# On resonant cavity thrusters

So the controversial EmDrive is making the rounds again, this time with a group of German experimentalists claiming to have measured a net thrust of 20 µN for 700 W of input power (link to paywalled paper). This post isn't going to pass judgment on whether the effect is real or not, but rather whether it is actually of practical use given what has been claimed so far. In order to do this I'm going to use a toy scenario I like to think about every now and then: getting a PocketQube satellite from low Earth orbit (LEO) to the Moon.

PocketQube - the satellite form factor that fits in your hand!

Since we're starting in LEO we first need to know: is this drive capable of delivering enough thrust to keep our orbit from decaying? This means compensating for drag, which according to Wikipedia is somewhere between 7.5 - 100 m/s per year depending on altitude. The questions then are "how much power do we have?", "how high will our thrust be?" and "how high is our mass?". For these I'm assuming a 5x5x5 cm PocketQube with maximum allowed mass (180 g).

If we have five of the sides of the satellite covered in solar panels, folded out like flower petals and optimally aligned with the Sun, with an efficiency of 20%, then our total power with an insolation of 1300 W/m² (solar constant) becomes: 5*0.05²*1300*20% = 3.25 W. In LEO we're shaded by the Earth roughly half of the time, so the average power becomes 3.25 / ≃ 1.6 W. Assuming the thrust of the device is linear we then have an average thrust of 20*1.6/700 ≃ 46 nN.

With a thrust of 46 nN and a mass of 180 g (0.18 kg) the average acceleration becomes 256 nm/s². Over a year the accumulated delta-v is 256/10⁹*60*60*24*365 ≃ 8.1 m/s. In other words: if we get to start at an altitude above 600 km we're probably not going to fall back down again (but only just barely).

So, how long is this trip going to take us? Again I'm going to use Wikipedia, and look up how much delta-v is needed to get from LEO to LLO with this kind of low-thrust drive: 8.0 km/s. I'm also going to be kind and disregard the drag for this one: 8000 / 8.1 = 988 years (!). Now, it's been a while since we went to the Moon, but something tells me if we're still around it's going to happen a lot sooner than the year 3003 :)

Incidentally, this is why for electric propulsion thrust per unit of power is much more important than specific impulse. All the efficiency in the world isn't going to be of much use if you're dead by the time your probe arrives at its destination..