4.2.3

Escape Velocity & Synchronous Orbits

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Escape Velocity

Escape velocity is the velocity needed for an object to escape a planet's gravitational pull.

Equations for escape velocity

Equations for escape velocity

  • The escape velocity, ve, needed for an object to leave the gravitational influence of a planet can be estimated by equating the expressions:
    • KE=12mv2KE = \frac12 mv^2
    • GPE=mΔV=0−(−GMmRP)=GMmRPGPE = m\Delta V = 0 - (-\frac{GMm}{R_P}) = \frac{GMm}{R_P}
  • Where M is the mass of the planet, RP is the radius of the planet and m is the mass of the satellite.
Calculation for escape velocity

Calculation for escape velocity

  • When an object is removed from a planet’s gravitational pull, it loses kinetic energy equal to the gravitational potential energy it gains.
  • The kinetic energy lost is equal to the potential energy gained when the object is moved an infinite distance from the planet and has zero velocity.
    • 12mve2=GMmRP\frac12 m v_e^2=\frac{GMm}{R_P}
    • ve2=2GMRPv_e^2 = \frac{2GM}{R_P}
    • ve=2GMRPv_e = \sqrt{\frac{2GM}{R_P}}
Earth's escape velocity

Earth's escape velocity

  • For the Earth, RP = 6.4 × 106 m and M = 6.0 × 1024 kg.
  • This gives ve of approximately 11 km/s.

Synchronous Orbits

A geosynchronous orbit has a period of exactly one day.

Satellites

Satellites

  • A satellite in a geosynchronous orbit remains at the same point above the Earth at all times.
  • These satellites can be used for weather mapping and observation as they can watch the same place for long periods of time.
Calculation

Calculation

  • By definition, a geosynchronous orbit has a period of one day, this can be used to calculate the radius of the orbit.
    • r3=GmT2/4π2r^3=GmT^2/4{\pi}^2
  • Remember to convert the period into seconds and the take the cubed root to find r.
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1

Space, Time & Motion

1.1

Motion

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1.2

Forces

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1.3

Momentum & Impulse

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1.4

Work, Energy & Power

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2.1

Thermal Concepts

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2.2

Modelling a Gas

2.2.1Ideal Gases2.2.2Ideal Gases 22.2.3End of Topic Test - Thermal Energy & Ideal Gases2.2.4Exam-Style Question - Ideal Gases
3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves3.1.2Simple Harmonic Motion
3.2

Travelling Waves

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3.3

Wave Characteristics

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3.4

Wave Behaviour

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3.5

Standing Waves

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3.6

Simple Harmonic Motion

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3.7

Single Slit Diffraction

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3.8

Interference

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3.9

Doppler Effect

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4

Fields

4.1

Circular Motion

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4.2

Newton's Law of Gravitation

4.2.1Newton's Law4.2.2Orbits of Planets & Satellites4.2.3Escape Velocity & Synchronous Orbits4.2.4End of Topic Test - Gravitational Fields
4.3

Fields

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4.4

Fields at Work

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4.5

Electric Fields

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Magnetic Effect of Electric Currents

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Heating Effect of Currents

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Electromagnetic Induction

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Power Generation & Transmission

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Capacitance

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5

Nuclear & Quantum Physics

5.1

Discrete Energy & Radioactivity

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5.2

Nuclear Reactions

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5.3

The Interaction of Matter with Radiation

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5.4

Nuclear Physics

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6

Measurements

6.1

Measurements & Errors

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6.2

Uncertainties & Errors

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6.3

Vectors & Scalars

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Practice questions on Escape Velocity & Synchronous Orbits

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  1. 1
    Select the object which has the higher escape velocity:True / false
  2. 2
    What is the period of a geosynchronous orbit?Multiple choice
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Orbits of Planets & Satellites

End of Topic Test - Gravitational Fields