Answer to Question #155375 in Physics for Andu

Question

Calculate the first cosmic velocity for a satellite launched from the Moon, near the surface several hundred km. Compare this value with that of the Earth, which as you know is about 8 km / s. The radius of the Moon is R = 1740 km, while the acceleration of the free fall near the surface of the Moon is g = 1.6 m / s²

Answer 1

The first cosmic velocity for a satellite launched from the Moon, near its surface, is

$$v_1=\sqrt{2gr}=\sqrt{2\cdot1.6\cdot1740000}=2360\text{ m/s},$$

or around 2.4 km/s. This value is smaller than the first cosmic velocity for our planet because the mass of the moon is smaller.