Re: Does the rotation of the earth and it's orbit around the sun affect gravity

OK, special relativity dictates this. An object's mass increases with its 
speed. Likewise, the force of gravity from it increases as well (F = ma 
still holds). But the effect is negligibly small, probably well beyond 
what can be measured with current technology. The earth's speed is 
only about 20 km/s.  Regardless, the earth's speed is small 
compared to the speed of light; so relativistic effects in changes of 
mass are negligibly small. 

Greater, but not much greater. Increased mass does mean 
increased gravitational force and thus increase weight. But if the 
earth suddenly stopped orbiting the sun, we wouldn't notice any 
difference in our weight. We cannot sense the difference, and we do 
not have the technology to measure changes that small.

There's something else to consider. Since the earth is spinning, 
people on the equator weigh noticeably less than they do at the 
poles. Off hand I'd guess probably a hundredth of a percent.  This is 
not related to relativity but to plain old Newtonian mechanics, i.e., 
centripetal force. One way to think about it is as follows: at the 
equator, some of the force of the earth's gravity is "used up" to make 
the person move in a curved path as the earth rotates. Thus, the 
person weighs less. (This is not the case at the earth's pole because 
the person is not moving relative to the earth's center.) If the earth 
rotated quickly enough at just the right speed, the person at the 
equator would experience no weight whatsoever. That person would 
essentially be in orbit around the earth's center. He'd have to be 
going about 7 km/s; so the earth would have to be spinning really 
fast.