basically i wouldn't say that there will be any change........... you are kind of mixing general and special theory consequences, When according to special theory, the mass of one will increase, then relatively the mass of other will consequently increase, then it will be upon which of the object has changed its frame of reference.
And according to GTR the gravity influence changes only if the body is accelerating relative to observer, and in this case its 80% c, so basically its not accelerating,
but then we will also have to consider the effects of circular motion, if it is not a constant circular motion results might vary........