Spiraling Towards the Center: Solving the Orbit Equation

[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 don't see that through this equation. could someone explain this to me? thanks

 

[berkeman]

I don't think that your first equation is the full orbit equation. What are you starting with?

http://en.wikipedia.org/wiki/Orbit_equation

 

[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?