Osculating plane

Imagine you are playing with your toy car and you put it on top of a small hill. The car will start to slide down the hill, but if you look very closely, you will notice that the car is not just rolling straight down - it is also turning as it moves. This is because the hill is not perfectly straight and flat, but has a slight curve to it. The car is following the curve of the hill, and to do this, it has to both roll downward and turn at the same time.

Now, let's think about something much bigger than a toy car - like a planet moving around the sun. Just like the car on the hill, the planet is not moving in a perfectly straight line but is following a curve. This curve is called an orbit, and it is actually a very special kind of curve called an ellipse.

The osculating plane is the imaginary flat surface that sits at a specific point on this curved orbit. This point is always changing as the planet moves around the sun, so the osculating plane is always shifting slightly as well. Imagine the osculating plane as a flat sheet of paper that perfectly touches the curved orbit at one point.

The reason the osculating plane is so important is that it helps us understand how the planet is moving. Just like the car on the hill, a moving planet is also turning and changing direction as it follows its curved orbit. The osculating plane helps us visualize this turning and changing direction by giving us a flat surface to look at.

In summary, the osculating plane is an imaginary flat surface that touches a curved orbit at a specific point. It helps us understand how a planet is turning and changing direction as it follows its orbit.