A geosynchronous satellite at 35780 km moves at about 3.08 km/s with orbital radius 42180 km (use π = 3.14). Approximately how long does it take to complete one revolution?

1. In one revolution the satellite travels the circumference $2\pi r$, so $T = \dfrac{2\pi r}{v}$. 2. Substitute: $T = \dfrac{2 \times 3.14 \times 42180}{3.08}$ (km and km/s). 3. Numerator: $2 \times 3.14 \times 42180 \approx 264890$. 4. Divide: $T \approx \dfrac{264890}{3.08} \approx 86003\text{ s}$. 5. Convert: $86003 \div 3600 \approx 23.89\text{ hr}$, i.e. about 23 hr 54 min. 6. The 90-minute value (rule out) is for Low Earth Orbit satellites. So the period is about 24 hours. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 10 "Space Missions", p.148_