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D.1.12 Effects of Drag on Orbital Motion — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 14 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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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.
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Lesson summary

D.1.12 Effects of Drag on Orbital Motion — IB PHYSICS HL notes: Explain how viscous drag on a low-orbit satellite lowers its total energy and orbit and increases its speed.Which satellites — those in low orbits (below about 600 km) pass through a very thin upper atmosphereDensity…

  • Cause of energy loss
  • Stronger when
  • Kinetic energy
  • Total energy in orbit
  • Orbital speed
  • Energy exchange

Part 1 of 8Drag on low-orbit satellites

Which satellites
  • Which satellites those in low orbits pass through a very thin upper atmosphere
    • (below about 600 km)
Density
  • Density the air is of very low density but not zero
Force
  • Force a small drag force opposes the velocity but acts continuously over each orbit
Cause of energy loss
  • Cause of energy loss friction between air particles and the surface of the satellite
Stronger when
  • Stronger when the atmosphere expands in high solar activity or the satellite has a large area and small mass

Part 2 of 8Energy dissipation

Kinetic energy
  • Kinetic energy some is dissipated as thermal energy in the surroundings and satellite
Total energy
  • Total energy it is reduced
Total energy in orbit
  • E = −GMm/2r, so a more negative E means a smaller radius
Result
  • Result the satellite spirals towards the Earth

Part 3 of 8Why the speed increases

Orbital speed
  • Orbital speed v = √(GM/r) so a smaller radius means a higher speed
Energy exchange
  • Energy exchange the potential energy falls by twice the total energy lost while kinetic energy rises by the amount of total energy lost
Gravity
  • Gravity it does more positive work pulling the satellite inward than drag removes
Conclusion
  • Conclusion drag makes the satellite faster, not slower
Total energy
  • Total energy it decreases because the fall in potential energy is larger than the rise in kinetic energy

Part 4 of 8Consequences of decay

1
Lower altitude, higher speed and shorter period
2
Higher kinetic energy and lower potential and total energy
3Denser air
  • Denser air drag and heating increase, so the decay accelerates and the final stages are rapid
4Almost circular
  • Almost circular circular-orbit formulae still apply at each stage

Part 5 of 8Size of the effect

Energy change
  • Energy change for a small fall Δr, ΔE = (GMm/2r2)Δr = ½mgΔr
Drag work
  • Drag work the work done by drag over a distance s is Fs, which can be equated to the energy lost
Prediction
  • Prediction re-entry time is hard to predict because air density varies with solar activity

Part 6 of 8Practical consequences

1Reboost burns
  • Reboost burns periodic engine burns restore the altitude of stations such as the ISS
2Communications satellites
  • Communications satellites placed in high orbits where drag is negligible
3Disposal
  • Disposal satellites at end of life may be lowered so they burn up on re-entry

Part 7 of 8Writing an explanation of decay

1
Air molecules collide with the satellite and exert a force opposite to its motion, doing negative work.
2
The total mechanical energy of the satellite decreases.
3
Since E = −GMm/2r, a lower total energy means a smaller orbital radius.
4
Since v = √(GM/r), a smaller radius means a higher speed.
5
The lost energy appears as thermal energy.

Part 8 of 8More from the specification

1Gravitational field strength of planets
  • Gravitational field strength of planets surface gravitational field strength varies between planets depending on planetary mass and radial distance from the planet centre.
2Planetary escape velocity requirement
  • Planetary escape velocity requirement escaping a planet's gravitational field requires accelerating an object past escape speed,
    • where kinetic energy overcomes potential well.
3Radial field lines around spherical bodies
  • Radial field lines around spherical bodies field lines around planets point symmetrically towards the centre, unlike approximately uniform fields near local ground surfaces.
4Atmospheric drag on low Earth orbits
  • Residual atmospheric drag exerts resistive forces on low Earth orbit satellites, dissipating total mechanical energy and reducing orbital radius.
5Orbital decay and speed increase
  • As a satellite's orbit decays to lower altitude, gravitational potential energy is converted to kinetic energy, paradoxically increasing orbital velocity.
6Planetary gravitational fields
  • Surface gravitational field strength depends directly on planetary mass and inversely on the square of planetary radius.
7Field lines
  • Lines showing the direction and strength of a magnetic field.
8Escape speed
  • Minimum launch speed to reach infinity, √(2GM/R).
9Equipotential line
  • A line joining points of equal gravitational potential.
10Potential gradient
  • The rate of change of potential with distance, equal to −E
11Centripetal force
  • Net force toward the centre, mv2/r.
12Escape velocity
  • Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
13Planet
  • A large body that orbits the Sun and whose gravity clears its orbit.
14Uniform
  • Same density throughout, so the weight acts at the centre.
15Newton
  • Unit of force, kg m s-2.
16Constant
  • Not changing.
17Equipotential
  • A surface of constant potential
18Gravitational field
  • Region where mass experiences gravitational force.
19Gravitational potential
  • Work done per unit mass in bringing a test mass from infinity to the point.
20Field strength
  • G = Fg/m.

Key terms

TermMeaning
Atmospheric dragA resistive force on a body moving through air, opposing its motion.
Orbital decayThe gradual lowering of an orbit due to energy loss.
ReboostAn engine burn that raises a satellite's orbit.
Re-entryThe descent of a satellite into the dense atmosphere where it heats up and burns.
Thermal energyEnergy transferred to the random motion of molecules by drag.

Avoid these mistakes

1
Saying drag makes the satellite slow down — its speed increases as it spirals in.
2
Forgetting that drag removes total mechanical energy, making E more negative.
3
Believing a satellite moves outward when it speeds up — it moves to a smaller orbit.
4
Using a constant radius while computing energy loss from drag.
5
Claiming gravity does negative work — it does positive work as the satellite descends.

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