Gravity fails to explain the motion of planets. And it always fails to explain the reason why the orbits of planets have lasted as long as they have. If the universe was really billions of years old, the orbits of many planets would have decayed already and entered the sun. There is a deity hence there has to be a flat earth model. There is another force at work besides gravity that makes the orbits established. Just mere Big Bang does not suffice...
The 'magic' is the mass of the globe. Space is like a fabric, although it is not a real fabric the same principle works. Lay down on your bed. Put a marble next to you. Where does the marble go? It will move towards you. You have lots of mass, the mass of the marble is very tiny, so it moves towards you. You bent your matress and form a slope.
Now in space the same principle applies. The mass forms a slope. Objects with lower mass are pulled towards the objects with high mass. Hence we orbit the sun, because it has a huge mass.
Put two marbles on your bed and nothing will happen, move them closer to each other and see them move towards eachother. Use some heavy marbles though, because your mattress is pretty stiff. Or use a cloth you span across horizontally over some object (with the middle clear of any obstructions).
Now why don't we move towards the sun is because of our speed. We have an orbital speed, which allows us to stay in our track around the sun. The same thing as a roulette table. The ball is located on a slope, but due to the high speed it maintains its path and spins around. It slows down due to friction with the table and the air, slowly going towards the middle. The same would happen to the earth if you were able to stop it from moving around. In space there is no friction and all the planets are nicely lined up so they do not affect each other's path. This was different about 4.5 billion years ago when our solar system was formed. It just all settled in the many, many years that were to come.
Edit: It needs to be explained that mass and weight are two complete different things. Weight is the force that is acting down on you, where mass is the actual 'weight' an object has. If you take a plane and make a parabolic flight, once you go down you feel weightless. Zero gravity. It is expressed in g-force and 0 g-force is when you could float through the air. You also experience this in a rollercoaster (much cheaper alternative). Once you go down with high speed, you will actually start to become weightless, hence the safety harness to keep you aboard. Once you go up, you feel very heavy, and you are pushed inside your seat.
However do you actually lose weight while on a ride in a rollercoaster? Would a scale tell you, you weigh different when measuring before or after the ride? The answer is no (unless you puked, but that is never a significant change). You remain your same body as you go along in the ride, yet you feel heavier. You did not gain in mass, obviously, you are still the same person, but you feel heavier and that has to do with the kind of force that (what's in the word?) weighs upon you.