Hyperbolic trajectory

Ok kiddo, let me explain to you what a hyperbolic trajectory means.

Imagine you have a ball in your hand and you throw it up in the air. When it goes up it slows down, then stops for a moment, and then starts falling back down towards the ground. As it gets near the ground it speeds up again, until it bounces back up.

Now, let's imagine you throw the ball really hard. Its path up into the air will look different than before. Instead of slowing down and stopping, it may keep going up, and up, and up. It will still fall back down, but this time it won't bounce back up as high as before. This is what we call a hyperbolic trajectory.

In space, things can move in hyperbolic trajectories too. For example, if we wanted to send a spaceship to another planet, we would give it a big push to get it moving really fast. It would start off moving away from us, and would keep going faster and faster until it reached its destination. When it got there, instead of bouncing back like our ball did, it would go into orbit around the planet, and keep moving in a big circle or ellipse.

So, a hyperbolic trajectory is when something moves away from us really fast and keeps going, instead of slowing down and coming back like the ball we threw in the air. Hopefully that makes sense to you, little one!