How does Newton's second law relate to the force of gravity?

Newton's second law is ##F=ma##, gravity accelerates objects.

Gravity exerts a force on things: 1). without mass because gravitational fields (in particular, strong gravitational fields) change the shape of space-time (e.g.. gravity bends light) and 2). with mass because of the gravitational field. Newtons second law can be expressed by the following equation: ##F=ma##. In objects with mass a net external force is applied to the object by the gravity of other objects. The effect of this acceleration could be a comet in space changing direction when it moves past a planet.

On Earth, apples only fall because of the force of gravity. Newtons first law explains that if there was no net external force acting on the apple it would have no therefore it is the force of gravity that makes the apple fall.