Hi, thanks for putting how you did the calculation. I am also going through Tong's (generally excellent) course and came across the same issue. For future reference, I think the reason we may treat psi in this case as an annihilation operator and psi^+ as a creation operator is because only the...
If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c.
The relevant formula is:
u_y = u_y'/(gamma * [1+v u_x' / c^2])
Apologies for formatting.
Details: gamma = 1/sqrt(1-v^2/c^2)...
Thanks for helping anyway! Yes, that looks like the result I am now getting.
I sent an email to the Horizons team and they said they would change them from g to kg for Saturnian cases.
Thanks for the help! I removed Titan and the orbit was elliptical and worked fine. You're right - I checked the masses, and they are 1000 times too big for both Rhea and Titan. This was because for some reason the mass data for those moons were provided in grams, not kilograms.
After modifying...
Hi everyone,
I have created a simulation of the major bodies in the Solar System, using the exact positions, velocities, and masses etc. at midnight on Jan 10 (as provided by the NASA HORIZONS project). Using Newtonian gravity I numerically simulate the forces between all the bodies (with a...
This was a bad example, as there are two solutions for u.
Would u be a function of (x,t) if instead x=x(u,t)=u+t?
Then you could argue that u=x-t so u depends on x and t.
Do you have to specify which variables are independent and which are dependent?
Thanks for both your answers, they are very helpful.
I am interested about the different meanings of \partial z \over \partial x.
I can see applications for z_x (such as finding the minima/maxima of a 2d function), but when would you use z_1?
It seems that if you want to calculate z_x you can't...
Thanks for the answer!
So does that mean you can only calculate a total derivative wrt x when ALL the dependencies of z eventually depend on x?
You can look at z as a function of (x,y,t) or of (u,v,t); I assume this mens you could also look at it as a function of (x,u,v,t) by substituting for y...
If you have a function x = x(u,t)
then does u necessarily depend on x and t? so u = (x,t)
For example, if x(u,t)=u^2 t it seems that because t=x/u^2 , t=t(x,u)
I am having difficulty working out the general equation for dz \over dx if z=z(x,y,t) x=x(u,t) y=y(u,v,t)
The chain rule...
I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice.
As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration...
Thanks for the responses.
The way I'm visualising the electrons produced on the electrodes is as spherical concentrations of charge; the potential is given by kQ/r where Q is the charge on the electrode and r is the distance to the electrode; as I understand it the amount of charge on the...
But surely you can have a potential difference without any charge being moved (very high resistance circuit)? I don't understand how voltage depends on the amount of charge being moved (in what time?)http://en.wikipedia.org/wiki/Test_charge'][/PLAIN]
When a metal (electrode) is in contact with water, an equilibrium forms:
Mg ⇔Mg2++e-
Adding more of the metal Mg should convert some of it into more electrons so that the ratio of Mg to Mg2+ remains the same (as the equilibrium requires).
Therefore twice the amount of metal in contact with water...