A satellite follows an approximately circular orbit with radius 7100 km measured from the planet's centre and period 97 min. (a) Calculate its mean orbital speed in m/s using v = 2πr/T. (b) Explain why its velocity changes even if its speed is constant. (c) State the force maintaining the orbit and explain why orbital radius is not the satellite's altitude.

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Accepted Answer

7665 m/s; velocity changes direction; gravity supplies the inward force; radius equals planet radius plus altitude. One circular orbit covers a distance equal to its circumference, 2πr. Convert the data first: r = 7100000 m and T = 5820 s; kilometres and minutes cannot be inserted directly into an answer in m/s. Hence v = 2π × 7100000/5820 = 7665 m/s. This is the orbital path length divided by one full period. Speed describes only the magnitude of motion, whereas velocity includes direction. The satellite continually changes direction around the circular path, so its velocity changes and it accelerates towards the centre even at constant speed. The planet's gravitational attraction supplies the inward force; no outward force is needed to sustain the orbit in this description. Radius is measured from the planet's centre, while altitude is measured above its surface, so altitude alone would underestimate the circumference.

Timing an orbit 2

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