# How is gravity time symmetric since it is only an attractive force?

I've read that gravity is time symmetric, and from what I understand, that means that if I were to record a video of objects moving only under the influence of gravity and play it in reverse, it would not go against the laws of physics. But an apple can fall down. When reversed, the apple would float upwards as though it were being repelled?

Under time reversal, $t\to-t$. Other physical quantities may change due to this transformation. For example, position does not change under time reversal. (Imagine pausing a simulation, then reversing the direction of playback. Before you begin playing back, while still paused, all objects are still where they were). On the other hand, velocity reverses direction under time reversal. (The instant you begin playing the video backwards, the objects will be moving in the opposite direction they had been been traveling.) In general, quantities depending on time with only even powers are symmetric (do not change, like position and acceleration) while quantities with odd powers are anti-symmetric (they reverse like velocity).
Another question might be "why is acceleration due to gravity unchanged under time reversal"? Briefly, acceleration has even powers of time, $a \varpropto \dfrac{x}{t^2}$, so in that instant when time is reversed, acceleration does not change. Then, the force due o gravity has no time dependence, so it too is unaffected and the apple will have the same gravitational force acting on it at each position as it did when it fell.