Some questions regarding gravity

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saln1
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2 random thoughts that struck me:

Q1. If an object is moving downwards towards a large mass at just under the speed of light, will the effects of gravity effectively "stop working" in order to keep the velocity below c?

Q2. If a bullet is fired vertically upwards on the surface of the moon, will the speed at which it lands be the exact same as the speed at which it left the gun, since it's effectively moving in a vacuum?
 
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saln1 said:
2 random thoughts that struck me:

Q1. If an object is moving downwards towards a large mass at just under the speed of light, will the effects of gravity effectively "stop working" in order to keep the velocity below c?

Q2. If a bullet is fired vertically upwards on the surface of the moon, will the speed at which it lands be the exact same as the speed at which it left the gun, since it's effectively moving in a vacuum?

Q1: Gravity will continue increasing the object's velocity and momentum. The velocity approaches c, but the momentum, which is given by [itex]p=m\gamma v[/itex] keeps increasing without approaching a limit, because [itex]\gamma[/itex] approaches infinity as v approaches c.

Q2: yes