To determine the height at which an artificial satellite must be placed to remain above a specific point on Earth, we need to consider the concept of a geostationary orbit. A satellite in this type of orbit has an orbital period that matches the Earth's rotation period, allowing it to stay fixed over one location on the Earth's surface.
Understanding Geostationary Orbit
A geostationary orbit occurs at a specific altitude where the satellite's orbital period is equal to the rotational period of the Earth, which is approximately 24 hours. This orbit is circular and lies in the plane of the Earth's equator.
Calculating the Required Height
The formula to find the radius of a geostationary orbit is derived from Newton's law of gravitation and the centripetal force required to keep the satellite in orbit. The formula is:
- r = (G * M * T² / (4 * π²))^(1/3)
Where:
- r = radius of the orbit from the center of the Earth
- G = gravitational constant (6.674 × 10^-11 N(m/kg)²)
- M = mass of the Earth (approximately 5.972 × 10^24 kg)
- T = orbital period (in seconds, which is 86400 seconds for 24 hours)
After performing the calculations, we find that the radius of a geostationary orbit is approximately 42,164 km from the center of the Earth. Since the average radius of the Earth is about 6,400 km, we can find the height above the Earth's surface by subtracting the Earth's radius from the orbital radius:
Height Above Earth's Surface
Height = r - Earth's radius = 42,164 km - 6,400 km = 35,764 km.
However, this value is typically rounded to 36,000 km for practical purposes. Therefore, the correct answer to your question is:
Key Takeaways
In summary, a satellite that remains above a specific point on Earth must be in a geostationary orbit, which is approximately 36,000 km above the Earth's surface. This unique position allows the satellite to synchronize its orbit with the Earth's rotation, providing continuous coverage of the same area.
