Note: This chapter was removed from the NCERT curriculum in the 2022 rationalization. Retained here as gravitation underlies orbital mechanics, satellite technology, ocean tides (tidal energy), and geophysics — GS3 science & technology.

Gravitation is the force that holds planets in orbit, causes ocean tides, and determines whether a submarine sinks or floats. For UPSC, this chapter connects to India's tidal energy potential (Gulf of Khambhat, Gulf of Kutch), submarine technology (INS Arihant), space missions, and the geophysics behind gravity surveys for mineral exploration. GS3 tests energy sources, ocean energy, and science & technology — gravitation is the thread connecting all three.

PART 1 — Quick Reference Tables

Gravitation — Core Quantities

Quantity Value / Formula Notes
Universal Gravitational Constant (G) 6.674 × 10⁻¹¹ N⋅m²/kg² Same everywhere in universe; discovered experimentally by Cavendish (1798)
g on Earth surface 9.8 m/s² (≈ 10 m/s²) Acceleration due to gravity; varies slightly by location
g on Moon 1.62 m/s² (≈ g/6) Astronaut weighs 1/6th on Moon; same mass
Gravitational Force (F) F = G(m₁m₂)/r² Inverse square law; doubles distance → force reduces to 1/4th
Weight (W) W = mg Force of gravity on mass; measured in Newtons; changes with location
Mass (m) constant Amount of matter; measured in kg; same everywhere in universe

Tides — Types and Causes

Tide Type Cause Effect Timing
High Tide Moon's gravity pulls ocean water toward it on near side Sea level rises at coast When coast faces Moon
Low Tide Water drawn away from that coast toward Moon Sea level falls When coast is 90° from Moon
Inertial bulge Water on far side left behind as Earth accelerates toward Moon Second high tide Opposite side of Earth from Moon
Spring Tide Sun + Moon aligned (new/full moon) → gravitational forces add up Highest high tides, lowest low tides New and Full Moon
Neap Tide Sun + Moon at right angles (quarter moon) → partially cancel Weaker tides Quarter Moon phases

India's Ocean Energy Potential

Source Estimated Potential Key Sites Status
Tidal energy ~9.6 GW total Gulf of Khambhat (~8.5 GW), Gulf of Kutch (~1.1 GW), Sundarbans (~100 MW) No commercial plant yet in India
Wave energy ~40 GW (Indian coastline) West coast (higher wave energy) Pilot projects by NIOT
Ocean Thermal Energy Conversion (OTEC) Large potential Lakshadweep Islands, Andaman coast NIOT pilot plant operational
Ocean current energy Significant Gulf of Mannar, Palk Strait Research stage

PART 2 — Detailed Notes

1. Newton's Universal Law of Gravitation

Every particle in the universe attracts every other particle with a gravitational force that is:

  • Directly proportional to the product of their masses (more mass → stronger pull)
  • Inversely proportional to the square of the distance between them (farther apart → much weaker pull)

F = G(m₁m₂)/r²

G = 6.674 × 10⁻¹¹ N⋅m²/kg² (universal gravitational constant — same everywhere).

This inverse square law is profound: double the distance → force becomes 1/4th; triple the distance → force becomes 1/9th. This is why gravity from distant stars, though real, is negligible.

Key Term

The Universal Law of Gravitation is "universal" because it applies to ALL objects with mass — not just large bodies like planets. Two people sitting 1 metre apart exert gravitational force on each other, but the force is unimaginably small (G is extremely small). Gravity becomes significant only when at least one mass is very large (a planet, star, etc.).

2. Gravitational Acceleration (g)

The acceleration due to gravity near Earth's surface is derived from Newton's law:

g = GM/R² where M = Earth's mass (5.97 × 10²⁴ kg), R = Earth's radius (6.371 × 10⁶ m), G = 6.674 × 10⁻¹¹ N⋅m²/kg² → g ≈ 9.8 m/s²

Variations in g:

  • With altitude: g decreases as you move away from Earth's surface (r increases in g = GM/r²). At very high altitudes (satellites), g is still non-zero — satellites are in continuous free fall.
  • With depth: g also decreases as you go below Earth's surface.
  • With latitude: g is slightly higher at poles than at the equator because (a) Earth is oblate (flattened at poles) — poles are closer to Earth's centre, and (b) Earth's rotation creates a centrifugal effect at the equator that slightly reduces effective g. g(poles) ≈ 9.83 m/s²; g(equator) ≈ 9.78 m/s².

