Most likely, a time travel path would be along a line of freefall (geodesic). ie. Imagine if you could fall through the ground, wobbling back and forth from one side of the planet to the other.

For any given initial velocity, there would only be certain periodic times when you *wouldn't* end up inside the planet. And the position on the planet where you come out would also be problematic. If you're not satisfied with those precise times and places, then you can adjust your velocity a tad, to get another set of options.

If you're in orbit then you have much less to worry about.