Motion of orbiting satellites
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA satellite in a circular orbit moves at exactly the speed where gravity curves its path into a closed loop, vorb = √(GM / r). Push past it and the loop stretches into an ellipse; reach √2 times that speed and the path opens and never returns. The satellite's own mass never enters, and a bound orbit always carries negative total energy.
Half a dozen relationships have to stay straight here. Escape speed is √2 times the circular speed, not twice it. The orbiting body's mass cancels out of both the speed and the period. A bound orbit's total energy is negative; for a circular orbit E = -GMm / 2r (swap r for the semi-major axis a on an ellipse). Gravity weakens as GM / r² with distance but never vanishes in orbit. And Kepler's third law ties the period to orbital size as T² ∝ r³ for a circular orbit (T² ∝ a³ in general), so a wider orbit is much slower.
Motion of orbiting satellites
3 ways in · any order
Lesson
Motion of orbiting satellites
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Orbital mechanics for circular orbits: the orbital speed v orbital equals the square root of GM over r, why the satellite's mass cancels, escape speed as the square root of two times the circular speed, the negative total energy of a bound orbit minus GMm over 2r, gravity that weakens as GM over r squared, and Kepler's third law T squared proportional to r cubed. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the five Topic 6.6 mistakes: confusing orbital speed with escape speed, thinking a heavier satellite orbits faster, mishandling the sign of the orbital energy, treating gravity as constant instead of GM over r squared, and misreading Kepler's third law. Take it cold to see what still trips you up, or after the lesson to confirm it does not.
Targeted Practice
Drill a single misconception
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Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.