3. Mass vs Weight

Property Mass Weight
Definition Amount of matter in a body Gravitational force acting on a body
Formula — (intrinsic property) W = mg
Unit kilogram (kg) Newton (N); sometimes expressed in kgf
Type Scalar Vector
Varies with location? No — same on Moon, Mars, ISS Yes — less on Moon, zero in free fall
Explainer

An astronaut of mass 70 kg has mass = 70 kg everywhere. On Earth: weight = 70 × 9.8 = 686 N. On Moon: weight = 70 × 1.62 = 113.4 N (about 1/6th). On ISS in orbit: the astronaut is in free fall → apparent weight = 0 (weightlessness) → mass is still 70 kg. This is why mass is the fundamental measure of "how much matter," not weight.

4. Free Fall and Terminal Velocity

Free fall: Motion under gravity alone, with no air resistance. All objects fall with the same acceleration g, regardless of mass (Galileo's famous Leaning Tower of Pisa experiment — a 10 kg and a 1 kg ball dropped together hit the ground simultaneously in vacuum).

Terminal velocity: In reality, air resistance acts upward on a falling object. As speed increases, air resistance increases. Eventually, air resistance = gravitational force → net force = 0 → acceleration = 0 → object falls at constant speed (terminal velocity).

  • Skydivers in free-fall position: terminal velocity ~195 km/h; with parachute deployed: ~18–20 km/h (parachute increases drag dramatically)
  • Raindrops: terminal velocity depends on size; a large raindrop falls at ~9 m/s — without terminal velocity (if no air resistance), raindrops would reach ~200 km/h and be lethal

5. Tides — Gravitation at Planetary Scale

Tides are caused by the differential gravitational pull of the Moon (and to a lesser extent the Sun) on different parts of Earth.

The Moon's gravity is stronger on the side of Earth facing the Moon — it pulls ocean water toward it, creating a high tide. On the far side of Earth, the Moon's pull is weakest — Earth's centre is pulled toward the Moon more than the far side water → the far side water is "left behind" → another high tide (inertial bulge).

Between these two high tides, water is drawn away → two low tides per day (one between each pair of high tides). This gives most coastal regions two high tides and two low tides approximately every 24 hours and 50 minutes (slightly more than 24 hours because the Moon also orbits Earth).

UPSC Connect

UPSC GS3 — Tidal Energy and India's Ocean Energy Potential:

Tidal energy is a predictable, renewable, and non-intermittent energy source (unlike solar and wind). It harnesses the kinetic and potential energy of tidal flows.

India's tidal energy potential:

  • Gulf of Khambhat (Cambay), Gujarat: ~8.5 GW potential — highest in India due to large tidal range (up to 11 metres — among the highest in the world) and funnel shape that amplifies tides
  • Gulf of Kutch, Gujarat: ~1.1 GW potential; also large tidal ranges
  • Sundarbans, West Bengal: ~100 MW potential; ecologically sensitive area — development challenging

Why no commercial tidal plant in India yet:

  • High upfront capital cost; complex marine engineering
  • Environmental concerns (barrages affect fish migration, estuarine ecology)
  • Alternative: tidal stream generators (like underwater wind turbines) — less ecological impact but lower output

Globally operational tidal plants:

  • La Rance Tidal Power Station, France (1966) — world's first and one of the largest; 240 MW capacity; barrage type
  • Annapolis Royal, Canada — 20 MW; oldest tidal plant in North America
  • Sihwa Lake Tidal Power Station, South Korea (2011) — 254 MW; currently world's largest tidal power plant

National Institute of Ocean Technology (NIOT), Chennai: India's nodal body for ocean energy R&D under the Ministry of Earth Sciences. Working on tidal current energy devices, wave energy converters, and OTEC (Ocean Thermal Energy Conversion) plants.

Ministry of New and Renewable Energy (MNRE): Responsible for promoting ocean energy in India. Ocean energy included under renewable energy for meeting RPO (Renewable Purchase Obligation) targets.

6. Archimedes' Principle and Buoyancy

Archimedes' Principle: Any object fully or partially submerged in a fluid (liquid or gas) experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

Buoyant force = weight of displaced fluid = ρ_fluid × V_submerged × g

  • If buoyant force > weight of object → object floats
  • If buoyant force < weight of object → object sinks
  • If buoyant force = weight of object → object is in neutral buoyancy (floats at that depth)

This is equivalent to saying: objects float if their average density is less than the fluid's density (a hollow steel ship floats because its average density — including the air inside — is less than water's density).

