Recent content by Sabertooth

Hi all:) In my recent exploration of Elliptic Function, Curves and Motion I have come upon a handy equation for creating orbital motion. Essentially I construct a trigonometric function and use the max distance to foci as the boundary for my motion on the x-plane. When I plot a point rotating...

There is a vortex forming just behind where the soap is drawn into the syringe, along the metal. When the liquid in front of the "syringe-hole" is pulled into the syringe it causes the soap behind the syringe hole to be pulled forwards. Seems the phenomena would also be present in other...

Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions. This is a GIF of the motion...

Am I correct in assuming that acceleration and kinetic energy values under the circumstances given in the graph above would transform to the inverse gamma(γ) formula ?

Just found something amazing with this approach, assuming a constant increase in velocity like depicted above, which goes directly to C over 100 seconds. (impossible scenario admittedly) This equation dictates that the minimum t value is equal to exactly t````````'= ((π/4)*100) seconds

Wow, seems like it worked perfectly. Thanks! I'm getting two different values, depending on whether I square a & x separately. Not sure which one of these is correct and why - however it would be easy to estimate which approach is correct. That's awesome, been spending a bunch of hours on this...

The graph shows t in stationary observer time, so that when we plug in the velocities into the formula we should get a lower value t' for the spaceship.

So for example, at second 1, my velocity is 1 000 000 m/s, at second 2 my velocity is 2 000 000 etc. For every single time interval I want to plug in my y-values into the formula: \sqrt{1-v^2/c^2} where we insert our 100 different y-values as the v^2 component.

I want to transform every velocity in the table, into the formula: \sqrt{1-v^2/c^2}for 1 second each, then sum them all up to get a good approximation of the total amount of time dilation during this 100 second acceleration. You cannot use Newtonian mechanics, since the Lorentz transformation...

Hey everyone, I have generated a nice little velocity vs time graph that I would love if somebody could help me put to use. I have marked data points on the x-axis for the Y-value for every second on the function. Just to be clear: X-axis = time in seconds & Y-axis = velocity in meters/second...

since it would take way too many hours to calculate 10 000 sections manually what approach can we use to make it work?

Is that the notation we use to say that we need to divide the curve up into n number of sections and calculate the lorentz factor for each section, then add them together and compare? Let's say we split it up into 10 000 sections. That should give us reasonable accuracy, I presume. Because the...

Pretty much everything there is to know on that front. It's the calculus part bothering me, as I need to be able to do the dilation calculations when velocities are varying with time in a smooth curve. I would also be able to apply this answer to dozens of different scenarios and problems that...

Which I'm definitely prepared to do, but from what I gathered from your reply I need some type of formula that isn't present. Can the formula or the function (the thing that is missing) be calculated manually with some type of integral or derivative?

hmm, not a lot of help from the certified science advisor it seems :/ It's okay if you're not in a helpful mood. There is always tomorrow.