Question E2A10:
What type of satellite appears to stay in one position in the sky?  

Choices:  
A: HEO  
B: Geostationary  
C: Geomagnetic  
D: LEO    

Correct Answer is  B: Geostationary  

Correct answer: Geostationary

Why it’s correct:
- A geostationary satellite is in a circular, equatorial orbit with an orbital period equal to Earth’s sidereal rotation period, so it appears fixed at one point in the sky to a ground observer.
- Conditions:
  - Zero inclination (equatorial)
  - Circular orbit
  - Orbital period $T$ equals Earth’s sidereal day ($\approx 23\,\text{h}\ 56\,\text{m} = 86{,}164\ \text{s}$)

Why the others are incorrect:
- HEO (Highly Elliptical Orbit): Moves slowly near apogee but still drifts across the sky; not stationary.
- Geomagnetic: Refers to Earth’s magnetic field, not an orbit type.
- LEO (Low Earth Orbit): Orbits in about 90–120 minutes and rapidly crosses the sky in a few minutes per pass.

Useful formulas and rules of thumb:
- Orbital period for a circular orbit:
  $$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$
  where $\mu = GM_{\oplus} \approx 3.986\times 10^{14}\ \text{m}^3/\text{s}^2$ and $a$ is the orbital radius from Earth’s center.
- For geostationary:
  - Set $T = 86{,}164\ \text{s}$ ⇒ $a \approx 42{,}164\ \text{km}$, so altitude above Earth’s surface:
    $$h \approx 42{,}164\ \text{km} - 6{,}378\ \text{km} \approx 35{,}786\ \text{km}$$
- Rule of thumb: “Geostationary = equatorial, circular, 24-hour period, ~35,786 km altitude; appears fixed in az/el.”