Theme D — Fields
D.1.11 Orbital Motion, Speed and Energy — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 13 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.1.11 Orbital Motion, Speed and Energy — IB PHYSICS HL notes: Derive orbital speed from gravity as the centripetal force and use the kinetic, potential and total energy of a satellite.Near-circular orbits — the gravitational force between planet and star, or planet and satellite…
- Mass cancels
- Larger orbits
- Acceleration
- Kepler's third law
- Geostationary orbit
- Projectile picture
Part 1 of 8Gravity as the centripetal force
Near-circular orbits
- Near-circular orbits the gravitational force between planet and star, or planet and satellite, provides the centripetal force
Direction
- Direction both forces are perpendicular to the direction of travel
Equation
- GMm/r2 = mv2/r
Free fall
- Free fall the satellite is in constant free fall around the planet
Part 2 of 8Orbital speed
Equation
- Equation v = √(GM/r)
Mass cancels
- Mass cancels all satellites at one radius travel at the same speed
Symbols
- M is the larger mass in kg, r the orbital radius from the centre in m
Larger orbits
- Larger orbits smaller speed
Acceleration
- Acceleration the centripetal acceleration points towards the planet
Part 3 of 8Orbital period
Period
- T = 2πr/v = 2π√(r3/GM)
Kepler's third law
- T2 = 4π2r3/GM so T2 ∝ r3
Geostationary orbit
- Geostationary orbit period 24 h above the equator, fixed over one longitude
Part 4 of 8Weightlessness
Gravity
- Gravity it has not vanished, and at the space station's height the field is about 89% of the surface value
Free fall
- Free fall the astronaut and station fall together with the same acceleration, so there is no contact force
Projectile picture
- Projectile picture a satellite is a projectile fired fast enough that the Earth's surface curves away as quickly as it falls
Part 5 of 8Energy of an orbiting satellite
Kinetic energy
- Ek = ½mv2 = GMm/2rWhat the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
Potential energy
- Ep = −GMm/r
Total energy
- E = Ek + Ep = −GMm/2r
Relations
- Ek = −E and Ep = 2E
Bound
- Bound the negative total energy shows the satellite is bound
Constant
- Constant in a given orbit Ek, Ep and E are constant
Part 6 of 8Comparing orbits
| Quantity | Smaller orbit X | Larger orbit Y |
|---|---|---|
| Gravitational force | Larger | Smaller |
| Speed | Higher | Lower |
| Kinetic energy | Higher | Lower |
| Potential energy | Lower | Higher |
| Period | Shorter | Longer |
Raising an orbit
- Raising an orbit engines must increase the total energy and the satellite ends up moving more slowly
Scaling
- Scaling v ∝ r−1/2, T ∝ r3/2 and Ek ∝ 1/r
Part 7 of 8Energy graphs
Ep
- Ep below the axis and rising towards zero with r
Ek
- Ek positive and falling towards zero
Total energy
- Total energy lies halfway between them, negative and rising to zero
v2 against 1/r
- v2 against 1/r a straight line through the origin with gradient GM
Part 8 of 8More from the specification
More from the specification
Orbital speed relation
- Orbital speed relation balancing centripetal requirements against gravitational force provides a direct physical means to determine orbital velocity.
Gravitational Field Strength Definition
- Gravitational field strength g at a point in space is defined as the gravitational force per unit test mass placed at that position (g = F / m), directed along field lines toward the attracting centre.
Escape Speed from a Celestial Object
- Escape speed is the minimum initial launch speed needed for an object to overcome the gravitational field strength of a planet without additional thrust, given by vesc = √(2GM / R).
Gravitational Potential Graphs
- On a graph of gravitational potential V against distance r, the field is non-uniform (V = -GM/r);
- the negative gradient (-dV/dr) at any point equals the local gravitational field strength g.
Escape velocity
- Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
Distance
- Total length of path travelled, a scalar.
Uniform
- Same density throughout, so the weight acts at the centre.
Newton
- Unit of force, kg m s-2.
Density
- Mass per unit volume.
Equipotential
- A surface of constant potential
Field strength
- G = Fg/m.
Field lines
- Lines showing the direction and strength of a magnetic field.
Escape speed
- Minimum launch speed to reach infinity, √(2GM/R).
Key terms
| Term | Meaning |
|---|---|
| Orbital speed | v = √(GM/r), the speed of a circular orbit. |
| Centripetal force | The inward force required for circular motion, here supplied by gravity. |
| Geostationary orbit | An equatorial orbit with a 24 h period so the satellite stays above one point. |
| Free fall | Motion under gravity alone, giving apparent weightlessness. |
| Total orbital energy | −GMm/2r. |
Avoid these mistakes
1
Believing orbiting astronauts are beyond the pull of gravity.
2
Using the satellite's mass in the orbital speed formula — it cancels.
3
Saying a higher orbit needs a higher speed — the speed is lower.
4
Giving a positive total energy for a bound orbit.
5
Measuring r from the surface instead of the centre.
Marked practiceQuizzes for this lesson
Last updated:
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).