Theme D — Fields
D.1.3 Gravitational Field Lines — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 5 of 39 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
D.1.3 Gravitational Field Lines — IB PHYSICS SL notes: Draw and interpret gravitational field lines for point masses, planets and pairs of masses, linking line density to field strength.Uniform sphere — for a point outside it, the mass can be treated as a point mass at its centre…
- When to use it
- Extension of Newton's law
- Field lines (lines of force)
- Acceleration
- Radial field
- Comparison
Part 1 of 7Point mass approximation
Point mass approximation
Uniform sphere
- Uniform sphere for a point outside it, the mass can be treated as a point mass at its centre
- A uniform sphere has its mass distributed evenly.
- The field lines around it are identical to those around a point mass.
When to use it
- When to use it a body can be a point mass when the distances involved are very large compared with its size
- This applies to stars, planets and moons.
Extension of Newton's law
- Extension of Newton's law the law applies to spheres of uniform density by assuming the mass is concentrated at the centre
Part 2 of 7What field lines show
What field lines show
Field lines (lines of force)
- Field lines (lines of force) a diagram of a field in which the tangent at a point gives the direction of the force on a small mass placed there
Arrows
- Arrows they show that the force is attractive and point towards the mass producing the field
- Gravity is always attractive, so lines never point away from a mass.
Acceleration
- Acceleration the lines also show the direction of acceleration of a mass in the field
Not paths
- Not paths a mass released from rest follows a line only if the line is straight
- A mass with initial velocity can move across the lines.
Rules
- Lines never cross, because the force at a point has one direction.
- Lines leave or meet the surface of a spherical mass at right angles.
Part 3 of 7Line density and field strength
Meaning
- Meaning closely packed lines mean a strong field and widely spaced lines mean a weak one
Radial field
- Radial field around an isolated sphere the lines point radially inward
- The same number of lines spreads over a sphere of area 4πr2 as you move away.
- The line density therefore falls as 1/r2, matching g = GM/r2.
Counting
- N lines through a sphere of radius r give N/4πr2 lines per square metre
Comparison
- Comparison a point twice as far from the centre has one quarter of the line density
Information
- Information the arrows show direction and the density shows magnitude
Continuous field
- Continuous field lines only guide the eye, so no line at a point does not mean no field
Part 4 of 7Common patterns
Single sphere
- Single sphere lines radiate inwards, evenly spaced and more crowded close to the surface
Radial fields
- Radial fields they are non-uniform, since g depends on the distance from the centre
Uniform field
- Uniform field equally spaced parallel lines pointing down towards the surface
- Near the Earth's surface g is the same throughout.
- The surface looks uniform only because the curvature is slight; on a larger scale the lines converge.
Two equal masses
- Two equal masses far away the pattern resembles that of a single body
- Midway between them is a neutral point where g = 0.
Two unequal masses
- Two unequal masses the neutral point is nearer to the smaller mass
Part 5 of 7Drawing diagrams
1
Use a ruler for straight lines.
2
Add arrows pointing towards the mass or the surface.
3
Keep equal angular spacing for a symmetrical source.
4
Label any neutral point.
- Arrows
- always label them, since gravitational forces are attractive only
Part 6 of 7Gravitational and electric lines compared
Gravitational lines
- Gravitational lines they always end on masses and never start away from one
Electric lines
- Electric lines they can start on positive charges and end on negative ones
Similarity
- Similarity both follow the same rules about crossing and density
Part 7 of 7More from the specification
More from the specification
Gravitational field lines and inverse-square law
- Gravitational field lines around a point mass are directed radially inwards, with field strength decreasing according to the inverse-square law: 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)
Newton's law of universal gravitation
- The attractive gravitational force between two masses is F = G M m / r2, where G is the universal gravitational constant.
Kepler's third law of orbital motion
- For planets in circular orbits, gravitational force provides the centripetal requirement, resulting in T2 = (4 pi2 / GM) r3.
Period
- Time for one revolution.
Weight
- Gravitational force on a mass.
Proportional
- Changing by the same factor as another quantity.
Constant
- Not changing.
Orbital period
- Time for one orbit.
Gravitational constant
- Constant G in Newton’s law of gravitation.
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.
Key terms
| Term | Meaning |
|---|---|
| Field line | A line whose tangent gives the direction of the field at that point. |
| Radial field | Lines directed towards (or away from) a single centre, as for a sphere. |
| Uniform field | Parallel, equally spaced lines; same g everywhere. |
| Neutral point | Position where the resultant field is zero. |
| Line density | Number of lines per unit area, proportional to field strength. |
Avoid these mistakes
1
Drawing field lines that cross.
2
Putting arrows pointing away from a mass — gravity lines always point towards the mass.
3
Believing lines show the trajectory of a moving mass.
4
Saying the field is zero where no lines are drawn — lines are only a sample of a continuous field.
5
Claiming that a planet's lines are parallel at all scales — they are only near-parallel over small regions.
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