Photonic Propulsion

Question

How efficient are photons when used for propulsion? Percentage-wise? Compared to rockets using massive fuel? How much thrust or force does 1000W of 400nm photons cause to a 1kg object if that light was emitted to the back of that object (no reflection/absorption)? What would its acceleration (m/s²) be?

Answer 1

All your answers are found in the form of the ideal rocket equation.

$$V_f= V_e \ln \frac {m_0}{m_f}$$

In the case of photons, they do not carry mass but the they do carry energy, so in order for them to be an effective propellent their generation must either be from some process that reduces mass of the rocket, or be somehow sourced from the external environment.

We know via $E = mc^2$ that 1 kilogram [kg] = 8.99E+16 joule [J], so 1000 joule is almost negligible however it could be inserted in the equation to determine the log of the mass ratio $$\ln \frac {m_0}{m_f} = \ln \frac{8.99E+16}{8.99E+16-1000}$$ which in this case is 1.11E-14.

If you mulitply that with the escape velocity $c$ which is 299,792,458 meters per second, you come up with a final velocity of 0.0000033 meters per second.

The question regarding thrust depends heavily on the irradiance. Photons provide a thrust equal to their irradiance (power) divided by $c$, or 3.3E-9 Newtons per Watt. (Also see article giving 1/c ≈ 3.34 N/GW)

One watt of power is equal to the rate at which one joule of energy is delivered in one second.

One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.

So the acceleration is very dependent on the rate at which the energy is expended. For sake of simplification, we will assume the 1000 joules is expended in one second yielding 1000 watts of power for one second. The newton force over the second is 3.3E-6 newtons. Per $F=ma$ we can simply divide the force by the mass and get an acceleration of 3.3E-6 meters per second per second.

If you use the equation $v = at$ then 3.3E-6 $m/s^2$ times 1 second gives 3.3E-6 meters per second...which is equivalent to what we calcuated in the rocket equation of 0.0000033 meters per second.