Question

The velocity required for a satellite to remain in a circular orbit close to Earth is called:

• A. Escape velocity
• B. Orbital velocity
• C. Terminal velocity
• D. Relative velocity
• E. Critical velocity

Hint:

For a satellite close to Earth's surface (\( r \approx R_{earth} \)), the orbital velocity is approximately 7.9 km/s, while the escape velocity is 11.2 km/s.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A satellite in orbit is essentially in a state of continuous "free fall." To stay in a circular path, the gravitational attraction must be exactly balanced by the required centripetal force.
Step 2: Key Formula or Approach:
Centripetal Force = Gravitational Force
\[ \frac{m v^2}{r} = \frac{G M m}{r^2} \]
Where \( m \) is the satellite mass, \( M \) is the Earth's mass, \( r \) is the radius of orbit, and \( G \) is the gravitational constant.
Step 3: Detailed Explanation:
Solving for velocity \( v \):
\[ v = \sqrt{\frac{GM}{r}} \]
This specific velocity is called the Orbital Velocity.
- If the velocity is lower than this, the satellite will spiral down and crash into Earth.
- If the velocity is higher (reaching \( \sqrt{2} \times v_{orbital} \)), it becomes the **Escape Velocity**, and the satellite leaves Earth's orbit.
- **Terminal velocity** is a concept in fluid mechanics (falling through air), not orbital mechanics.
Step 4: Final Answer:
The velocity required for a circular orbit is defined as the Orbital velocity.