The escape velocity from the Moon for a lunar landing module sitting on the surface is approximately 2.38 km/s (1.48 miles/s).

Here's how to calculate it:

* Escape velocity formula: v = √(2GM/r)

* v = escape velocity

* G = gravitational constant (6.674 × 10⁻¹¹ m³/kg s²)

* M = mass of the Moon (7.342 × 10²² kg)

* r = radius of the Moon (1.737 × 10⁶ m)

* Plug in the values: v = √(2 * 6.674 × 10⁻¹¹ m³/kg s² * 7.342 × 10²² kg / 1.737 × 10⁶ m)

* Calculate: v ≈ 2380 m/s ≈ 2.38 km/s

Important note: This is the theoretical escape velocity. In reality, factors like the landing module's trajectory and atmospheric drag (which is minimal on the Moon) can affect the actual velocity needed to escape the Moon's gravitational pull.