Step 1: Understanding the Concept:
A geostationary satellite is an earth-orbiting satellite placed in a circular orbit directly above the Earth's equator.
In this orbit, the satellite's orbital period matches the Earth's rotational period (one sidereal day, approximately 23 hours, 56 minutes, and 4 seconds).
This allows the satellite to appear stationary at a fixed position in the sky to ground-based observers. Step 2: Detailed Explanation:
Let us use the laws of orbital mechanics to understand how this specific altitude is determined:
For a satellite to remain in a stable circular orbit, the gravitational pull of the Earth must equal the required centripetal force:
\[ \frac{G \cdot M \cdot m}{r^2} = m \cdot \omega^2 \cdot r \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, \( r \) is the orbital radius from the center of the Earth, and \( \omega \) is the angular velocity.
Solving for the orbital radius \( r \) using the Earth's rotation rate:
\[ r = \sqrt[3]{\frac{G \cdot M}{\omega^2}} \]
This calculation yields an orbital radius of approximately \( 42,164 \text{ km} \) from the center of the Earth.
To find the altitude (\( h \)) above the Earth's surface, we subtract the Earth's mean radius (\( R_e \approx 6,378 \text{ km} \)):
\[ h = r - R_e = 42,164 \text{ km} - 6,378 \text{ km} = 35,786 \text{ km} \]
This value is commonly rounded to \( 36,000 \text{ km} \) in general scientific and technical literature.
Therefore, geostationary satellites are positioned at this altitude to support applications such as continuous weather monitoring and telecommunications. Step 3: Final Answer:
Geostationary satellites are placed at an altitude of approximately 36000 km above the Earth's surface.
