Question

A geo-statinoary satellite is orbiting the earth at a height of 6 R above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5 R from the surface of earth is -

• A. $6\sqrt{2}$hr
• B. 6 hr
• C. $5\sqrt{2}$hr
• D. 10 hr

Answer 1

Answer: (A)

$6\sqrt{2}$hr

Answer 2

Geo-satellite mean whose time period is

T = 24 hr & from law

T² µ R³ Ž $\frac{T_{2}^{2}}{T_{1}^{2}} = \frac{R_{2}^{3}}{R_{1}^{3}}$Ž $\frac{T_{2}^{2}}{(24)^{2}}$ = $\frac{(R + 2.5R)^{3}}{(R + 6R)^{3}}$

T₂ = $\sqrt{\frac{24 \times 24}{8}}$ = 6$\sqrt{2}$ hr.