I Centrifugal term in mechanical energy in gravitation

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1. Apr 9, 2016

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

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

2. Apr 9, 2016

drvrm

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.

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.

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