An artificial satellite moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth's surface, will be at a height_______________ km.

Explanation

To solve the problem, we need to find the height of an artificial satellite moving in a circular orbit around the Earth at a speed that is half the escape velocity from the Earth's surface.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
The escape velocity \( v_e \) from the Earth's surface is given by the formula:
\[
v_e = \sqrt{2gR}
...