NDA Physics · Teaching notes

Gravitation — NDA Physics

Gravitation is the universal pull every mass exerts on every other mass — the force that holds you to the ground, keeps the Moon in orbit, and shapes the solar system. For the NDA it is a compact, formula-driven earner that splits into three movements: (1) Newton's Law of Gravitation — the inverse-square law F = Gm₁m₂/r², the universal constant G, and the action-reaction nature of the force; (2) Gravitational Field and Potential — surface gravity g = GM/R², how g depends on a planet's mass, radius and density, the field-versus-potential distinction, and weightlessness in orbit; (3) Orbits, Kepler and Escape — Kepler's third law T² ∝ a³, orbital and escape speeds, and what actually keeps a satellite up. Almost every mark comes from one of a handful of formulas and from scaling them correctly when a planet's mass, radius or density is changed by a factor. Learn the formulas, track the powers, and the marks follow.

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Subtopic notes

PYQ weightage by concept

14 concepts · 17 PYQs — where the marks actually sit, so you know what to drill first

Newton's Law of Gravitation6 PYQs · 35%

Concept	PYQs	Share
The universal gravitational constant G	3	18%
Gravitational force is action-reaction — equal and opposite	2	12%
Scaling the force — changing masses and distance together	1	6%
Newton's law of gravitation — the inverse-square lawfoundation	—	—

Gravitational Field and Potential7 PYQs · 41%

Concept	PYQs	Share
g is the same for all bodies — free fall and weight	2	12%
Surface gravity — g = GM/R²	1	6%
Surface gravity from density — g = (4/3)πGρR	1	6%
Average density of a composite body	1	6%
Gravitational field versus potential	1	6%
Weightlessness in orbit — zero normal reaction	1	6%

Orbits, Kepler and Escape4 PYQs · 24%

Concept	PYQs	Share
Kepler's third law — T² ∝ a³	2	12%
Escape velocity — v_e = √(2GM/R) and how it scales	1	6%
What keeps a satellite up — no fuel required	1	6%
Orbital velocity — v_o = √(GM/R)foundation	—	—

Formula & revision sheet

13 formulas · 1 reference tables · 17 gotchas across all subtopics — the exam-eve cheat-sheet

Newton's Law of Gravitation

Formulas (3)

Newton's law of gravitation — the inverse-square law · Newton's law of gravitation $F = \dfrac{G\,m_1 m_2}{r^2}$
Scaling the force — changing masses and distance together · Force scaling factor $\dfrac{F'}{F} = \dfrac{a \cdot b}{c^2}$
Gravitational force is action-reaction — equal and opposite · Action-reaction pair $\vec{F}_{12} = -\,\vec{F}_{21}, \qquad |\vec{F}_{12}| = |\vec{F}_{21}| = \dfrac{G m_1 m_2}{r^2}$

Reference tables (1)

The universal gravitational constant G5 rows

Property	Value / Statement
SI unit	N·m²/kg² (newton metre-squared per kilogram-squared)Q NDA 2025 — the unit of G is N-m²/kg², derived from G = Fr²/(m₁m₂).
Dimensional formula	M⁻¹L³T⁻²
Approximate value	6.674 × 10⁻¹¹ N·m²/kg²
Universality	Same for ALL pairs of bodies, everywhere; independent of mass, distance, location, or local gQ NDA 2017 — G is a universal constant; it does NOT depend on the local value of g.
Force, in contrast, is NOT universal	F itself depends on the masses and separation, so it differs for every pair of bodiesQ NDA 2018 — the false statement is 'gravitational force is the same for all pairs of bodies'. The force varies; only G is constant.

G is the constant; the FORCE is not. Don't confuse 'G is universal' with 'the gravitational force is the same for all bodies' — the latter is false.

Watch out for (5)

Distance enters as a square, masses do not
→ Newton's law of gravitation — the inverse-square law
G is universal, but the FORCE is not
→ The universal gravitational constant G
Don't confuse G with g
→ The universal gravitational constant G
Square only the distance factor
→ Scaling the force — changing masses and distance together
The bigger mass does NOT exert the bigger force
→ Gravitational force is action-reaction — equal and opposite

Gravitational Field and Potential

Formulas (6)

Surface gravity — g = GM/R² · Surface gravity $g = \dfrac{GM}{R^2}$
Surface gravity from density — g = (4/3)πGρR · Surface gravity from density $g = \dfrac{4}{3}\pi G \rho R$
Average density of a composite body · Average density of a composite body $\bar{\rho} = \dfrac{m_1 + m_2}{V_{\text{total}}} = \dfrac{\rho_1 V_1 + \rho_2 V_2}{V_1 + V_2}$
Gravitational field versus potential · Work and equal potential $W = -\,m\,(V_B - V_A); \qquad V_A = V_B \Rightarrow W = 0$
Weightlessness in orbit — zero normal reaction · Apparent weight = normal reaction $W_{\text{apparent}} = N = 0 \quad (\text{free fall}); \qquad F_{\text{gravity}} \neq 0$
g is the same for all bodies — free fall and weight · Weight and spring extension scale with g $W = mg, \qquad x = \dfrac{mg}{k} \propto g$

Watch out for (7)

Radius enters as a square in g, just like in F
→ Surface gravity — g = GM/R²
Same density does NOT mean same gravity
→ Surface gravity from density — g = (4/3)πGρR
Average density is volume-weighted, not the mean of densities
→ Average density of a composite body
Equal potential, not equal field, decides the work
→ Gravitational field versus potential
Weightless does NOT mean gravity-free
→ Weightlessness in orbit — zero normal reaction
In vacuum, mass and shape don't change the fall time
→ g is the same for all bodies — free fall and weight
Spring extension follows g, not just the mass
→ g is the same for all bodies — free fall and weight

Orbits, Kepler and Escape

Formulas (4)

Kepler's third law — T² ∝ a³ · Kepler's third law $T^2 \propto a^3 \qquad\Longleftrightarrow\qquad \dfrac{T_1}{T_2} = \left(\dfrac{a_1}{a_2}\right)^{3/2}$
Orbital velocity — v_o = √(GM/R) · Orbital velocity $v_o = \sqrt{\dfrac{GM}{R}}$
Escape velocity — v_e = √(2GM/R) and how it scales · Escape velocity and its density scaling $v_e = \sqrt{\dfrac{2GM}{R}} = \sqrt{2gR}; \qquad v_e \propto R\sqrt{\rho}$
What keeps a satellite up — no fuel required · Orbit is sustained by gravity alone $F_{\text{gravity}} = \dfrac{GMm}{R^2} = \dfrac{mv_o^2}{R} \;\Rightarrow\; \text{no propulsion needed}$

Watch out for (5)

It's T² ∝ a³, not T ∝ a
→ Kepler's third law — T² ∝ a³
Orbital speed is set by the orbit, not the satellite
→ Orbital velocity — v_o = √(GM/R)
Halving R while quadrupling ρ leaves v_e UNCHANGED
→ Escape velocity — v_e = √(2GM/R) and how it scales
Escape velocity is independent of the projectile's mass and launch angle
→ Escape velocity — v_e = √(2GM/R) and how it scales
Orbiting needs no fuel — gravity does the work
→ What keeps a satellite up — no fuel required