Gravitation NEET Notes: Complete Guide with Formulas & Solved Examples

Gravitation
for NEET Physics

Q: Why is gravitational potential energy negative?

It is negative because work is done by the gravitational field to bring a mass from infinity to that point. By convention, potential energy at infinity is zero, so at finite distance it is less than zero.

Q: What is the difference between g and G?

g is acceleration due to gravity (varies with location), G is the universal gravitational constant (constant everywhere in the universe).

Q: Can a satellite orbit in any plane around Earth?

Yes, theoretically. But geostationary satellites must be in equatorial plane; polar orbits are in plane through poles.

Q: Does escape velocity depend on the mass of the escaping object?

No, escape velocity depends only on the mass and radius of the planet/body, not on the mass of the object escaping.

Master Newton's law of gravitation, Kepler's laws, variation of g, gravitational potential, satellites, and escape velocity — the cosmic force explained for NEET aspirants.

Newton's Law Kepler's Laws Variation of g Gravitational Potential Satellites Escape Velocity

📌 What you'll learn: NEET-level problem solving • All essential formulas • Step-by-step numericals • Quick revision hacks

🔍 Detailed concept explanation

🌌 1. Newton's 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 m₁m₂ / r², where G = 6.67×10⁻¹¹ Nm²/kg² (universal gravitational constant).

Characteristics: Central force, conservative, acts along line joining centers, independent of medium.

➕ 2. Principle of Superposition

Net gravitational force on a mass due to multiple masses is the vector sum of individual forces: F_net = F₁ + F₂ + F₃ + ...

📉 3. Acceleration Due to Gravity (g)

g = GM/R² (at surface). Variation:

Height h: g' = g (1 - 2h/R) for h << R; g' = GM/(R+h)² for larger h.
Depth d: g' = g (1 - d/R). At center, g = 0.
Latitude λ: g' = g – ω²R cos²λ (due to Earth's rotation). At poles λ=90°, g'=g; at equator λ=0°, g' minimum.

🌀 4. Gravitational Field and Potential

Field intensity E = F/m = GM/r² (radially inward). Gravitational potential V = –GM/r (at infinity zero). Relation: E = –dV/dr.

For spherical shell: Inside (r

For solid sphere: Inside: E = GMr/R³, V = –(GM/2R³)(3R² – r²); Outside: same as point mass.

🛰️ 5. Kepler's Laws of Planetary Motion

First law (Law of orbits): All planets move in elliptical orbits with the Sun at one focus.

Second law (Law of areas): Radius vector sweeps equal areas in equal times (areal velocity constant) — consequence of angular momentum conservation.

Third law (Law of periods): T² ∝ a³, where T is time period and a is semi-major axis. For circular orbits, T² = (4π²/GM)r³.

🚀 6. Satellites

Orbital velocity: v₀ = √(GM/r) = √(gR²/(R+h)). For low Earth orbit, v₀ ≈ 7.9 km/s.

Time period: T = 2πr/v₀ = 2π√(r³/GM).

Escape velocity: vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km/s for Earth.

Geostationary satellites: Orbit above equator, T = 24 h, height ≈ 36,000 km. Polar satellites: pass over poles, used for weather/imaging.

💫 7. Gravitational Potential Energy

For two masses: U = –Gm₁m₂/r (negative, increases with separation). For system of particles, sum over all pairs.

📋 Complete formula sheet

Newton's law F = Gm₁m₂/r²

g at surface g = GM/R²

g with height g' = g (1 - 2h/R) [h<

g with depth g' = g (1 - d/R)

Gravitational field E = GM/r²

Gravitational potential V = –GM/r

Orbital velocity v₀ = √(GM/r)

Escape velocity vₑ = √(2GM/R)

Kepler's third law T² ∝ r³

Potential energy U = –GMm/r

Quantity	Formula
Orbital time period	T = 2π√(r³/GM)
Kinetic energy in orbit	KE = GMm/(2r)
Total energy in orbit	E = –GMm/(2r) (bound system)
Binding energy	BE = +GMm/(2r)
Height of geostationary satellite	h = (GMT²/4π²)⅓ – R ≈ 36,000 km
Gravitational field inside solid sphere	E = GMr/R³

✏️ Solved NEET-level examples

Example 1 (Variation of g)

At what height above Earth's surface does acceleration due to gravity become 64% of its value on the surface? (R = 6400 km)

1 g' = g R²/(R+h)². Given g' = 0.64 g ⇒ R²/(R+h)² = 0.64.

