# Impulse of photons

A 65 kg astronaut is floating in empty space. If she shines a 1.0 W flashlight in a fixed direction, how long will it take her to accelerate to 10 m/s?

Answer

$F = d P/d t = d(m c)/d t = (1/c)*d(m c^2)/d t = (1/c)*d E/d t = P/c$

or simpler

Power = Force*speed

$F = P/c$

$F= 10/3*10^8 =3.33*10^{-8} N$

$a = F/m = 3.33*10^{-8}/65 =5.128*10^{-10} m/s^2$

$t = V/a = 10/5.128*10^{-10} =1.95*10^{10} sec =618.34 years$