Theme D — Fields
D.1 Gravitational Fields — IB Physics HL Revision Notes & Topical Questions
5 min read 12 parts Lesson 2 of 39 1 quiz
Curriculum Equation Key Circular Motion & Gravitation LawsFast Exam Solution
a_c = v² / r | F_c = (m × v²) / r | F_g = G × (m₁ × m₂) / r² | v_orbit = √(G×M / r)
Lesson summary
D.1 Gravitational Fields — IB PHYSICS HL notes: Apply Newton's law of gravitation and Kepler's laws, and use gravitational field strength, potential, potential energy, escape speed and orbital energy.Statement — the force between two point masses is proportional to the product of…
- What the symbols mean
- Separation
- Inverse square
- Definition
- Point or spherical mass
- Dependence
Part 1 of 10Newton's law of gravitation
Statement
- Statement the force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation
- F = Gm1m2/r2What the symbols mean: F = gravitational force (N) · G = 6.67 × 10−11 N m2 kg−2 · m1, m2 or M, m = masses (kg) · r = distance between their centres (m)
Separation
- Separation r is measured between centres, so for a satellite add the planet radius to the altitude
Point masses
- Point masses planets and stars are treated as points, and a uniform sphere acts as if all its mass were at its centre
Inverse square
- Inverse square doubling the distance reduces the force to a quarter
Constant
- G = 6.67 × 10−11 N m2 kg−2
Part 2 of 10Gravitational field strength
Field
- Field a region where a test mass experiences a force due to the gravitational attraction of another mass
Definition
- Definition g = F/m, the force per unit mass, in N kg−1
Point or spherical mass
- Point or spherical mass g = GM/r2 from equating mg with GMm/r2
Dependence
- Dependence g depends on the mass producing the field and r, not on the test mass
Vector
- Vector it points towards the mass, and fields from several masses add as vectors
g and G
- g and G g is the field strength and G is Newton's gravitational constant
Part 3 of 10Gravitational field lines
Gravitational field lines
Direction
- Direction field lines point towards the centre of the mass because gravity is attractive only
Point mass or uniform sphere
- Point mass or uniform sphere radial lines, which make a non-uniform field with g varying with distance
Near the surface
- Near the surface parallel equally spaced lines make a uniform field
Spacing
- Spacing closer lines mean a stronger field
Labelling
- Labelling always put arrows on field lines
Part 4 of 10Kepler's laws and circular orbits
1First law
- First law each planet moves in an ellipse with the Sun at one focus
2Second law
- Second law the line from Sun to planet sweeps out equal areas in equal times
- A planet moves fastest when closest to the Sun
3Third law
- T2 ∝ r3 for bodies orbiting the same central mass
4Orbital speed
- GMm/r2 = mv2/r gives v = √(GM/r), independent of the satellite's mass
5Period
- Period with v = 2πr/T, T2 = 4π2r3/GM
6Log plot
- Log plot log T against log r is a straight line with a gradient of 3/2
Part 5 of 10Gravitational potential
Definition
- Definition the work done per unit mass in bringing a test mass from infinity to the point
- Vg = −GM/r in J kg−1
Zero at infinity
- Zero at infinity it is negative elsewhere because work must be done to move a mass away from the body
Scalar
- Scalar contributions add algebraically
Distance
- Distance potential becomes less negative as a mass moves away and is more negative closer in
M
M only the mass producing the field appears in the equation
Part 6 of 10Potential energy and work
Radial field
- Ep = mVg = −GMm/r, the work to bring a mass from infinity
Change
- ΔEp = GMm(1/r1 − 1/r2)
- ΔVg = GM(1/r1 − 1/r2) for a move from r1 to r2, negative when the mass moves closer
Work
- W = mΔVg
- Near the surface this is W = mgΔh
Force–distance graph
- Force–distance graph the area under it is the change in potential energy
mgh
- mgh valid only near the surface where the field is uniform
Part 7 of 10Potential gradient and equipotentials
Gradient
- Gradient g = −ΔVg/Δr, the negative gradient of the potential–distance graph
V–r graph
- V–r graph a −1/r curve with all values negative
- Draw a tangent and take its gradient to find g
Equipotentials
- Equipotentials surfaces of equal potential, perpendicular to field lines and drawn dotted without arrows
Radial field
- Radial field concentric circles that get further apart away from the planet
Uniform field
- Uniform field horizontal, parallel and equally spaced lines
Along an equipotential
- Along an equipotential no work is done
Part 8 of 10Orbital energy
Kinetic energy
- Ek = GMm/2r
Potential energy
- Ep = −GMm/r
Total energy
- E = −GMm/2r, negative for a bound orbit
Smaller orbit
- Smaller orbit larger force, speed and Ek, lower Ep and shorter period
Larger orbit
- Larger orbit smaller force, speed and Ek, higher Ep and longer period
Part 9 of 10Escape speed and drag
Escape speed
- Escape speed the minimum speed to escape a gravitational field with no further energy input
- ½mv2 = GMm/r gives vesc = √(2GM/r) = √2 × orbital speed
Independence
- Independence it is the same for all masses and directions
Drag
- Drag viscous drag from a thin atmosphere removes total energy in low orbits
- (below about 600 km)
- The orbital radius decreases and the satellite speeds up
Part 10 of 10More from the specification
1Radial gravitational field potential
- Radial gravitational field potential evaluating work required to move unit masses from infinity provides a calculus-based means to define gravitational potential.
2Newton's Law of Universal Gravitation
- The attractive gravitational force acting between two spherical bodies of mass M and m separated by distance r is given by F = G * M * m / r2, directed toward their centres of mass.
3Orbital Motion and Centripetal Force
- In circular orbital motion of a satellite orbiting Earth at distance r, the gravitational force provides the necessary centripetal force,
- (G * M * m / r2 = m * v2 / r)
- leading to orbital speed v = sqrt(G * M / r).
4Escape Velocity from Earth's Surface
- The escape velocity represents the minimum initial speed an object must have at the surface of Earth to escape gravitational pull without further propulsion, derived by energy conservation as vesc = sqrt(2 * G * M / R).
- (at Earth radius R)
5Gravitational Field Strength and Radial Variation
- Gravitational field strength g = GM / r2 decreases with distance r; for a planet of uniform density rho, g increases linearly with radius inside the planet before following an inverse-square decline outside.
- (g proportional to r)
6Density
- Mass per unit volume.
7Centripetal force
- Net force toward the centre, mv2/r.
8Escape velocity
- Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
Key terms
| Term | Meaning |
|---|---|
| Gravitational field strength | The force per unit mass on a small test mass placed at the point. |
| Newton's law of gravitation | Every point mass attracts every other with a force proportional to the product of the masses and inversely proportional to the square of their separation. |
| Field line | A line whose direction at each point shows the direction of the force on a test mass. |
| Orbital period | The time for one complete orbit. |
| Gravitational potential | The work done per unit mass in bringing a small test mass from infinity to the point. |
| Equipotential surface | A surface on which the potential is the same at every point. |
| Escape speed | The minimum speed needed for a body to escape from a gravitational field to infinity. |
Avoid these mistakes
1
Measuring r from the surface instead of the centre.
2
Using the satellite's mass in the orbital speed formula — it cancels.
3
Saying a higher orbit needs a higher speed — orbital speed is lower for a larger radius.
4
Giving a positive total energy for a bound orbit.
5
Confusing g with G.
Topic quiz · 57 questionsQuiz for this lesson
Last updated:
\n