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I am writing a novel, and although I have a background in physics, I am unsure of the exact equations to use.

Specifically:

For a photon-sail ship, how powerful would a driving laser need to be in order for the ship to reach an acceleration of ~0.5g?

Assuming we are only talking within the solar system here, and assuming that the ship is heavy enough to carry passengers.

Would such a thing ever be feasible? I am trying to strike the right balance between fun and feasibility for some method of regular interplanetary transport (think the space equivalent of commercial jets).

Kyle Kanos
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iRoygbiv
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1 Answers1

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Photons generate what we call Radiation Pressure. From wikipedia, http://en.wikipedia.org/wiki/Radiation_pressure, we get the equation: $$ P_{absorb} = \frac{E_f} {c} cos\space\alpha\\ \text{and} \space P_{reflect}=\frac{2E_f} {c} cos^2\space\alpha $$ Where:$P_{absorb}$ is the Radiation Pressure on an absorptive surface (in Pascals).
$P_{reflect}$ is the Radiation Pressure on a reflective surface e.g. mirror (in Pascals).
$E_f$ is the energy flux/intensity (in $\frac{W} {m^2}$)
$c$ is the speec of light, and
$\alpha$ is the angle between the surface normal and the incident radiation.

Assuming that the ship has a reflective sail and the sail is orthogonal the the laser beam, we get $P=\frac{2E_f} {c}$. From $F=ma$ and $F=PA$, $$ \frac{2E_fA}{c}=ma $$ I will stop here since there are parameters to be filled (namely, $m$ and $A$, which depends on your design of the ship.) After plugging in all the values, including $a=0.5g$, you shall obtain $E_f$, which is proportional to the power of the laser.

krismath
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