Centrifugal term in mechanical energy in gravitation

[Soren4]

I'm studying effective potential in Newtonian gravitation. The mechanical energy of a body can be written
$$E=\frac{1}{2}\mu {\dot{r}}^2+\frac{L^2}{2\mu r^2}-\gamma \frac{m M}{r^2} \tag{1}$$

Where [itex]\mu[/itex] is the reduced mass of the system planet-star.

Consider now the term $$U_{centrifugal}=\frac{L^2}{2\mu r^2}$$
I don't understand this explanation found on Morin.

The [itex]L^2/2mr^2[/itex] term in the effective potential is sometimes called the angular momentum barrier.It has the effect of keeping the particle from getting too close to the origin.Basically, the point is that [itex]L ≡ mr^2\dot{ θ}[/itex] is constant, so as r gets smaller, [itex]\dot{θ}[/itex] gets bigger. But [itex]\dot{θ}[/itex] increases at a greater rate than r decreases, due to the square of the [itex]r[/itex] in [itex]L=mr^2\dot{ θ}[/itex]. So eventually we end up with a tangential kinetic energy, [itex]mr^2\dot{ θ}^2/2[/itex], that is greater than what is allowed by conservation of energy.

Why [itex]mr^2\dot{ θ}^2/2[/itex] is greater than maximum KE allowed by conservation of energy in this case?

In general how does [itex]U_{centrifugal}[/itex] prevent the planet to collide with the star (provided the planet has non zero angular momentum)?

 

[drvrm]

Why mr2˙θ2/2mr2θ˙2/2mr^2\dot{ θ}^2/2 is greater than maximum KE allowed by conservation of energy in this case?

do not compare the two terms , rather one should compare the total potential and the kinetic energy - and for a bound state the total energy should be negative that id the potential energy should be greater than the kinetic energy.-or plot the graph of potential + centrifugal term and see that the bound state energy is -ve.

In general how does UcentrifugalUcentrifugalU_{centrifugal} prevent the planet to collide with the star (provided the planet has non zero angular momentum)?

if you look at the above potential energy plot you will see the barrier as its positive and goes to infinity as r goes to minimum distance of approach. say r0.