
#1
Aug3108, 10:19 PM

P: 231

Suppose for a senond that the only objects in the entire univesre are 2 stars, both about as massive as the sun.
Also, this univesre is completely static. It is not expanding. The stars, at least initially, are not moving relative to each other. Under these conditions, about how much distance would need to be between the stars so as to ensure that they never collide? Or does gravitational influence never deminish to zero, no matter how far away you get? 



#2
Sep108, 12:10 AM

P: 2,258

gravity=1/d^2
it equals zero at infinity 



#3
Sep108, 01:02 AM

P: 231

That is pretty interesting when you think about it. 



#4
Sep208, 02:35 PM

P: 145

Gravitational influence??? 



#5
Sep208, 03:04 PM

P: 15,325

2] It will take more than one anomaly to overturn centuries of verification and countless confirming experiment after countless confirming experiment of gravity's effect. 



#6
Sep208, 03:13 PM

P: 2,258





#7
Sep708, 11:39 AM

P: 5





#9
Sep708, 01:37 PM

P: 2,043





#10
Sep708, 01:39 PM

Sci Advisor
PF Gold
P: 1,542

The amount of time will be
[tex]t \approx 2\pi\sqrt{\frac{(0.5 d)^{3}}{G(m_{1}+m_{2})}}[/tex] where d is the distance that separates them, and m_{1} and m_{2} are their masses. 



#11
Sep708, 01:55 PM

P: 2,159

So, you can simply use the uncertainty relation to estimate the maximum distance beyond which it becomes impossible to let the grains hit each other with reasonable probability. 



#12
Sep808, 09:18 AM

P: 5

but even if they mis they could reattract eachother and have a "second chance"
etc. etc. 



#13
Sep808, 03:58 PM

P: 15,325

In fact, one orbit will bring them back to their initial starting point, 50Gly apart and stopped wrt each other. BTW, this whole problem makes the assumption that the universe is of infinite age (which, I guess, if there are only two particles in it, is pretty much a given) because these passes will take longer than our current universe's likely age. 



#14
Sep808, 04:01 PM

P: 2,043





#15
Sep808, 04:17 PM

P: 145





#16
Sep908, 10:10 AM

P: 5

well were tqlking about 'in the end' so technically, we have eternity which seems long enough :p




#17
Sep908, 11:31 AM

P: 2,159

Take two grains of sand a distance of r (say about 50 billion lightyears) apart at rest. The mass of a grain of sand is m
(say 10^6 Kg) . The potential energy is: E = G m^2/r For the system to be in a bound state, the momentum of the grains must not exceed P, given by: P^2/m = G m^2/r > P = Sqrt[G m^3/r] If the intital state is given by some wavepacket then in momentum space the spread must be significantly less than P. The uncertainty relation then gives a spread of the wavefunction in configuration space of: Delta X = hbar/2 Sqrt[r/(G m^3)] This is about 140 nm for the two dust grains placed 50 billion lightyears apart. I don't think it is realistic to assume that this wavefunction won't decohere into a statistical mixture of wavefunctions with much sharper defined positions. 


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