Question

Two small satellites move in circular orbits around the earth, at distances r and r + ∆r from the centre of the earth. Their time period of rotation are T and T + ∆T. (∆r << r, ∆T << T)

• A. ∆T = $\frac{3}{2}T\frac{\Delta r}{r}$
• B. ∆T = -$\frac{3}{2}T\frac{\Delta r}{r}$
• C. ∆T = $\frac{2}{3}T\frac{\Delta r}{r}$
• D. ∆T = T$\frac{\Delta r}{r}$

Answer 1

Answer: (A)

∆T = $\frac{3}{2}T\frac{\Delta r}{r}$

Answer 2

T² ∝ r³ or T² = cr³

Sol. ⇒ 2T∆T = 3cr²∆r.

Dividing, $\frac{2T\Delta T}{T^{2}} = \frac{3cr^{2}\Delta r}{cr^{3}}$.