Gravity is a natural force that planets have; time is a system humans came up with to measure one moment to the next, so I will say they are independent of each other
Gravity is the warping of space / time by the weak attractive force of matter.
Time is no more the human system used to measure it than your electricity bill is an electro magnetic wave or a stream of charged particles.
Time is measured in certain humanly devised units, but what exactly is being measured?
Time is entirely relative and not constant. The rate that time actually passes depends entirely on how fast you are traveling. At speed of light time would be stationary. Within the event horizon of the gravitational pull of a black hole, time probably ceases to exist at all and light is not only bent but actually pulled backwards by the gravitational force, giving rise to the name black hole.
Read Einstein, Stephen Hawkins and others.
Newtons laws are insufficiently accurate to calculate and predict correctly the exact orbital position of our own moon. This is because time is relative to motion. Laser technology has proved a discrepancy of up to 300 yards, caused by the fact that the moon is in motion relative to the earth and therefore experiences time differently than we do on earth.
Satellite navigational systems constantly have to be adjusted to compensate for the fact that time passes more slowly on the satellite than it does on earth. Without this compensating factor the systems would be miles out instead of yards out of perfect accuracy.
I notice you would not commit yourself on whether light is a wave or a particle. So there are some things you atheists are actually unsure of after all.