What is the effect of distance on the force created by a laser in outer space?

[bmb2009]

Homework Statement

Two astronauts are at rest in outer space, one 15.3 m from the Space Shuttle and the other 30.6 m from the Shuttle. Using a 123.0-W laser, the astronaut located 30.6 m away from the Shuttle decides to propel the other astronaut toward the Space Shuttle. He focuses the laser on a piece of totally reflecting fabric on her space suit. If her total mass with equipment is 129.0 kg, how long will it take her to reach the Space Shuttle?

Homework Equations

Force=Power/c

The Attempt at a Solution

Since Force=Power/speed of light

F=(123W)/(3x10^8)
F=4.1E-7 since F=ma (4.1E-7)/129kg = accel= 3.178E-9 m/s^2

the laser causes constant acceleration so...
Df=Do + VoT+ 1/2aT^2
and I solved for T... with Df = 15.3 meters, Do and Vo both equal 0.

but this didn't work and I have no idea where to go from here. Does the distance of the second astronaut (the one shooting the laser) affect the calculation? Any help?
Thanks!

 

[Vodkacannon]

This is just a suggestion:
If it's a totaly reflecting surface shouldn't the force (F) of the beam be doubled?

Just like if water hits the back of a spoon as compared to the front of a spoon. The water hitting the front is deflected and therefore puts a greater force on the spoon.

 

[bmb2009]

I just tried your hunch and you were correct. Thanks a bunch!