Lesson Overview

Unit 5 explains gravitational interactions, gravitational field intensity, potential, energy, orbital motion of satellites, geostationary orbits, and escape velocity. These concepts are essential for understanding planetary motion and space science.

1. Core Concepts (Short Notes)

5.1 Newton’s Law of Universal Gravitation

• Any two masses attract each other.

• F = G m₁m₂ / r²

• Gravitational force is always attractive.

• “G” (gravitational constant) = 6.67 × 10⁻¹¹ N m² kg⁻².

5.2 Gravitational Field & Field Intensity (g)

• Field: Region where a mass experiences a gravitational force.

• g = F / m

• Field intensity due to mass M: g = GM / r²

• Units: N kg⁻¹.

5.3 Gravitational Potential (V)

• Work done per unit mass to bring a mass from infinity to a point.

• V = – GM / r

• Always negative.

5.4 Gravitational Potential Energy (U)

• U = mV = – GMm / r

• U becomes less negative as distance increases.

5.5 Satellite Motion

• Centripetal force is supplied by gravitational attraction.

• Orbital velocity: v = √(GM / r)

• Time period: T = 2π √(r³ / GM)

• Geostationary orbit: 24-hour period, above equator.

5.6 Escape Velocity

• Minimum velocity needed to leave a planet’s gravitational field.

• vₑ = √(2GM / R) = √(2gR)

2. Detailed Notes for Each Section

5.1 Newton's Law of Gravitation

Definition

The force between two point masses:

Properties

• Attractive only.

• Acts along the line joining the masses.

• Inversely proportional to r².

Mass of the Earth (using g):

5.2 Gravitational Field & Intensity (g)

Field Intensity

• g = GM / r² (for a point or spherical mass).

• Decreases with square of distance from the centre.

Graphs (as in TG):

• g vs r: decreasing curve (page 2).

• At infinity: g → 0.

Earth’s Surface

• g ≈ 9.8 m/s².

• Variations occur due to:

  • Shape of Earth

  • Rotation

  • Altitude

5.3 Gravitational Potential (V)

Definition

Potential at infinity = 0.

For a point mass:

Shape of the Graph:

• Steep near mass

• Approaches zero from negative side

Relation Between g and V:

5.4 Gravitational Potential Energy (U)

Expression:

Total Energy of Orbiting Body:

Interpretation:

• Bound orbit → negative total energy.

• Larger radius → less negative → weaker binding.

5.5 Satellite Motion

Centripetal Force Condition

Time Period:

Geostationary Satellite Conditions:

• Orbital period = 24 h.

• Orbits above equator.

• Moves west → east.

• Same angular speed as Earth.

Applications:

• GPS

• Communication satellites

• Weather forecasting

5.6 Escape Velocity

Definition

Velocity needed to reach infinite distance with zero remaining kinetic energy.

Derivation:

Earth:

• Approx. 11.2 km/s.

Applications:

• Rocket launches

• Understanding atmosphere retention

3. Formula Summary (Unit 5)

• F = G m₁m₂ / r²

• g = GM / r²

• V = – GM / r

• U = – GMm / r

• Eorbit = – GMm / 2r

• v = √(GM / r)

• T = 2π √(r³ / GM)

• vₑ = √(2GM / R)

4. Common Mistakes to Avoid

• Forgetting the minus sign in potential and potential energy.

• Confusing radius from centre with altitude above surface.

• Using R instead of (R+h) for satellite orbits.

• Mistaking weightlessness as absence of gravity (gravity acts, but objects are in free fall).

5. Exam Tips

• Clearly label orbital radius vs altitude.

• State assumptions: “Treat Earth as perfect sphere”.

• Always check units when substituting (m, kg, s).

• Draw neat graphs for g vs r and V vs r.

• Satellite motion questions often combine circular motion + gravitation.

6. Quick Revision Table