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6.1.6Space Physics

Orbital Speed Equation — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

5 min read 9 parts Lesson 11 of 24 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision
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Lesson summary

6.1.6 Orbital Speed Equation — IGCSE Physics Notes — IGCSE PHYSICS notes: Use v = 2πr / T to calculate orbital speed and explain how gravity keeps a body in a near-circular orbit.Force — orbital motion results from the gravitational attraction between two bodies.Direction — the f…

  • Circular motion
  • Steady speed
  • What the symbols mean
  • Orbital period
  • Rearranged
  • Measured from the centre

Part 1 of 7Gravity keeps bodies in orbit

Force
  • Force orbital motion results from the gravitational attraction between two bodies.
Direction
  • Direction the force acts towards the centre of the larger body.
Circular motion
  • Circular motion a body moving in a circle is accelerating because its direction keeps changing.
  • A resultant force towards the centre (a centripetal force) is needed.
  • For a planet this force is the Sun's gravitational attraction.
Steady speed
  • Steady speed the force is at right angles to the motion, so it changes direction but not speed.

Part 2 of 7Orbital speed equation

Equation
  • Equation v = 2πr / T.
    What the symbols mean: v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m) · T = period (s)
Meaning
  • Meaning in one orbital period a body travels once round the circumference of the circle, 2πr.
Quantities
  • v is the orbital speed in metres per second (m/s).
  • r is the average orbital radius in metres (m).
  • T is the orbital period in seconds (s).
Orbital period
  • Orbital period the time taken for an object to complete one orbit.
Rearranged
  • T = 2πr / v and r = vT / 2π.

Part 3 of 7Orbital radius

Measured from the centre
  • Measured from the centre r is the distance from the centre of the body being orbited to the orbiting object.
Height above the surface
  • Height above the surface add the radius of the body to the height to find r.
Reason
  • Reason the mass can be assumed to act at the centre of the body.

Part 4 of 7Units and conversions

Time
  • Time convert T into seconds (1 minute = 60 s, 1 day = 86 400 s, 1 year = 3.15 × 107 s).
Distance
  • Distance convert r into metres (1 km = 1000 m).

Part 5 of 7How orbital speed depends on radius

Further from the Sun
  • Further from the Sun the Sun's gravitational field strength is weaker, so the centripetal force is smaller.
Result
  • Result a planet further out has a smaller orbital speed and a longer orbital period.
Closest planets
  • Closest planets move fastest, and the furthest planets move slowest.
PlanetOrbital radius (million km)Orbital speed (km/s)Orbital period
Mercury57.947.988 days
Venus108.235.0225 days
Earth149.629.8365 days
Mars227.924.1687 days
Jupiter778.613.111.9 years
Saturn1433.59.729.5 years
Uranus2872.56.884 years
Neptune4495.15.4165 years

Part 6 of 7Satellite orbits

Low Earth orbit
  • Low Earth orbit a few hundred km up, about 7.7 km/s with a period near 90 minutes.
  • Used for imaging, weather observation and the International Space Station.
Geostationary orbit
  • Geostationary orbit about 36 000 km above the equator with a period of exactly 24 hours.
  • The satellite stays above the same point on the Earth.
  • Used for television and communications.
Stable orbit
  • Stable orbit each height has one speed that gives a stable circular orbit, and higher orbits are slower.

Part 7 of 7More from the specification

More from the specification
Orbital speed variation in comets
  • Orbital speed variation in comets highly eccentric trajectories cause periodic comets to accelerate rapidly near perihelion, obeying Kepler's second law.
Hemisphere
  • Half of the Earth, northern or southern.
Nebula
  • Cloud of gas and dust in which stars form.
Comet
  • An icy body on a highly elliptical orbit around the Sun.
Solar system
  • A star with the objects that orbit it.
Artificial satellite
  • A man-made object orbiting a body in space.
Elliptical orbit
  • Elliptical orbit a body speeds up as it moves closer to the Sun, gaining kinetic energy as its gravitational potential energy falls.

Key terms

TermMeaning
Orbital speedThe speed of a body along its orbit, v = 2πr / T.
Orbital periodThe time for one complete orbit.
Orbital radiusDistance from the centre of the body being orbited to the orbiting object.
Centripetal forceThe resultant force towards the centre of a circle; for orbits it is gravity.
Geostationary orbitAn orbit above the equator with a period of 24 hours.

Avoid these mistakes

1
Using the height above the surface as r — r is measured from the centre of the planet.
2
Leaving T in days or years — convert T to seconds.
3
Saying no force acts on a planet moving at steady speed — gravity acts all the time and changes its direction.
4
Thinking larger orbits have larger speeds — they have smaller speeds.
5
Forgetting the factor 2π — the circumference is 2πr.

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