The escape velocity on the surface of the moon is small because (1) the moon's gravitational pull is small (2) the moon has no atmosphere (3) the moon is not a planet (4) the moon is revolving around the earth

Escape velocity is the minimum speed an object must have to break free from the gravitational pull of a celestial body, such as a planet or moon. The formula for escape velocity is given by: \(v_{esc}=\sqrt{\dfrac{2GM}{r}}\) where \(v_{esc}\) is the escape velocity, \(G\) is the gravitational constant, \(M\) is the mass of the celestial body, and \(r\) is the distance from the center of the celestial body.

Now that we know the formula for escape velocity, we can analyze each option: 1. The moon's gravitational pull is small. This option is closely related to escape velocity, as a lower gravitational pull would indeed result in a smaller escape velocity. As the gravitational pull is proportional to the mass of the celestial body (\(F=G\dfrac{Mm}{r^2}\)), this option seems promising. 2. The moon has no atmosphere. The absence of an atmosphere has no direct influence on the escape velocity. An atmosphere-less moon might make it easier for an object to navigate through once it has achieved the escape velocity, but it doesn't affect the escape velocity itself. 3. The moon is not a planet. Whether the moon is a planet or not has no influence on the escape velocity. The escape velocity depends on mass and distance from the center, not the classification of the celestial body. 4. The moon is revolving around the earth. The fact that the moon is revolving around the earth does have a small effect on the required escape velocity due to centripetal force. However, this effect only becomes significant when the object to be launched is already at a significant altitude. The moon's orbit around the earth has a minimal influence on the escape velocity at the moon's surface.

Among the given options, the most relevant factor that would affect the escape velocity on the moon's surface is option 1: the moon's gravitational pull is small. Smaller gravitational pull results in a smaller escape velocity required to break free from the moon's gravitational force.