2 Taking square root: R/(R+h) = 0.8 ⇒ R = 0.8R + 0.8h ⇒ 0.2R = 0.8h.

3 h = (0.2/0.8)R = R/4 = 6400/4 = 1600 km.

Example 2 (Satellite)

A satellite orbits Earth at a height of 3600 km above surface. Find orbital velocity and time period. (R = 6400 km, M = 6×10²⁴ kg, G = 6.67×10⁻¹¹ SI units)

1 r = R + h = 6400 + 3600 = 10,000 km = 10⁷ m.

2 v₀ = √(GM/r) = √[(6.67×10⁻¹¹ × 6×10²⁴)/10⁷] = √(4.002×10¹⁴/10⁷) = √(4.002×10⁷) ≈ √(4×10⁷) = 6324.5 m/s ≈ 6.32 km/s.

3 T = 2πr/v₀ = 2×3.14×10⁷ / 6324.5 ≈ 6.28×10⁷/6324.5 ≈ 9927 s ≈ 2.76 h.

Example 3 (Escape velocity)

Calculate escape velocity on a planet whose mass is 8 times Earth and radius is 2 times Earth. (Earth's escape velocity = 11.2 km/s)

1 vₑ = √(2GM/R). For planet: vₑ' = √(2G(8M)/(2R)) = √(8/2 × 2GM/R) = √(4 × 2GM/R).

2 vₑ' = √4 × √(2GM/R) = 2 × 11.2 = 22.4 km/s.

Example 4 (Kepler's third law)

Two planets orbit the Sun with radii r₁ and r₂. If T₁/T₂ = 8, find r₁/r₂.

1 From Kepler's third: T² ∝ r³ ⇒ (T₁/T₂)² = (r₁/r₂)³.

2 (8)² = 64 = (r₁/r₂)³ ⇒ r₁/r₂ = 64⅓ = 4.

📈 Important graphs & key points

g vs r (distance from center) : increases linearly inside (solid sphere), then 1/r² outside
V vs r : –GM/R constant inside shell, –GM/r outside
E vs r : zero inside shell, peak at surface, then 1/r²
Kepler's second law : areal velocity constant → angular momentum conserved

⭐ Gravitational force is conservative: work done in closed loop is zero.

⚡ Quick revision box

Newton's law F = Gm₁m₂/r², G = 6.67×10⁻¹¹

g variation g' = g(1-2h/R) [height], g' = g(1-d/R) [depth]

Orbital mechanics v₀ = √(GM/r), T² ∝ r³, vₑ = √(2GM/R)

Energy in orbit KE = –E, PE = 2E, E = –GMm/(2r)

⚠️ Common mistakes to avoid

Taking g constant at all heights — it varies significantly for h comparable to R.
Forgetting that gravitational potential is negative and increases (becomes less negative) with distance.
Confusing orbital velocity and escape velocity: vₑ = √2 v₀.
Using radius of Earth instead of distance from center in orbital formulas.
Ignoring vector nature of gravitational field (direction always toward mass).
In superposition, forgetting to add forces as vectors.

🧠 Exam strategy tips

Memorize standard values: g=9.8, R=6400 km, G=6.67×10⁻¹¹ for quick calculations.
For satellite problems, remember that total energy is negative for bound orbits.
In Kepler's law questions, use proportionality to avoid lengthy calculations.
Draw diagrams for gravitational field due to multiple masses to apply superposition correctly.
Practice problems on geostationary satellites — they often appear.

❓ Frequently asked questions

📌 Why is gravitational potential energy negative?