Step 1: Physical idea behind satellite motion.
A satellite moving around the Earth is not supported by any external force. Instead, it is constantly falling toward the Earth under gravity, but its sideways motion keeps it moving along a circular path.
Step 2: Balance of forces.
For a satellite to remain in a stable circular orbit, the gravitational pull of the Earth must provide exactly the centripetal force needed for circular motion:
\[ \frac{m v^2}{r} = \frac{G M m}{r^2} \]
Here, \( m \) is the mass of the satellite, \( M \) is the mass of the Earth, \( r \) is the orbital radius, and \( G \) is the gravitational constant.
Step 3: Required velocity.
Solving the above equation for velocity gives:
\[ v = \sqrt{\frac{GM}{r}} \]
This is the precise speed a satellite must have to keep moving in a circular orbit at radius \( r \).
If the satellite moves slower than this speed, gravity pulls it downward and it falls toward Earth. If it moves faster, and especially if the speed reaches \( \sqrt{2}\,v \), it can escape Earth’s gravitational field.
The term terminal velocity applies to objects moving through air and is unrelated to orbital motion.
Step 4: Final conclusion.
The speed required to keep a satellite in a circular orbit is called the orbital velocity.