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

*Correct Answer is  B: Geostationary*  

### AI Response: (may contain errors)  

A geostationary satellite appears to stay in one position in the sky because it orbits the Earth at the same rotational speed as the Earth itself. This means it completes one orbit every 24 hours, matching the Earth's rotation period.

### Explanation:

- **Correct Answer: B: Geostationary**
  - A geostationary satellite orbits the Earth at an altitude of approximately 35,786 kilometers (22,236 miles) above the equator. At this altitude, the satellite's orbital period matches the Earth's rotation period, making it appear stationary relative to a fixed point on the Earth's surface. This is useful for applications like weather monitoring and communications.

### Why the Other Choices are Incorrect:

- **A: HEO (Highly Elliptical Orbit)**
  - Satellites in highly elliptical orbits have an elongated orbit that takes them far from the Earth at one end and much closer at the other. They do not appear stationary because their speed and position change significantly throughout their orbit.

- **C: Geomagnetic**
  - "Geomagnetic" refers to the Earth's magnetic field and is not a type of satellite orbit. It is unrelated to the concept of a satellite appearing stationary in the sky.

- **D: LEO (Low Earth Orbit)**
  - Satellites in low Earth orbit are much closer to the Earth, typically at altitudes between 160 to 2,000 kilometers (99 to 1,242 miles). They move quickly across the sky and do not appear stationary because they complete an orbit in about 90 to 120 minutes.

### Useful Formula:

The orbital period $T$ of a satellite is given by:

$$
T = 2\pi \sqrt{\frac{a^3}{\mu}}
$$

where:
- $a$ is the semi-major axis of the orbit (distance from the center of the Earth to the satellite),
- $\mu$ is the standard gravitational parameter for Earth, approximately $3.986 \times 10^{14} \, \text{m}^3/\text{s}^2$.

For a geostationary orbit, $T$ is 24 hours, which matches the Earth's rotational period.