# What is the maximum speed an ion engine can propel a spacecraft at?

I read that with our current ion propulsion technology it is possible we could send a craft moving the maximum of 100km per second, or around 62 miles. However we seem to be limited by how strong of a power generator we are able to put aboard the craft.. Is it possible that with enough power we could accelerate a spacecraft beyond this 100km per second limit? What is the maximum speed we could send a craft moving in space at with our current ion engine technology?

• (0.999999...)c. – Erik Jun 30 '17 at 1:01
• @Erik Not without fantasy engineering. – Russell Borogove Jun 30 '17 at 1:08
• But it is possible with current technology. – Erik Jun 30 '17 at 1:09
• @Erik It's really not -- see my answer. – Russell Borogove Jun 30 '17 at 1:13
• – Russell Borogove Jun 30 '17 at 1:45

The limit isn't due to power, but to engine lifetime and fuel limits.

Ion engines produce very little thrust, so in order to reach speeds of 100km/s they must accelerate continuously for months or years. The Dawn spacecraft, for example, was built with three redundant ion thrusters to extend its lifetime, and got nowhere near 100km/s; it carried enough propellant to change its speed by about 10km/s, and took 15000 hours (~1.7 years) of continuous thrust to change its speed by 4.3km/s.

To achieve a ∆v of 100km/s with an ion engine like those on Dawn (with a specific impulse of 3100 s (exhaust velocity of 30400 m/s)) we turn to the Tsiolkovsky rocket equation:

$$\Delta v = v_\text{e} \ln \frac {m_0} {m_f}$$

Where $v_\text{e}$ is the rocket exhaust velocity and ${m_0}$ and ${m_f}$ are the mass of the craft full of fuel and empty respectively.

$$100000 = 30400 \ln \frac {m_0} {m_f} \Rightarrow 3.29 = \ln \frac {m_0} {m_f} \Rightarrow \frac {m_0} {m_f} = e^{3.29} = 26.8$$

So an ion-thruster spacecraft intending to reach 100km/s must carry 26 times its dry mass in xenon propellant. This is an extremely high mass ratio, not generally achievable in a single-stage spacecraft. A two- or three-stage spacecraft could do it with reasonable mass ratios.

Ion engines are already very power-hungry, and need to be paired with a lot of mass in solar panels or RTGs. More powerful thrusters could increase the exhaust velocity by a small amount, driving down the mass ratio, but at the cost of greatly increasing the dry mass with the larger power supply.

Note that I'm referring to a change in speed or ∆v throughout this answer, rather than a maximum speed. This is because the speed of objects in space must be described relative to a particular reference point, and speed limits don't work the way they do for Earth-bound vehicles.

• It's a bit of a nitpick, but shouldn't that be $\Rightarrow$ (\Rightarrow) rather than $\rightarrow$ (\rightarrow)? The first time I read this, I read $\rightarrow$ as $\to$ (the "goes to" operator; in LaTeX, \to). – a CVn Jun 30 '17 at 7:58
• @MichaelKjörling Thank you -- it looked wrong to me but I wasn't sure if there was a formal convention. \rightarrow was the first thing I tried that looked vaguely useful. – Russell Borogove Jun 30 '17 at 14:19
• I don't know if it's formally correct, but it is what I learned back in school. – a CVn Jun 30 '17 at 17:55