Thanks for that, I'll give it a try. Ideally it needs to start at the origin, go to large numbers at 8 and the curve needs to fit as good as possible. Alas I don't have the likes of Maple. :(
Using trial and error I've managed to get:
y=exp((x/5.5)^4)
It'll probably have to do for now. :(
Ah, didn't realize it takes a while to be approved. That's exactly what I tried but it didn't work alas. The shape of the curve isn't conducive to an Excel trend line - which is about as advanced as my equation guessing techniques go!
I need to work out an equation (and also the gradient) of the attached graph for use in a toy model. Alas I don't have stuff like Mathematica here and I don't normally do this kind of thing so I've just been stuck to using Grapher to chuck random equations in and Excel to try to plot points for...
Ok, I've done that now.
One thing though, I also found the following equations which I found http://microsat.sm.bmstu.ru/e-library/Ballistics/kepler.pdf :
a=\frac{GMr}{2GM-rv^{2}}
and
e=\sqrt{1-\frac{h^{2}}{GMa}}
I've tested both sets of equations and I get the same numbers for...
aha, so I can use:
\textbf{h}=\textbf{r}\times\textbf{v}
to find the specific angular momentum and then
a\left(1-e\right)=\frac{h^{2}}{GM}
But then how can I separate the eccentricity and semi-major axis?
Can anyone suggest how to calculate the semi major axis of a body in an elliptical orbit when all I've got is x,y,z,vx,vy and vz?
I'm guessing I need to calculate the eccentricity too. I really suck at conversions like this. :(
So radial velocity would be vr = sqrt(vx^2+vy^2). However, for an orbiting body, radial velocity is largely zero, which with that equation would imply that vx and vy are both largely zero, which is not the case.
The signs are because x and y become negative and the signs on the velocities need...
I think I'm getting muddled up with different co-ordinate systems, rotational velocities and the spin dependence of elephants when eating carrot sticks.
Looking at everything again, I basically need to be able to convert between azimuthal and radial velocities and x and y velocities for a body...
Can anyone help explain how to convert velocities to different co ordinate systems? I've always been shocking at converting between co ordinate systems as it is.
I know that converting from Cartesian to Cylindrical for positions it is:
r = sqrt(x^2 + y^2)
theta = atan(y/x)
z = z
and...
What country are you hoping to do an MSc in? I have a friend who's doing an MSc in the UK at the moment, he's from India too. You really have to choose a field to go into at this point. There are some generic Physics MSc courses although they're aimed more at being conversion courses for...
Are you thinking of doing an MSc after a BSc or straight to research? Honestly, it'd probably be better to choose modules where you can get the highest marks in.
Wow, I can't believe how long things take in the states. First Bachelor's degrees are 4 years, then masters degrees are 2, then PhDs seem to be 5 years minimum. Unreal.
Although I said it before, I'll add now that I'm from the UK. I knew that I wanted to do a PhD in Astronomy at the end of my...
I knew I wanted to do do a PhD in Astronomy at the end of my second year so that's what I've picked here. As to what I wanted to do my thesis in... well I worked that out during PhD applications during my masters.