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Theme D — Fields

D.1.4 Gravitational Potential — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 6 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

D.1.4 Gravitational Potential — IB PHYSICS HL notes: Define gravitational potential and use V = −GM/r, including its sign, scalar nature and variation with distance.Gravitational potential — the work done per unit mass in bringing a test mass from infinity to a defined pointUnit …

  • Dependence
  • Direction of change
  • Attractive force
  • Moving away
  • Closer to a planet
  • Several bodies

Part 1 of 7Definition

Gravitational potential
  • Gravitational potential the work done per unit mass in bringing a test mass from infinity to a defined point
Unit
  • J kg−1
Dependence
  • Dependence the mass of the body producing the field and the distance from its centre to the point
Direction of change
  • Direction of change potential decreases as a mass moves closer to the body

Part 2 of 7The equation

Equation
  • Vg = −GM/r
G
Newton's gravitational constant
M
M the mass of the body producing the field in kg, not the mass of the test object
r
r the distance from the centre of the mass to the point in m, so r = planet radius + height

Part 3 of 7Why it is negative

Reference
  • Reference the potential is defined as zero at infinity
Attractive force
  • Attractive force as r decreases, positive work is done by the field on the mass coming in from infinity
Moving away
  • Moving away work must be done on the mass to carry it towards infinity
Closer to a planet
  • Closer to a planet the potential is smaller (more negative)
Moving away
  • Moving away the potential becomes larger (less negative) and reaches 0 at infinity

Part 4 of 7Scalar quantity

Scalar
  • Scalar gravitational potential has no direction, unlike field strength which is a vector
Several bodies
  • Several bodies add potentials algebraically
Large r
  • Large r the force tends rapidly to zero and so does the potential

Part 5 of 7Potential and field strength

Field strength
  • Field strength g = GM/r2, a vector pointing towards the mass
    What the symbols mean: g = gravitational field strength (N kg−1) · G = 6.67 × 10−11 N m2 kg−2 · M = mass of the body (kg) · r = distance from its centre (m)
Potential
  • Vg = −GM/r, a scalar that is negative
Link
  • Link g = −ΔVg/Δr

Part 6 of 7Using the equation

1
Find the radius from the centre by adding the height to the planet radius.
2
Use the mass of the planet and not of the object moving in the field.
3
Convert distances to metres.
4
Substitute into Vg = −GM/r.
5
Keep the negative sign in the answer.

Part 7 of 7More from the specification

1Gravitational potential definition
  • Gravitational potential definition determining external mechanical work required per unit mass from infinity provides a consistent theoretical means to quantify potential.
2Gravitational Potential Definition
  • Gravitational potential Vg at a distance r from a mass M is the work done per unit mass in bringing a small test mass from infinity to that point.
    • (Vg = -G M / r, in J kg-1
3Orbital Speed of a Satellite
  • For a satellite of mass m orbiting Earth at radius r, the required centripetal force is supplied by gravitation, yielding orbital speed v = sqrt(G M / r).
    • (G M m / r2 = m v2 / r)
4Escape Speed from Earth's Surface
  • The escape speed is the minimum launch speed required for a projectile to escape Earth's gravitational field to infinity, calculated by equating initial kinetic energy to gravitational potential: vesc = sqrt(2 G M / R).
5Gravitational Field Lines and Uniform Approximations
  • Radial field lines converge toward the center of spherical masses;
    • however, close to Earth's surface over short vertical distances, the field can be modeled as uniform with constant g.
6Gravitational Potential Definition
  • Gravitational potential Vg at a distance r from a mass M is the work done per unit mass in bringing a small test mass from infinity to that point.
    • (Vg = -G M / r, in J kg-1
7Orbital Speed of a Satellite
  • For a satellite of mass m orbiting Earth at radius r, the required centripetal force is supplied by gravitation, yielding orbital speed v = sqrt(G M / r).
    • (G M m / r2 = m v2 / r)
8Escape Speed from Earth's Surface
  • The escape speed is the minimum launch speed required for a projectile to escape Earth's gravitational field to infinity, calculated by equating initial kinetic energy to gravitational potential: vesc = sqrt(2 G M / R).
9Gravitational Field Lines and Uniform Approximations
  • Radial field lines converge toward the center of spherical masses;
    • however, close to Earth's surface over short vertical distances, the field can be modeled as uniform with constant g.
10Kinetic energy
  • K = ½mv2, energy of motion.
11Escape speed
  • Minimum launch speed to reach infinity, √(2GM/R).
12Potential gradient
  • The rate of change of potential with distance, equal to −E
13Centripetal force
  • Net force toward the centre, mv2/r.
14Escape velocity
  • Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
15Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
16Uniform
  • Same density throughout, so the weight acts at the centre.
17Period
  • Time for one revolution.
18Density
  • Mass per unit volume.
19Equipotential
  • A surface of constant potential
20Potential energy
  • Energy stored by the configuration of a system.
21Field lines
  • Lines showing the direction and strength of a magnetic field.
22Orbital period
  • Time for one orbit.

Key terms

TermMeaning
Gravitational potentialThe work done per unit mass in bringing a test mass from infinity to the point.
Vg = −GM/rThe potential at distance r from the centre of mass M.
ScalarA quantity with magnitude but no direction.
InfinityThe reference point where potential is defined as zero.

Avoid these mistakes

1
Using the mass of the moving object in V = −GM/r — only the mass producing the field is used.
2
Using the height above the surface instead of the distance from the centre.
3
Giving a positive potential — gravitational potential is negative.
4
Treating potential as a vector.
5
Confusing potential (J kg−1) with potential energy (J).

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