Astronomy Practice Exam

What is the approximate escape velocity from Earth?

1. 8 km/s

2. 11 km/s

3. 15 km/s

4. 20 km/s

The correct answer is: 11 km/s

Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body, such as Earth, without any further propulsion. For Earth, the escape velocity is approximately 11.2 kilometers per second. This value is derived from the formula for escape velocity, which can be expressed as \( v_e = \sqrt{\frac{2GM}{r}} \), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth from the center to the surface. Breaking this down, the mass of the Earth and its radius leads to the approximate result of 11.2 km/s. This means that any spacecraft or object must reach this speed to leave Earth's gravitational influence. Speeds lower than this would result in the object falling back to Earth, whereas speeds higher than this would enable it to escape into space. In terms of the other values, 8 km/s is less than the required speed for escape, making it insufficient for overcoming Earth's gravity. 15 km/s and 20 km/s exceed the escape velocity and, while technically correct in terms of being able to escape, they are not the most accurate representation of what's required to leave Earth, indicating