What Is the Collision Time for Stars in Andromeda and Milky Way?

[AUK 1138]

Homework Statement

The problem is assume Andromeda and the Milky Way are going to collide. the relative speed of them moving is 10^6m/s. assume each star has the radius of our sun (6.955*10^8m) the distance between each star is 3.1*10^18 m. how long will it take for a star to collide with the sun?

Homework Equations

i believe it might solved with the mean free path with mean free time= lamda/v, lambda being 1 over the area of the object in question.

The Attempt at a Solution

I've done a few things with this problem, first i divided the radius by the distance then divided by velocity, but that doesn't work due to the units. i tried the mean free path way, but then the distance isn't involved and it seems like it should be. the other thing i tried was to find the area of disc with radius of the distance and the subtracting the area of radius then use that for the mean free time. that seemed all right, but i still have a unit problem. also the answers have seemed low. only the first way provided an answer that i felt was correct, but again, unit problems.

i'm now thinking maybe i have to use 1/distance and then divide the radius by that then by velocity, but I'm not sure why.
i am stuck, please help

 

[voko]

What is the number of particles per unit volume in this problem? How can you use the distance between particles to compute that?

 

[phinds]

"How long" seems like a very odd question in this circumstance. Wouldn't "what's the probability be of a collision?" be a lot more meaningful question? You don't really think there would be a collision with the sun, do you?

 

[AUK 1138]

What is the number of particles per unit volume in this problem? How can you use the distance between particles to compute that?

i figure the number of particles is 4 per (3.1*10^18)^2.

and no, i don't expect there to be a collision with the sun and another star. that's one of the reasons i posted this question. it seems almost absurd. but it's a homework problem nonetheless.

any help is appreciated.

 

[voko]

i figure the number of particles is 4 per (3.1*10^18)^2.

Why 4 and why (3.1*10^18)^2? The latter is not volume dimensionally.

 

[AUK 1138]

i figure 4 due to assuming 1 star on every corner one a square. i assume one of my answers is right, but i don't know which.

 

[voko]

A square does not have any volume. The mean free path is defined in terms of number of particles per volume. Imagine a star in space. How many stars do you have within a sphere of a certain radius? What is the volume of this sphere?