and even objects we experience in everyday life. In this chapter, we move from familiar observations—such as objects falling towards the Earth—to a universal law that explains how every mass in the universe attracts every other mass. The chapter develops a clear logical bridge between Newton’s Universal Law of Gravitation and its wide-ranging consequences, including…

🎓 Class 11 📐 Physics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

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