That object is not moving. Only the rocket around it is moving. This is like asking, why the cup moves towards the water, when you pour water into it; that doesn't make much sense, because it isn't the cup that is moving - it is the water.
When all the surroundings are moving, but you aren't it is easy for your brain to get tricked. It creates an illusion of you moving, because the brain assumes that the surroundings are stationary. This is the origin of the so-called but non-existing "centrifugal force" - when turning in your car, you feel squeezed towards the window. But it is actually not you moving into that window, it is rather the window moving into you (the car is turning sideways, while your body expected to continue forwards).
Imagine a roller-skater standing on wheels in a bus. The bus suddenly accelerates. From your eyes when you are sitting inside the bus, it looks like the roller-skater is moving backwards. But he isn't. He is just standing still. Rather, it is the bus-floor that is moving forwards away from him.
Likewise, the answer to your example is fairly simple: the object isn't moving, the surroundings are. Nothing makes the object "attract downwards". It is just an illusion. It isn't moving at all.