Quick Revision Gravitation

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Quick concept reinforcement. 20 cards covering all key ideas.

Question

What is Newton's Universal Law of Gravitation?

F = Gm₁m₂/r²

G = 6.674×10⁻¹¹ N·m²/kg². Always attractive. Acts along the line joining centres.

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📋 Formula Dump — All in One Place

⚖️ Forces & Gravity

F = Gm₁m₂/r²

Newton's law. r = centre to centre

g = GM/R²

Surface gravity. g = 9.8 m/s²

g_h = g(1−2h/R)

Height (approx, h<<R)

g_h = GM/(R+h)²

Height (exact formula)

g_d = g(1−d/R)

Depth (linear decrease)

g' = g−ω²Rcos²λ

Due to rotation. Max at equator.

🚀 Escape & Orbital Velocity

Vₑ = √(2GM/R)

Escape velocity. = √(2gR)

Vₑ = R√(8πGρ/3)

Density form. Vₑ ∝ R (same ρ)

v₀ = √(GM/r)

Orbital speed. r = R+h

Vₑ = √2 × v₀(surface)

Relation between Vₑ and v₀

📏 Kepler's Laws

T² = 4π²a³/GM

3rd law. a = semi-major axis

T₁²/T₂² = r₁³/r₂³

Ratio form. Use for NEET speed.

dA/dt = L/2m = const

2nd law = angular momentum conservation

🛸 Satellites

T = 2π√(r³/GM)

Period. Near Earth ≈ 84 min

E = −GMm/2r

Total energy (always negative)

KE = +GMm/2r

KE = −E_total

PE = −GMm/r

PE = 2E_total

BE = GMm/2r

Binding energy = −E_total

L = mv₀r = m√(GMr)

Angular momentum (conserved)

🌍 Potential & Field

V = −GM/r

Potential. Always negative. J/kg

U = −GMm/r

PE. Always negative. J

g = −dV/dr

Field = −gradient of potential

g_inside = GMr/R³

Solid sphere: linear increase

g_inside = 0

Hollow shell: zero inside

🔢 Critical Values

G = 6.674×10⁻¹¹

Universal constant (N·m²/kg²)

g_Earth = 9.8 m/s²

Surface value

Vₑ = 11.2 km/s

Earth escape velocity

v₀ = 7.9 km/s

Near-Earth orbital speed

h_geo = 36,000 km

Geostationary orbit altitude

🧠 Memory Tricks

🎯 Trick #1: Escape vs Orbital

"Escape is √2 times orbital" — Vₑ = √2 × v₀(surface). At 11.2 km/s (escape) vs 7.9 km/s (orbital). Ratio ≈ √2 ≈ 1.41. Remember: 7.9 × 1.41 ≈ 11.2. ✓

🎯 Trick #2: Satellite Energy Mnemonics

"KE + PE + Total = +, −, −" → KE positive, PE negative, Total negative. And KE = −E (Total), PE = 2E (Total). Easy: Total ÷ 2 = −KE.

🎯 Trick #3: g variation comparison

"Altitude drops g twice as fast" — rate: 2g/R (altitude) vs g/R (depth). So at same small distance h from surface: g_altitude drop = 2 × g_depth drop.

🎯 Trick #4: Kepler T ratio

"T ratio = r ratio to the power 3/2" — T₁/T₂ = (r₁/r₂)^(3/2). If orbit radius becomes 4× → period becomes 4^(3/2) = 8× longer. Quick: 4^(3/2) = (4³)^(1/2) = 64^(1/2) = 8.

🎯 Trick #5: g = 0 at centre

"Centre = Peaceful" — at the centre of a solid sphere, all the shells surround you equally → forces cancel → g = 0. Also g_d = g(1 − d/R): at d = R → g = 0.

🎯 Trick #6: Shell theorem

"Outside = Point mass; Inside Shell = Zero" — Outside a shell: full mass at centre. Inside a hollow shell: nothing. For solid sphere inside: only mass below counts.

🎯 Trick #7: Weightlessness definition

"Weightless ≠ No gravity" — Weightless means apparent weight = 0, i.e., Normal force = 0. This happens in free fall. ISS is in free fall (orbit). Gravity still acts on everything inside.

🎯 Trick #8: Binary Star ω formula

"Same ω, total mass" — For binary stars: ω = √[G(M₁+M₂)/d³]. Use TOTAL mass. Both stars have identical ω (same T). But different radii (r ∝ 1/M).

✅ Pre-Exam Checklist

Check each topic you've mastered. Aim for 100% before your exam.

📗 CBSE Level

✓

Newton's Law of Gravitation — formula, G value, properties

✓

Derivation: g = GM/R²

✓

g at height h (exact + approximate)

✓

g at depth d (linear formula)

✓

Kepler's 3 Laws + Derivation of 3rd Law

✓

Escape velocity — derivation + value

✓

Orbital velocity + time period

✓

Satellite total energy (KE + PE)

✓

Weightlessness — explanation + conditions

✓

Geostationary satellite — properties

⚡ JEE Level

✓

Shell theorem — both parts (outside and inside)

✓

Gravitational potential V = −GM/r

✓

g = −dV/dr relationship

✓

Density form: Vₑ = R√(8πGρ/3)

✓

Satellite binding energy

✓

Binary star system — ω = √[G(M₁+M₂)/d³]

✓

Elliptical orbit — E = −GMm/2a, T = 2π√(a³/GM)

✓

Tunnel SHM — T = 2π√(R/g)

✓

Cavity in sphere — superposition method

✓

Gravitation + Electrostatics analogy

🔢 Quick Reference

G (Universal)

6.674 × 10⁻¹¹ N·m²/kg²

Earth Surface g

9.8 m/s²

Equator value

Earth Escape Velocity

11.2 km/s

Earth Orbital Speed

7.9 km/s

Near surface

Earth Mass

5.972 × 10²⁴ kg

Earth Radius

6.371 × 10⁶ m

6400 km approximately

Moon g

g_moon = g/6 ≈ 1.63 m/s²

Moon Escape Velocity

2.4 km/s

Geostationary h

≈ 36,000 km

Above equator

Low Earth Orbit T

≈ 84 minutes

Sun-Earth distance

1.496 × 10¹¹ m

1 AU

Earth-Moon distance

3.84 × 10⁸ m

🎯

Exam Day Tip

Start with the topic you're most confident in. In Gravitation — g variation and Kepler's law ratio problems are easiest to solve fast. Solve those first for momentum.

❌

Never Forget

r in Newton's law = centre to centre (not surface). Sign of PE = always negative. Total satellite energy = always negative. Escape velocity ≠ orbital velocity.

🧠

Final Mindset

Physics exams test thinking, not memory. If stuck, go back to first principles: F=ma, energy conservation, angular momentum conservation. These three unlock everything.

Last-Minute Revision — Gravitation