Angular momentum and starship enterprise

[syang9]

the starship enterprise is cruising along at constant speed v when it encounters a mysterious space station. (enterprise = x, space station = S)

http://x402.putfile.com/4/11618084116.jpg

the enterprise is headed such that it will pass the space station at a distance d, as shown above. the question states:

argue that angular momentum conservation does not allow the tractor beam to make the enterprise reach the space station if we treat them both as point particles. given, v_enterprise, d.

so.. here's what i tried.
system = ship + station; no external torques, so angular momentum is conserved.

let l = the top side of the triangle (distance that enterprise would travel if not being pulled by tractor beam)
let r = hypotenuse

L_i = r X p

|r| = sqrt(l^2 + d^2); |p| = mv

let the space station be at the origin, therefore
L_f = 0

so..

sqrt(l^2 + d^2)*(mv)*sin(phi) = 0; sin(phi) = L/r

sqrt(l^2 + d^2)*(mv)*(L/r) = 0

now.. i have absolutely no idea what to do.. could i get a hint, anyone?

 

[Doc Al]

What's the angular momentum of the system? (Measure with respect to the space station.) This should be easy to answer. (Hint: the distance you call "l" is irrelevant.)

Since, as you correctly point out, angular momentum is conserved, what does that tell you about how close the ship can approach?

 

[syang9]

well.. since the only thing moving is the ship, wouldn't the total angular momentum of the system just be r*(mv)*sin(phi)..?

if angular momentum is conserved, that means it has to go somewhere, so the ship can't reach the station because that angular momentum has to remain constant. so the ship can't ever be at rest at the station, if we consider the station to be at rest at all times..

 

[Doc Al]

well.. since the only thing moving is the ship, wouldn't the total angular momentum of the system just be r*(mv)*sin(phi)..?

Yes, but simplify that expression. Once you get a simpler expression, it will be easier to explain why the ship cannot reach the station.