Nope - why should it turn? Gravitational pull does not work like a string...not at all - please do not use this metaphor again. It's like "We should nail horse-shoes to the tires of your car! Because cars are like horses - try to ride a horse without horseshoes regularly and you'll see what happens." The object would only turn if the frontside would feel another gravitational pull than the backside. Wich it doesn't! And even if it would, the effect would be very hard to notice - a far cry from "allways face the same side to the celestial body". No! The grenade will hit the ground with it's nose because of aerodynamics. Why do you think genades are formed the way they are? Some of the even have fins to facilitate this! You add the gravity vector to every point of the grenade, therefore it does not turn (Same argument as above). But you do realize, that lower orbits are faster than higher orbits, yes? Not the other way around.... Another example: The earth rotates more than once in a year! If your model was true Earth would allways has to face the same side to the sun. No days, no nights - one side a burning hell, the other one shrouded in eternal darkness.