The paradox is that you have one line of reasoning that shows that Achilles will never reach the Tortoise, and another line of reasoning that shows that Achilles will eventually reach the Tortoise.

If both lines of reasoning are correct, you get a contradiction. But it's not obvious where the mistake is, hence being called a paradox.

The resolution to this paradox is the realization that an infinite series can have a finite sum. That is, the first line of reasoning shows that it will take an infinite number of steps for Achilles to reach the Tortoise, but since each step gets shorter, it can be done in a finite amount of time.

Here's a website that explains the math to calculate an orbital trajectory. The math isn't really something that can be explained like you're five though. You'll need to have a solid understanding of algebra and trigonometry to be able to use it.