5.2.3

Gravitational Potential

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Gravitational Potential

Understanding gravitational potential lets us consider the energy changes that objects moving in gravitational fields experience.

Zero value

Zero value

  • The zero value of gravitational potentials is defined as being at an infinite distance away from the mass generating the field.
  • This is done so that when a small test mass is placed in the gravitational field, the test mass has work done on it by the original mass and gains kinetic energy (KE).
  • To gain that KE, the object must have lost gravitational potential energy (GPE). In other words, the gravitational potential has become more negative.
Example

Example

  • Imagine a rubber sheet with a heavy object in the middle.
  • The sheet is deformed downwards. The undeflected sheet is defined to be at zero potential.
  • You can find the gravitational potential difference by subtracting the initial gravitational potential from the final gravitational potential.
    • E.g. In the diagram, the object has dropped from a potential of -30 J/kg to -50 J/kg.
    • The change is -50 - (-30) = -20 J/kg.
    • There has a been a drop in potential of 20 J/kg.
Work done on a moving mass

Work done on a moving mass

  • The work done on a moving mass in that gravitational potential can be found by multiplying the change in potential by the mass.
  • On the previous slide, if the mass of the object was 2.0 kg, then the work done on the mass would be 2.0 × 20 = 40 J.
  • We could say that the 2.0 kg mass has lost 40 J of GPE, or that the large mass has done 40 J of work on the mass.
Work done 2

Work done 2

  • If an object moves along an equipotential surface, then the potential has not changed and no work has been done on the object.
  • This is like satellites in circular orbit around a planet.
    • The planet does no work on the satellites. So there is no loss in potential, and no loss in GPE (the radius of the orbit does not change). This means the satellite does not change KE (and so has constant speed).

Gravitational Potential Graphs

Gravitational potential graphs, gravitational field strengths and changes in gravitational potentials are all inter-linked.

Gravitational potential

Gravitational potential

  • The gravitational potential surrounding a planet or point mass is given by the formula V=−GMrV = -\frac{GM}{r}.
  • The minus sign is important because it signifies an attractive force.
Gravitational potential

Gravitational potential

  • The graph shows the variation of gravitational potential with distance from a point mass.
Gravitational field strength

Gravitational field strength

  • The graph shows the variation of gravitational field strength with distance from a point mass.
Gradient

Gradient

  • The -1 × (gradient of the gravitational potential) graph gives the variation of the gravitational field strength with distance.
  • In a similar way, the gradient of a displacement-time graph gives the velocity-time graph.
Area under graph

Area under graph

  • The reverse operation (i.e. finding the area between the curve and the distance axis) for a gravitational field strength against distance graph will give the change in potential.
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Gravitational Potential

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    A satellite orbiting a planet has a gravitational potential energy of -1000 J. It propels itself up so that it now has a gravitational potential energy of -600 J. How much work has been done by the satellite?Multiple choice
  2. 2
    A satellite orbiting a planet has a gravitational potential energy of -60 J. It propels itself up so that it now has a gravitational potential energy of -20 J. How much work has been done by the satellite?Multiple choice
  3. 3
    What graph is formed when we take the negative of the gradient of a V-r (gravitational potential against distance) graph?Multiple choice
  4. 4
    What do we find if we take the area under a gravitational field vs distance graph?Multiple choice
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Gravitational Field Strength

Bulk Properties of Solids