PLEASE help Kepler's third law for electrical orbits

[PinkFlamingo]

PLEASE help! Kepler's third law for electrical orbits

Hi there! I hope someone can help me with this problem. I've been working on this for over 5 hours and I've gotten nowhere!

A positron is a particle with the same mass as an electron but with a positive charge. A positron and an electron can briefly form an unusual atom known as positronium. Imagine a situation where the two particles are in a circular orbit about their center of mass. Since the particles have equal mass, the center of mass is midway between them. Let r be the separation of the particles (so that the orbits are each of radius r/2).

(a) Show that the orbital period T is related to the separation distance r by:

T^2 = (16)(pi^3)(E0)(me)(mp) (r^3)
---------------------
(e^2)[(me) + (mp)]

This is a consequence of Kepler's third law for electrical orbits.

(b) Show that if an electron and a proton are in circular orbits about their center of mass (which is not at the midway point between them but much closer to the proton), then the same expression results.

* * * * *

OK, so so far, I'm guessing that I somehow use the formulae:

q = ne

F = 1 |Q||q|
-------- x ---------
4(pi)(E0) (r^2)

But I'm not really sure where the rest of it comes from

If someone could help me out, I would really appreciate it!

Thanks!

Mandy

 

[wave41]

same here

Hey! I have got the same problem right now in my book! Which book are you guys using? I know where the rest comes from, I am just not sure how to intigrate it!
I think you have to equal the two formulas Kepler's third law T^2= 4 pi^2/Gms r^3 and coulomb's law...I have gotten half way but can't get any farther...
So maybe someone can help with the rest?

 

[PinkFlamingo]

cool

I'm using a book called university physics right now... is it the same book? If it is maybe we could help each other out. I think this class is going to kill me. :yuck:

I figured out the problem I think. The trick is to use Newton's modified version of Kepler's law, which takes into account the masses of the positron and electron.

The part I'm not sure about though is part b... could anyone help me out with that? why does the formula stay the same no matter where the center of mass is?

Good luck

 

[wave41]

What I have done so far was to equal the two formulas and then simplify them...I think I got it but I am not sure about it...And about the second part, how can I make the changes so when the masses are different?
I too the Coulomb`s law and Kpeler`s third law for gravitation...
T^2= 4pi^2/Gm r^3 =1/4piE (qq/r^2)
what I got was this but I am not sure about it...
4pi^2/G(Me+Mp)r^3=e^2/4piEr^2
But beyond this I am not sure how they actually got to the final equation! GUYS I need help! hehe I have this assingment due tomorrow and it is 25 percent out of my fanal grade! I don`t want to be kicked out of engineering! hehehe joking...thanks a lot for your help guys please I really need it!

Bye bye