A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's orbital speed,if it makes one revolution every 90 min? (You might want to know that the radius of the Earth is approximately 6400 km).
A)1 km/s
B)2 km/s
C)4 km/s
D)8 km/s
E)16 km/s

Question

Quizplus · Accepted Answer

The orbital speed $v$ of a satellite is given by the formula $v = \frac{2\pi r}{T}$, where $r$ is the radius of the orbit, and $T$ is the orbital period. The radius of the orbit is the sum of the Earth's radius and the altitude of the satellite, which is $6400 \, \text{km} + 500 \, \text{km} = 6900 \, \text{km}$. The orbital period $T$ is 90 minutes, which is $1.5$ hours or $5400$ seconds. Plugging these values into the formula gives $v = \frac{2\pi \times 6900}{5400} \approx 8 \, \text{km/s}$.

A Spy Satellite Is in Circular Orbit Around the Earth