Newton's third law does apply here, but it is sometimes hard to conceptualize. The forces are equal and opposite, but apply to different bodies. If they applied to the same body, nothing would move. Think of pushing a box. At each interface, there are equal forces in each direction. So think about the side you're pushing. There is force on the box you are pushing, and a force backwards on you from your hands. Similarly, you are pushing off of the Earth, so there is a force forward on you, and backward on the Earth. So, the forces on you cancel, the box moves forward, and the force on the Earth is infinitely small compared to the size of the Earth. Does this help? I can draw and send you a diagram of the situation if that would help, just send another email. :)