i have always believed diagrams are the best way to explain things. this isn't exactly a scientifically scaled drawing but i hope it makes things a little clearer. also i would avoid using the solar system as it is very complex
the first picture is someone throwing a ball on the earth the trajectory will change such that the ball begins falling towards the earth.
similarly, the second is scaled up in velocity and distance from the centre of the earth. so the distance moved by the projectile now compensates exactly for how much the object has "fallen." The force of gravity in the second picture IS the centripetal force. It is the only force involved.
Centripetal force is the resultant of all the other forces in a system.
(the first picture would look the same but in this case the curvature of the earth is too small, or the speed of the projectile is too low, or the object isn't far away enough).
centrifugal forces don't really exist until you look in a rotating reference frame - i would definitely avoid this. like the plague. just view the solar system with the sun stationary and ignore the wobble due to planetary gravity and your life will be much more bearable.
