Question

The escape velocity of Earth is nearly: ____.

• A. 5.6 km/s
• B. 7.9 km/s
• C. 11.2 km/s
• D. 15 km/s

Hint:

Don't confuse escape velocity (11.2 km/s) with orbital velocity (7.9 km/s). Orbital velocity is the speed needed to stay in a circular orbit around Earth, while escape velocity is the speed needed to leave it entirely.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Escape velocity is the minimum speed an object must reach to break free from the gravitational pull of a celestial body (like a planet) without any further propulsion.

Step 2: Key Formula or Approach:
The formula for escape velocity ($v_e$) is: \[ v_e = \sqrt{\frac{2GM}{R}} \] where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is its radius.

Step 3: Detailed Explanation:
For Earth, substituting the approximate values ($M \approx 5.97 \times 10^{24}$ kg and $R \approx 6.37 \times 10^6$ m) into the formula yields: \[ v_e \approx 11,186 \text{ m/s} \approx 11.2 \text{ km/s} \] This means any object (like a rocket or a molecule of gas) must travel at this speed to leave Earth's atmosphere and never fall back due to gravity.

Step 4: Final Answer:
The escape velocity of Earth is nearly 11.2 km/s.