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Theme D — Fields

D.1.2 Gravitational Field Strength — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

D.1.2 Gravitational Field Strength — IB PHYSICS SL notes: Define gravitational field strength and calculate g for point masses and spherical bodies at any distance.Gravitational field — a region of space where a test mass experiences a force due to the gravitational attraction of…

  • Source size
  • Gravitational field strength (g)
  • What the symbols mean
  • Dependence
  • Surface factors
  • Distance example

Section 1 of 9Gravitational field

Gravitational field
  • Gravitational field a region of space where a test mass experiences a force due to the gravitational attraction of another mass
  • A planet creates a field in the space around it, and any mass placed there feels it.
  • This avoids action at a distance and lets us describe the field at a point even when nothing is there.
Direction
  • Direction the field acts towards the centre of the mass producing it, because gravity is always attractive
Range
  • Range gravity has infinite range
Source size
  • Source size the force is greater around objects of large mass such as planets and almost negligible for atoms

Section 2 of 9Definition of field strength

1Gravitational field strength (g)
  • Gravitational field strength (g) the force per unit mass experienced by a small test mass at a point
  • g = F / m
2
Symbols
  • g is in N kg−1, which equals m s−2.
  • F is the gravitational force on the test mass in N.
  • m is the test mass in kg, small enough not to disturb the source.
3Vector
  • Vector g points in the direction of the force on the test mass, towards the source
4Free fall
  • Free fall because F = mg, g is also the free-fall acceleration at that point
  • At the Earth's surface it is 9.8 N kg−1 or 9.8 m s−2.

Section 3 of 9Field of a point or spherical mass

Equation
  • Equation g = GM / r2
    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)
  • Equate mg with GMm/r2 and cancel the test mass.
  • M is the mass producing the field and r is the distance from its centre.
Dependence
  • Dependence g depends only on the source mass and position, and falls with the inverse square of distance
  • Objects of any mass in the field feel the same g.
Surface factors
  • Surface factors g at a planet's surface depends on the planet's mass (or density) and radius
Distance example
  • Distance example at the surface r = R, and at r = 2R the field is a quarter of the surface value
Graphs
  • Graphs g against r outside a body is a falling curve, and g against 1/r2 is a straight line with gradient GM
Validity
  • Validity the formula holds for any point outside a spherical body

Section 4 of 9Combining fields

Superposition
  • Superposition the net field at a point is the vector sum of the fields due to each mass
Neutral point
  • Neutral point along the line joining two masses the fields point in opposite directions, so a point exists where they cancel
  • It lies closer to the smaller mass, where GM1/r12 = GM2/r22.
Uniform field
  • Uniform field near a planet's surface, over heights small compared with the radius, g hardly varies
  • This justifies constant-acceleration equations and Ep = mgh for ordinary projectiles.

Section 5 of 9Field strength versus weight

Weight
  • W = mg, where g is the local field strength
  • Weight is a force that changes from place to place.
  • Mass is a fixed property of the object.
Moon
  • Moon an astronaut has the same mass but a weight about one sixth as large, since the Moon's surface g is about 1.6 N kg−1
Jupiter
  • Jupiter a very large g gives a large weight, so a human could hardly stand up
Two views of g
  • Two views of g a force per unit mass (N kg−1) or an acceleration (m s−2), so use whichever is convenient and keep units consistent

Section 6 of 9Comparing planets

Ratio method
  • Ratio method write g ∝ M/r2 and substitute ratios of mass and radius
With density
  • M = ρ × (4/3)πr3, so g ∝ ρr
Data booklet
  • Data booklet it gives g = GM/r2, and the volume of a sphere

Section 7 of 9More from the specification

More from the specification
Newton's Law of Universal Gravitation
  • Newton's law states that every point mass attracts every other point mass with a gravitational force directly proportional to the product of their masses and inversely proportional to the square of their separation distance (F = G·M·m / r²).
Radial Gravitational Field Strength
  • Gravitational field lines around a spherical mass point inward toward the centre, indicating a radial field where gravitational field strength g = G·M / r² decreases with distance squared.
Kepler's Third Law of Orbital Motion
  • For a planet or satellite in circular orbital motion, gravitational attraction provides the necessary centripetal force;
    • equating these forces derives Kepler's third law, stating that orbital period squared is proportional to orbital radius cubed (T² ∝ r³).
Newton
  • Unit of force, kg m s-2.
Period
  • Time for one revolution.
Proportional
  • Changing by the same factor as another quantity.
Field lines
  • Lines showing the direction and strength of a magnetic field.
Orbital period
  • Time for one orbit.
Orbital radius
  • Distance from the centre of the central body to the orbiting body.
Inversely proportional
  • One quantity falls as the other rises in the same ratio.
Radial field
  • Field directed to a center and varying with distance.

Section 8 of 9Key terms

TermMeaning
Gravitational fieldRegion where a mass experiences a gravitational force.
Field strength gForce per unit mass at a point; unit N kg⁻¹.
Test massA small mass used to probe a field without disturbing it.
SuperpositionThe net field is the vector sum of the individual fields.
Neutral pointA position where the net gravitational field is zero.
Uniform fieldA field with the same magnitude and direction everywhere, as near a planet's surface.

Section 9 of 9Exam technique

1
Confusing g with G — g is field strength and G is the gravitational constant.
2
Writing g = F/m as a scalar — it is a vector pointing towards the source.
3
Using the height above the surface as r in GM/r^{2}.
4
Believing g = 0 for astronauts in orbit — g is nearly the same as on the ground.
5
Saying g depends on the test mass — the mass cancels.

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