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Question

A satellite is moving in a circular orbit around earth. If percentage error in measuring its time period of rotation is 1% and in measuring the radius of orbit is 2%, then what is the maximum possible error in the angular momentum of the satellite about the centre of earth?

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Solution

$\begin{array}{l} L = m V r = m ω r^{2} = m \frac{2 π}{T} r^{2} \\ ∴ {(\frac{Δ L}{L})}_{\max} \times 100 % = 2 (\frac{Δ r}{r}) \times 100 % + (\frac{Δ T}{T}) \times 100 % \\ = 2 \times 2 % + 1 % \\ = 5 % \end{array}$

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