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TwiddleLab / Physics / Gravity and Orbits

Orbit Speed and Period

Lesson 4 of 10 · 7 min · Free, no account needed

What you will learn

  • In a circular orbit gravity is the centripetal force: GMm / r² = m v² / r gives v = √(GM / r).
  • Lower orbits are faster and have much shorter periods: the ISS laps Earth in about 92 minutes, GPS in about 12 hours.
  • At about 36,000 km up a lap takes one day, so a geostationary satellite hangs over one spot.

Start the lesson

How the lesson goes

  1. The ISS circles Earth in about 92 minutes, GPS satellites in about 12 hours. What decides the speed?

    Tap the satellite you think moves faster.

  2. Turn the height dial and fill the table. Which orbit is fastest?

  3. TV satellites never move in the sky. Drag the satellite until it stays above the city.

  4. Orbital speed and period

    For a circular orbit, gravity supplies the centripetal force: G M m / r² = m v² / r. So v = √(GM / r), the same for any satellite mass.

    The period is the time for one lap: T = 2πr / v. Higher orbit: slower and a longer way, so a much longer period.

    A geostationary orbit is about 35,800 km above the equator, with a period of one day. Simplified model: circular orbits, a perfectly round Earth, no air.

  5. Game: Constellation. Cover the whole equator with three satellites, as low as you can.

    Drag the yellow handle to set the ring's height, drag the satellites round it.

  6. An orbit 4 times as far from the centre. How many times longer is its lap?

    T = 2πr / v and v = √(GM / r). With r × 4 the path is × 4 and the speed is × ½, so T is × 8.

  7. Code: a simulator moves a satellite in small time steps. Try a big step, then a small one.

  8. Orbit A circles Earth at radius r. Orbit B circles a planet 4 times heavier at 2r. Which lap takes longer?

    T = 2π √(r³ / GM). For B, r³ is 8 times bigger and M is 4 times bigger, so T² is 2 times bigger and T is √2, about 1.4 times longer.

  9. Your constellation is up. Tap a city to make a call to the other side of the planet.

Previous lesson: Universal Gravitation: Inverse Square · Next lesson: Weightless Means Falling · Part of the course: Gravity and Orbits

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