WAEC Physics 2021 Theory — Question 14
Question 14 of 35 from the West African Examinations Council (WAEC) Physics 2021 Theory paper, with the correct answer and a full explanation.
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9(a). A satellite of mass m orbits the earth of mass M with a velocity v at a distance R from the centre of the earth. Derive the relationship between the period, T, of the orbit and R.
Model answer
Gravitational force provides the centripetal force: GMm/R² = mv²/R, so v²=GM/R. Since v=2πR/T, (2πR/T)²=GM/R, giving T²=(4π²/GM)R³ — i.e. T² is proportional to R³ (Kepler's third law).
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