Orbit equations

1. Oct 30, 2006

UrbanXrisis

So i solved the orbit equation:

$$\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0$$

the solution is:

$$\frac{1}{r} = A \theta +B$$

I am supposed to concude that this particle will sprial towards the center but I dont see that through this equation. could someone explain this to me? thanks

2. Oct 30, 2006

Staff: Mentor

3. Oct 30, 2006

UrbanXrisis

the original equation is:

$$\frac{d^2}{d {\theta} ^2} \frac{1}{r} + (1- \frac{ \mu k}{l^2}) \frac{1}{r} =0$$

describing the motion when the effective porential = 0, i get

$$\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0$$

so i was wondering how $$\frac{1}{r} = A \theta +B$$ tells me that I am sprial towards the center?