A spacecraft moves in a circular Low Earth Orbit at an orbital radius $r = 7200\text{ km}$. Taking Earth's standard gravitational parameter as $\mu = 3.986 \times 10^5\text{ km}^3/\text{s}^2$, what is the circular orbital speed of the spacecraft in km/s? (Round off to two decimal places).

Answer Key:

7.44

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Vis-Viva for Circle:** $v = \sqrt{\frac{\mu}{r}}$. 2. **Stage 2: Parameters:** $\mu = 398600\text{ km}^3/\text{s}^2$, $r = 7200\text{ km}$. 3. **Stage 3: Computation:** $v = \sqrt{398600 / 7200} = \sqrt{55.36111} = 7.4405\text{ km/s}$. 4. **Stage 4: Final Value:** 7.44 (range 7.40 to 7.48).

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