stunner5000pt
Jan17-06, 09:41 AM
this is due on wednesday i would really liketo hand it in on time
couple of my questions are in these threads which have not gotten any answers...
http://physicsforums.com/showthread.php?t=106913
http://physicsforums.com/showthread.php?t=106930
For a particle of mass m moving in a potential V(r) =\frac{-\alpha}{r} + W(r) (alpha>0) where W = \frac{-a}{r^4} is a small perturbation ( in a sense that W(r) << |\frac{\alpha}{r}| for r not too small), calculate the advnace of the perihelion
2 \Delta \beta = 2 \frac{\partial}{\partial L} \int_{0}^{\pi} \frac{m}{L} r^2 W d \phi
Express your answer in terms of alpha, m, a, L and the eccentricity \epsilon = \sqrt{1 + \frac{2EL^2}{m \alpha^2} and verify that your answer is dimensionless. (rrepresnets an angle in radians)
problem with the intergral is that r depends on phi.
i know that this is true
\frac{dr}{d \phi} = \frac{r^2 \sqrt{2m(E - V_{e}^{0})}}{L}
in this is E = \frac{1}{2} m \dot{r}^2 + V(r) ?
also what about V_{e}^{0} = V_{c} (r) + \frac{L^2}{2mr^2} = \frac{-GMm}{r} + \frac{L^2}{2mr^2}
are those two correct? Do i simply substitute those two expressions in the integral for r(phi) and solve for r(phi) thereby i can solve for beta?
Is this correct?
couple of my questions are in these threads which have not gotten any answers...
http://physicsforums.com/showthread.php?t=106913
http://physicsforums.com/showthread.php?t=106930
For a particle of mass m moving in a potential V(r) =\frac{-\alpha}{r} + W(r) (alpha>0) where W = \frac{-a}{r^4} is a small perturbation ( in a sense that W(r) << |\frac{\alpha}{r}| for r not too small), calculate the advnace of the perihelion
2 \Delta \beta = 2 \frac{\partial}{\partial L} \int_{0}^{\pi} \frac{m}{L} r^2 W d \phi
Express your answer in terms of alpha, m, a, L and the eccentricity \epsilon = \sqrt{1 + \frac{2EL^2}{m \alpha^2} and verify that your answer is dimensionless. (rrepresnets an angle in radians)
problem with the intergral is that r depends on phi.
i know that this is true
\frac{dr}{d \phi} = \frac{r^2 \sqrt{2m(E - V_{e}^{0})}}{L}
in this is E = \frac{1}{2} m \dot{r}^2 + V(r) ?
also what about V_{e}^{0} = V_{c} (r) + \frac{L^2}{2mr^2} = \frac{-GMm}{r} + \frac{L^2}{2mr^2}
are those two correct? Do i simply substitute those two expressions in the integral for r(phi) and solve for r(phi) thereby i can solve for beta?
Is this correct?