Spaceballs

Originally posted by kbaumen
People are trying integration 'n' stuff here while I consider the elementary school way much more simple, though longer.

First of all we have to calculate the gravitational force between the spheres. F = (G * m1 * m2) / R ^ 2; (G is the gravitational constant) F = (6.7 * 10^-11 * 1 * 1) / 1 ^ 2 = 6.7 * 10^-11 N. The distance between surfaces is 1 - 2 * 0. ...[text shortened]... e calculations I did where quickly scribbled without any thorough checking. I know I'm lazy.

The force between spheres, and therefore the acceleration is not constant! That is why we have to use some calculus!

Originally posted by wolfgang59
x= distance from sphere centre to mid-point

t=0 x=0.5 dx/dt=0

We need to find t when x=0.05

We know d^2x/dt^2 = (G/4) x^(-2)

So we have to integrate once to get dx/dt and use fact that dx/dt = 0

Then integrate again to get x in terms of t

Then solve for x=0.05

25 years ago I could do this!!

😕

If.. t = -GM/2 * (0.05) ln|0.05| assuming C and D are 0 since I haven't the foggiest...



5 *10^-10 seconds?

Edit: oh oops I turned the fraction upside down.. at least it should be

x/t = GM/2 *ln|x| +Cx +D with C and D = 0

t = 2/(GM) * x/ln|x| with x = 0.05

-5 * 10^7 (what's with the f*n minus? I give up)

Originally posted by wolfgang59
The force between spheres, and therefore the acceleration is not constant! That is why we have to use some calculus!

Oh yeah, missed a tiny little thing. Fine, gotta go learn some calculus.

Hmmm, having a little trouble finding a solution. I can't seem to find examples of ordinary differential equations of the forms:

x^2 * d^2(x)/dt^2 = k

or:

d^2(x)/dt^2 = k/x^2

Originally posted by PBE6
Hmmm, having a little trouble finding a solution. I can't seem to find examples of ordinary differential equations of the forms:

x^2 * d^2(x)/dt^2 = k

or:

d^2(x)/dt^2 = k/x^2

Couldn't find an explicit solution, but I did run a simple Excel program and it came out to about 75 hours, using a time step of 135 seconds.

Originally posted by PBE6
Couldn't find an explicit solution, but I did run a simple Excel program and it came out to about 75 hours, using a time step of 135 seconds.

I tremble to think what I guy like you could do with some software like Mathematica, or MatLab... I really do.

Edit: http://en.wikipedia.org/wiki/Scilab see if you like this software and please install it. I'm guessing you'd have lots of fun with it.

Originally posted by adam warlock
I tremble to think what I guy like you could do with some software like Mathematica, or MatLab... I really do.

Edit: http://en.wikipedia.org/wiki/Scilab see if you like this software and please install it. I'm guessing you'd have lots of fun with it.

I downloaded it last night! It looks a little complicated, I'm definitely going to have to spend some time with it and learn it.

Thanks! 😀

Originally posted by PBE6
I downloaded it last night! It looks a little complicated, I'm definitely going to have to spend some time with it and learn it.

Thanks! 😀

But I really do tremble while thinking what you can do with a software like that. If you have some kind of access to free Mathematica I'd avise you to install it. I think you could do wonders with it. Really!

Bump! (for comic effect - see topic listing)

Originally posted by PBE6
Bump! (for comic effect - see topic listing)

Unbump! 😛

Originally posted by PBE6
Bump!

That was clocked at exactly 37 hours and 52 minutes.

One more reason to hate differential equations. I might get it when I'm more awake (coffee).