Question

a satellite in geosynchronous orbit travels one earth circumference in a full day. from a point on the ground, the satellite appears stationary overhead. the orbital height for a geosynchronous satellite is about 36,000 km. the radius of earth is 6400 km. about how far does the satellite travel in 8 hours? assume the length of an earth day is exactly 24 hours.

Explanation:

Step1: Find satellite orbit radius

The orbit radius of the satellite is the sum of Earth's radius and the satellite's orbital height.
$r = 6400\ \text{km} + 36000\ \text{km} = 42400\ \text{km}$

Step2: Calculate orbit circumference

Use the circumference formula for a circle $C=2\pi r$.
$C = 2 \times \pi \times 42400\ \text{km} \approx 2 \times 3.1416 \times 42400\ \text{km}$

Step3: Compute distance in 8 hours

Since 8 hours is $\frac{8}{24}=\frac{1}{3}$ of a full day, the distance is $\frac{1}{3}$ of the circumference.
$\text{Distance} = \frac{1}{3} \times 2 \times 3.1416 \times 42400\ \text{km} \approx \frac{1}{3} \times 266403.84\ \text{km}$

Answer:

Approximately 88801 km (or $\approx 8.9 \times 10^4$ km)