Gravitation – One Page Formula Sheet

Last Minute Revision | High Retention | Exam Ready

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1. Newton’s Law of Gravitation

Force: F = G m₁ m₂ / r²

• G = 6.67 × 10⁻¹¹ N m² kg⁻²
• Always acts along line joining masses

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2. Gravitational Field & Potential

Field: g = GM / r²
Potential: V = −GM / r

• Field → Vector
• Potential → Scalar
• g = − dV/dr

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3. Acceleration due to Gravity (Earth)

At surface: g = GM / R²

• Height h: g_h = g (R / (R+h))²
• Depth d: g_d = g (1 − d/R)

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4. Orbital Motion

Orbital speed: v = √(GM/r)

Time period: T = 2π √(r³ / GM)

Kepler’s 3rd Law: T² ∝ r³

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5. Energy of Satellite

Kinetic Energy: K = GMm / (2r)

Potential Energy: U = −GMm / r

Total Energy: E = −GMm / (2r)

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6. Escape Velocity

Escape speed: v_e = √(2GM / R)

• Independent of mass
• No atmosphere assumed

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7. Important Energy Conditions

• E < 0 → Bound orbit
• E = 0 → Escape condition
• E > 0 → Hyperbolic path

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8. Inside Earth Results

• g ∝ r (inside Earth)
• Field zero at centre
• Potential minimum at centre

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9. Satellite Directional Changes

• Tangential push → Energy changes
• Radial push → Shape of orbit changes
• No push → Same orbit

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10. Ultra-Important Exam Reminders

• Never use energy conservation in inelastic collision
• Always write symbolic form first
• Check power of r carefully
• Use limiting cases to verify answer

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FINAL MANTRA:
Gravitation is not calculation-heavy, it is thinking-heavy.

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One Page Gravitation Formula Sheet – Completed ✅

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• Gravitation – Part 1
• Gravitation – Part 2
• Gravitation – Part 3
• Gravitation – Part 4
• Gravitation – Part 5
• Gravitation – Part 6
• Gravitation – Part 7
• Gravitation – Part 8
• Gravitation – Part 9
• Gravitation – Part 10
• Gravitation – Part 11
• Gravitation – Part 12
• Gravitation – Part 13
• Gravitation – Part 14
• Gravitation – Part 15
• Gravitation – Part 16
• Gravitation – Part 17
• Gravitation – Part 18
• Gravitation – Part 19
• Gravitation – Part 20
• Gravitation – Part 21
• Gravitation – Part 22
• Gravitation – Part 23
• Gravitation – Part 24
• Gravitation – Part 25
• Gravitation – Part 26
• Gravitation – Part 27
• Gravitation – Part 28
• Gravitation – Part 29
• Gravitation – Part 30
• Gravitation – Part 31
• Gravitation – Part 32
• Gravitation – Part 34
• Gravitation – Part 35
• Gravitation – Part 36
• Gravitation – Part 37
• Gravitation – Part 38
• Gravitation – Part 39
• Gravitation – Part 40
• Gravitation – Part 41
• Gravitation – Part 42

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