# Could radiated heat propel space-craft in outer space?

The comment chain on What is the feasibility of launching a probe to Sedna? indicates RTG thermocouples decay. With the passage of time the thermocouple may even have the ability to transduce an infinitesimal fraction of the power it could originally even when the RTG pile itself is still good.

At the other end this news-report writes to say

The cause of the so-called "Pioneer Anomaly," it turns out, is heat coming from the electrical current flowing through the probes' instrument and power systems. This heat pushed back on the spacecraft, causing them to decelerate slightly, according to a new study

The Pioneer Anomaly was/is an inadvertent side-effect. It may be possible to improve on it by designing to use heat as a propellant.

For instance: Surface asymmetry may cause a surface to heat in a dis-uniform fashion.

Assuming the report is in order

• Are there any studies on radiating heat to propel space-craft in outer space?
• How close are these studies (if any) to experimental confirmation?
• How much heat would be necessary to accelerate a 1Kg body through 0.01G in outer-space?

This is propulsion via infrared photons, which is similar to other photon propulsion methods. It's more common to hear about gamma (antimatter drives) and x-ray propulsion because we have mechanisms to drive higher power through it, whereas thermal photons are limited by the Stefan-Boltzmann law.

To the question:

How much heat would be necessary to accelerate a 1Kg body through 0.01G in outer-space?

The specific impulse for all photons is the same. After all, they all travel at the same speed (but I guess the limit-based argument is a little more nuanced). But you still need to correct for angle of emission. They're not perfectly collimated, so our best assumption is to assume isotropic emission over a half-sphere. Details come out to the same as analogs here:

http://en.wikipedia.org/wiki/Relativistic_rocket

In electron-positron annihilation, the gamma rays are emitted in a spherically symmetric fashion, and they almost cannot be reflected with current technology. Therefore they cannot be directed towards the rear. A simple solution would be to have a gamma ray absorber absorbing all the gamma rays moving in the forward direction, delivering part of the thrust; and letting the rest be emitted without any deflection (therefore with an angle of divergence of 180°), which cuts in half the (average) useful momentum of the gamma rays, resulting in the specific impulse being less of what it would be in the idealized case.

I think that's a factor of 1/2, going by memory from classes on transport.

With such a high specific impulse, we can trash the rocket equation in favor of an approximation for impulse. You seem to want (1 kg)x(0.01)x(9.8 m/s^2)=0.1 Newtons.

$$\text{ Power} \approx 2.0 \cdot \text{Force} \cdot c \approx 30 MW$$

• ...and obviously squeezing 30 megawatts out of a kilogram of machinery is going to be rather difficult... – SF. Mar 30 '18 at 10:03

The Pioneer Anomaly gives a first-order answer.
The Pioneer Anomaly was an acceleration of $(8.74±1.33)×10^{−10} m/s^2$. According to the paper in which the solution for the Anomaly was published, this acceleration was caused by about 50 W of heat output.
So you get $10^{-11} m/s^2W$, or 100 GW for 1 $m/s^2$, for a spacecraft that weighs ~250 kg. So 40 MW for 1kg at 0.01G. There are better ways to utilize that power.

• TY. The question failed to convey that the Pioneer anomaly was inadvertent. I had in mind something more by way of actually designing a craft to actively radiate heat for propulsion. Updated the question as such. – Everyone Feb 7 '14 at 4:29

Heat is radiated to space in form of infra-red radiation. Infra-red radiation is nothing else than long-wavelength light. And there is a theoretical concept for a spacecraft accelerated through a beam of light, called photon propulsion.

The great thing about photon propulsion is that it requires no propellant, that means that when you have access to an external energy source (like solar panels), you never run out of fuel.

Unfortunately it has a very, very low energy efficiency. This paper talks about just 20 µN of thrust per Watt, and that was for a directed laser beam under lab conditions, not infra-red radiation aimed away from the general direction where you want to go.

So yes, theoretically you can propel a spacecraft through directing its waste heat, but practically the effect is negligible.

There is also a larger-scale concept for a photonic rocket which is closer to your idea of using heat, the Nuclear Photonic Rocket. The idea is to use the heat generated by a nuclear reactor to generate thrust. But it's still not very efficient. A much better use of that much energy would be to use it to accelerate the reactor waste to generate thrust.