How does the size (radius) of an object affect escape velocity?

The larger the radius, the farther the surface is from the centre of gravity, so the lower the escape velocity at that point.


Gravity is inversely proportional to the square of the distance between the objects.





So if the Earth was twice the radius as now (but the same mass), then the surface is twice as far from the centre of gravity. Which means the surface gravity (and therefore escape velocity from the surface) would be one quarter what it is now.