Iron Sun 254 wrote:Actually, I'm talking about Special Relativity. My question is related to the gravitational force experienced by one body by another body based on the relative velocity of the two.
As Chris suggested, your thought experiment is incorrectly presented. You basic question is a good one, and special relativity does provide insight towards a conclusion, but you have misinterpreted what SR is telling you. Let's start by frankly stating that SR
does not explicitly deal with gravity. However, with constraints, you can deal with acceleration in SR:
http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html wrote:Can Special Relativity handle accelerations?It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames. It is claimed that general relativity is required because special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames but can still deal with them. Accelerating objects can be dealt with without even calling upon accelerating frames. ...
A good example is Einstein first described
gravitational time dilation by incorporating acceleration into SR.
Now take your example of two identical planets passing by each other at a known constant velocity. You are correct in that event timing measurements made by planet 1 of events on planet 2 will reveal SR time dilation, but applying that obervation to modifying gravity on the other planet is incorrect. Concluding that clocks on planet 2 are running slower is the correct SR interpretation. Nothing more, nothing less. In fact, a modified thought experiment will lead you to conclude that the mass is the same. The time dilation (slower clocks) cancels the false conclusion that planet 2 gravity / mass is less.
OK, here's the kicker, and SR is the source of this interpretive extrapolation: SR predicts that the relativistic mass (energy!) increases with velocity - Like time dilation, this is a fundamental result. Well, if your first thought is that gravity should
increase, you would be right!! The details are complicated, but the interpretation is not. From GR, gravity (space-time curvature) originates from all forms energy, kinetic, thermal, radiation, mass (=mc^2). Therefore, the real answer about gravity and motion is that planet 2 "gravity" increases with velocity, and detailed GR tests and calculations will reveal that effect to observers on planet 1.
So Iron Sun, it appears to me you were mislead by incorrectly applying SR and time dilation to conclude that gravity should change. But, your thought about SR telling you something, though indirectly, about gravity is valid. It's not time dilation though, but mass "dilation". I say this because mass/energy is scaled by the same factor, γ.