UPSC Connect

UPSC GS3 — Submarines and Buoyancy:

Submarines control their buoyancy using ballast tanks:

  • To dive: Open valves to let seawater flood ballast tanks → average density of submarine increases → buoyant force < weight → submarine sinks
  • To surface: Blow compressed air into ballast tanks, expelling seawater → average density decreases → buoyant force > weight → submarine rises
  • Neutral buoyancy: Balance ballast precisely → submarine hovers at desired depth without using engine power

INS Arihant: India's first indigenous nuclear-powered ballistic missile submarine (SSBN — Ship Submersible Ballistic Nuclear). Displacement: ~6,000 tonnes when submerged. Nuclear reactor provides propulsion without need to surface for air (unlike conventional diesel-electric submarines). Commissioned 2016. Armed with K-15 Sagarika SLBMs (submarine-launched ballistic missiles, range ~700 km) and K-4 missiles (range ~3,500 km). Strategic importance: Completes India's nuclear triad (land, air, and sea-based nuclear capability) — critical for second-strike capability, which underpins India's No-First-Use (NFU) nuclear doctrine.

Scorpène-class submarines (Kalvari class): Six conventional (diesel-electric) submarines built under Project-75 at Mazagon Dock Shipbuilders Limited (MDSL), Mumbai, in collaboration with Naval Group (France). INS Kalvari (first of class) commissioned 2017. Quieter than nuclear submarines for shallow water operations.

Project-75 India (P-75I): Follow-on programme for 6 advanced conventional submarines with air-independent propulsion (AIP) — allows submerged operation without surfacing for air; longer endurance. Under strategic partnership model.

7. Gravity in Geophysics

Variations in Earth's gravitational field (measured by gravimeters) reveal subsurface geological structures:

  • Gravity high: Dense rock (basalt, ore bodies) below surface → more mass → stronger g
  • Gravity low: Less dense rock (salt domes, sedimentary basins — often associated with oil) → less mass → weaker g

Gravity surveys help locate oil and gas fields, groundwater aquifers, and mineral deposits. The National Geophysical Research Institute (NGRI), Hyderabad conducts gravity surveys across India.

India's GRACE (Gravity Recovery and Climate Experiment) satellite data: NASA-Germany mission; revealed groundwater depletion rates in India (Indo-Gangetic Plain — one of the fastest depleting aquifers in the world). This data informed India's groundwater policy and the National Aquifer Mapping Programme (NAQUIM).

Exam Strategy

Prelims traps:

  • Mass is constant everywhere; weight varies — weight is zero in free fall but mass is NOT zero
  • g on Moon ≈ 1/6th of Earth's g (1.62 m/s²) — not 1/4th or 1/8th
  • Spring tides occur at new moon AND full moon (both, not just one); neap tides at quarter moon
  • Gulf of Khambhat (not Kutch) has the higher tidal energy potential (~8.5 GW vs ~1.1 GW)
  • La Rance (France) — world's first large tidal power station; Sihwa Lake (South Korea) — currently world's largest
  • INS Arihant is an SSBN (nuclear ballistic missile submarine), not a fast-attack submarine
  • India's nuclear triad: land (Agni missiles) + air (aircraft-delivered) + sea (INS Arihant Sagarika/K-4 SLBMs)

Mains linkages:

  • Tidal energy → India's coastal geography (Gulf of Khambhat shape) → clean energy targets → challenges of cost and ecology
  • Nuclear triad → INS Arihant → No-First-Use doctrine → credible minimum deterrence → maritime security
  • Gravity surveys → oil/gas exploration → import dependency → energy security

Previous Year Questions

Prelims:

  1. Which of the following pairs of locations in India is correctly matched with their tidal energy potential?
    (a) Gulf of Kutch — 8.5 GW; Gulf of Khambhat — 1.1 GW
    (b) Gulf of Khambhat — 8.5 GW; Gulf of Kutch — 1.1 GW
    (c) Gulf of Mannar — 8.5 GW; Gulf of Kutch — 1.1 GW
    (d) Gulf of Khambhat — 1.1 GW; Sundarbans — 8.5 GW

  2. With reference to INS Arihant, consider the following statements: 1. It is India's first indigenous nuclear-powered submarine. 2. It completes India's nuclear triad. 3. It is classified as an SSBN. Which of the above are correct?
    (a) 1 and 2 only
    (b) 2 and 3 only
    (c) 1, 2 and 3
    (d) 1 only

Mains:

  1. India has significant ocean energy potential but has yet to harness it commercially. Examine the types of ocean energy available to India, their potential, and the challenges in their exploitation. (CSE Mains 2021, GS Paper 3, 15 marks)