Theme D — Fields
D.1.10 Escape Speed — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 12 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.1.10 Escape Speed — IB PHYSICS HL notes: Define escape speed and derive and use vesc = √(2GM/r).Escape speed — the minimum speed that allows an object to escape a gravitational field with no further energy inputReaching infinity — the object arrives there with zero speedIndepen…
- Independent of mass
- Independent of direction
- Depends on
- Escape of the field
- Surface form
- Potential form
Part 1 of 7Definition
Escape speed
- Escape speed the minimum speed that allows an object to escape a gravitational field with no further energy input
Reaching infinity
- Reaching infinity the object arrives there with zero speed
Independent of mass
- Independent of mass it is the same for a rocket and a tennis ball at the same point
Independent of direction
- Independent of direction provided the path does not hit the planet
Depends on
- Depends on the mass and radius of the body creating the field, such as a planet, moon or black hole
Escape of the field
- Escape of the field not just of the planet's surface, which may be a large distance away
Part 2 of 7Derivation
1
All kinetic energy is transferred to gravitational potential energy, so total energy at infinity is zero.
2
Set ½mvesc2 = GMm/r.
3
Cancel the mass m on both sides.
4
Multiply by 2 and take the square root.
5
Result: vesc = √(2GM/r).
Symbols
- M is the mass of the body in kg, r the distance from its centre in m, vesc in m s−1
Surface form
- Surface form using g = GM/r2, vesc = √(2gr)
Potential form
- ½v2 equals the magnitude of the potential at the launch point
Part 3 of 7Dependence and typical values
Mass
- Mass a larger planet mass gives a larger escape speed
Radius
- Radius a larger distance from the centre gives a smaller escape speed
Earth
- 11.2 km s−1
Moon
- Moon about 2.4 km s−1
Part 4 of 7Escape speed and orbit
Orbital speed
- Orbital speed vorb = √(GM/r)
Relation
- Relation vesc = √2 × vorb at the same radius
Bound orbit
- Bound orbit negative total energy
- Escape needs total energy zero
Rockets
- Rockets they need not reach escape speed to enter orbit because thrust adds energy continually and orbit needs less energy than escape
Part 5 of 7Energy and atmospheres
Total energy
- E = ½mv2 − GMm/r at launch
Atmosphere
- Atmosphere light gases such as hydrogen can leak from low-mass planets because some molecules exceed the escape speed
Moon
- Moon it has virtually no atmosphere because its escape speed is small
Black hole
- Black hole a body whose escape speed would exceed c
Part 6 of 7Definition wording
Say field
- Say field describe escape from the gravitational field and avoid the words gravity or pull
Data booklet
- Data booklet the equation is given, but its derivation must be known
Part 7 of 7More from the specification
More from the specification
Escape velocity calculation
- Escape velocity calculation equating launch kinetic energy to gravitational binding potential provides an analytical means to derive escape velocity.
Escape Speed from a Gravitational Field
- Escape speed vesc is the minimum initial speed required for an unpowered object to escape the gravitational attraction of a massive body to infinity, derived by equating kinetic energy to the change in gravitational potential energy: ½·m·vesc² = G·M·m / r,
- giving vesc = √(2·G·M / r).
Gravitational Potential Energy and Field Strength Curves
- On a graph of gravitational force or field strength against radial distance r, gravitational field strength g follows an inverse-square curve (g ∝ 1/r²),
- while near a planet's surface the field can be approximated as uniform with parallel field lines.
Orbital Mechanics and Satellite Motion
- A satellite in stable circular motion around Earth experiences an inward resultant centripetal force equal to gravitational pull;
- its orbital speed vorbit = √(G·M / r) is related to escape speed by vesc = √2·vorbit, with orbital period T = 2π·r / v.
Field lines
- Lines showing the direction and strength of a magnetic field.
Equipotential line
- A line joining points of equal gravitational potential.
Potential gradient
- The rate of change of potential with distance, equal to −E
Centripetal force
- Net force toward the centre, mv2/r.
Escape velocity
- Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
Satellite
- A body that orbits a larger one; the Moon is the Earth's natural satellite.
Uniform
- Same density throughout, so the weight acts at the centre.
Period
- Time for one revolution.
Newton
- Unit of force, kg m s-2.
Constant
- Not changing.
Density
- Mass per unit volume.
Equipotential
- A surface of constant potential
Field strength
- G = Fg/m.
Key terms
| Term | Meaning |
|---|---|
| Escape speed | The minimum launch speed to reach infinity without further propulsion. |
| Total energy zero | The condition at the escape threshold where kinetic energy balances potential energy. |
| Bound orbit | An orbit with negative total energy. |
| √2 relation | vesc = √2 × vorb at the same radius. |
| Black hole | A body whose escape speed exceeds c at some radius. |
Avoid these mistakes
1
Thinking the mass of the escaping object changes the escape speed — it cancels.
2
Using altitude instead of distance from the centre.
3
Believing the projectile must keep moving at escape speed all the way — its speed falls to zero at infinity.
4
Mixing up escape speed with orbital speed — they differ by a factor √2.
5
Saying escape needs a vertical launch — any direction works.
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