A question about theory of relativity?

I was just thinking, its proven light in a vacuum is always constant and light is affected by gravity(Einstein proved light can bend due to gravity) . What will happen if I shoot a beam of light directly above my head on a planet without an atmosphere, shouldn't gravity slow it down, even if its in a vacuum?

Sorry. Gravity does not bend light. It bends space-time, and light follows the lines of space-time. It may seem a technical difference, but it is more than that. Light has no mass, and is not affected, per se,  by gravitational fields.

Gravitational fields will distort (bend) space, and an observer will note that time has slowed down in a gravitational field. So it will appear that light has slowed down. But an observer IN that field will not observe any change.

We can observe relativistic gravitational effects near objects the size of our sun, not usually near smaller celestial bodies like planets, but there is still this effect, for any object with mass.

gravity doesn't' concert with vacuum.it mean maybe there is vacuum but because of planet there is gravity .
in any case gravity can't bend light. it make a curvition in space

No, If you shoot a beam of light upwards from an atmoshpere'less planet, it will not slow down... Gravity does not slow down light,,,, gravity can only curve lights path, but the light continues at the same speed on that path anyway... Experimental data of moon distance measurements varify this. and Relativity, also the sun shoots light beams straight into the vacuum and those light beams do not slow down