How can i analyse this motion?

The kind of trajectory that you have drawn is unphysical.

I recommend that you look up depictions of the orbit of Halley's comet.

When Halley's comet has reached it's furthest distance to the Sun the comet is moving quite slowly. The subsequent motion back to the center of the solar system is almost straight towards the Sun. Except, it's not quite straight towards the Sun.

Because of the gravity of the Sun the comet gains velocity all the way to the center of the solar system. By the time the comet is close to the Sun the velocity is so large that the gravity of the Sun is not enough to pull the comet all the way in.

Instead the comet swings around the Sun, and then the velocity of the comet carries it away from the Sun again, all the way to the same distance away from the Sun.

In the case of the Earth:
If something would change the orbit of the Earth, away from circular orbit, then the orbit changes from circular to ellipse-shaped.

An inward spiral, in the way you represent, cannot happen. In the process of being attracted by the Sun the comet or planet or what have you gains velocity. It gains so much velocity that it will swing around the Sun.