\[p= \frac{h}{\lambda}\]
where \[p, \: h, \: \lambda\]
are momentum, Planck's constant \[6.626 \times 10^{-34} Js\]
and wavelength respectively.What power of laser would be required to accelerate a 1000 kg spacecraft by an average
\[1m/s^2\]
reaching a speed about 10% of the speed of light in 1 year, and making interstellar space travel feasible?The energy acquired by the craft is
\[\frac{1}mv^2=\frac{1}{2} \times 1000 \times (0.1 \times 3 \times 10^8)^2 =4.5 \times 10^{17} J\]
.Over a period of 1 year
\[3.1536 \times 10^7s\]
the power required would be \[\frac{4.5 \times 10^{17}}{3.1536 \times 10^7}=14.3MW\]
.A medium sized power station produces about 1000MW so this is feasible.
To achieve this a large reflective sheet would be launched into space, attached to the spacecraft and illuminated by a laser. The frequency of the laser light should be low enough to not cause the photoelectric effect, so energy and momentum are not carried away by electrons, and if an Earth based laser is used, should be such that the Earths atmosphere is transparent at that frequency.