I was just thinking about how if a planet is moving very quickly through space, everything we "throw" from it with mass would leave with a momentum from Earth, like a ball dropped in moving car, of course. But if light has only a constant speed, no relative speed, even when two beams travel in opposite directions, does that mean it gets "left behind", instantly falling backwards to our eyes if we were able to see it for a selected beam somehow? If we were traveling fast enough through space could we notice this, or do we already?
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Light travels at the same speed in all reference frames. This fact is well supported by experiments (starting with the famous experiment of Michelson and Morley). Furthermore, consequences of this fact were deeply explored by Einstein. Therefore light most certainly is not "left behind" and it certainly does not end up "instantly falling backwards to our eyes". A good starting reference to aid in understanding of this might be Spacetime Physics by Edwin F. Taylor and John Archibald Wheeler.
Nathan C
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When you drop a ball from a moving car, it has the same speed as the car. Then gravity pulls it downward.
You are right that it takes a piece of momentum with it. The total momentum before you drop the ball is $(m_{car} + m_{ball})v$. After you drop the ball, the car has momentum $m_{car}v$ and the ball $m_{ball}v$.
It gets more complex when you throw the ball. The before and after momentum is the same, but you transfer some of the car's momentum to the ball. If you throw it forward, the ball has velocity $v + v_{throw}$. The ball has momentum $m_{ball}(v + v_{throw})$ and the car has momentum $m_{car}v - m_{ball}v_{throw}$.
If you shine a flashlight forward from the car, the beam races forward at the speed of light. The car is left behind. You "throw" the beam forward. A little momentum is transferred from the car to the beam.
See this for more - How can a red light photon be different from a blue light photon?
mmesser314
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