# Power requirements for solar electric interplanetary vehicle

I am interested in electric propulsion for manned interplanetary craft. There must be a lot of models for a craft able to travel to Mars, for instance. I am wondering what the power requirements seem to be. One Mars mission craft has been described as 300 tons (ISS is 450 tons). I am imagining a plasma rocket like the VASIMR powered by solar arrays or a reactor. If anyone is familiar with these conversations, I wonder if they are talking about 200Kw, 600Kw, a megawatt or what would have to be supplied to the engines.

• " This technology clearly works better for the needs of thrusters than those of main engines" - I would not agree with that. Ion engines provide terrible thrust combined with incredibly high specific impulse. This makes them NOT suited to use as a thruster (the name of that type of engine gives it away as to what metric is more important - thrust or specific impulse). For a main engine however once you are past the van allen belts specific impulse becomes increasingly important - the tyranny of Tsailovsky's Rocket equation is harsh. – Lord Bubbacub Aug 22 '16 at 10:25
• To clarify, I didn't say Ion engines for those reasons. As I understand it (Correct me if I'm wrong) Plasma engines have more thrust and a better ratio of energy to forward movement. But while we're at it metrics on thrust and efficiency would be icing on the cake. – Johnny Robinson Aug 22 '16 at 17:13
• For long range interplanetary travel there is no practical difference between ion engines and VASIMR (I believe you are referring to this when you say plasma engine - though the gas inside an ion engine is also a plasma) except that there are working electrostatic ion drives now that provide superior efficiency (70% vs 50%) thus requiring substantially less in the way of heavy electrical power generation systems. I think a good way of rephrasing your question would be to talk about elecrostatic and electromagnetic electric propulsion in general rather than listing one overlyhyped example. – Lord Bubbacub Aug 22 '16 at 17:25
• An important metric for a space power source is watts per kilogram. The VASIMR 39 day trips to Mars assume a power source that can crank out two kilowatts electricity for every kilogram of power source. What Kirk Sorensen calls a magic power source. See hopsblog-hop.blogspot.com/2015/05/… – HopDavid Aug 22 '16 at 22:19

On the order of 300 kW (for a 70 t vehicle). In preparation for that, Asteroid Redirect Robotic Mission (ARRM) will step up our game to around 40 kW.

• What sort of acceleration do you get for 300kW on a 300 ton craft? – Russell Borogove Aug 22 '16 at 19:52
• The 300 kW is for a 70 t vehicle. I don't know where the 300 t in the question comes from. – Mark Adler Aug 22 '16 at 20:23
• The acceleration at 70 t would be about $0.00007\,\mathrm{m/s^2}$ at $2000\,\mathrm{s}$ $\mathrm{I_{sp}}$. – Mark Adler Aug 23 '16 at 1:50

I found a nice paper detailing different mission profiles from Earth to Mars: http://www.adastrarocket.com/VASIMR_for_flexible_space_exploration-2012.pdf One of their examples is a 2 MW VASIMR delivering 30 t of payload to Mars orbit within 230 days. Please note that this trajectory does not start in LEO, but at ESOI, an orbital height of about 1 million kilometers. Not starting from LEO seems a good idea for a manned low thrust mission - it takes long to escape Earth's gravity well for the main space ship, but passengers could board later using a light conventional rocket.

However, here is a back-of-the-envelope calculation on how much power is needed, given the assumptions made are correct:

How much power does an ion thruster need to get a 300 t spaceship to Mars? Naturally, the electric power can be arbitrarily low, given a very long transfer time. For a manned mission we should aim for a transit time of less than 2 years.

A transfer from LEO to LMO (Low Mars Orbit) seems to take about 6-7 km/s on a conventional trajectory. For this question we are going to assume that the same Δv is needed for a low-thrust mission. (Actually, low-thrust missions can not make use of the Oberth effect so that the needed Δv to escape the Earth gravity well is higher than with conventional rockets)

The first question is, how much force do we need to accelerate our spaceship by 6 km/s within 2 years? Using the well-known formula $F = m \cdot a$ and $v=a\cdot t$ we get $$F = m \cdot \frac{v}{t}$$ With $v = 6~\mbox{km/s}$ and $t = 2 \cdot 365 \cdot 86400~\mbox{s}$ we get $F = 28~\mbox{N}$

An ion thruster that could be built today can reach about 50mN/kW force. So we need a thruster with about 600 kW power (scaling linearly, e.g. 1.2 MW for a transfer time of one year).

In Earth orbit, sun provides about 1.3 kW per square meter power and a high-efficiency solar panel can produce about 300 W electrical power from that. This means, the required power could be supplied by a solar array of about 3000 m². But as Mars is further out, intensity of the sun light reaching the panels drops down so that the array size needs to be larger by a factor of 2.3, i.e. 6900 m². Compare this to the ISS solar array size of about 2500 m² (albeit with lower efficiency).

• Low thrust trajectories don't enjoy an Oberth benefit and have high delta V budgets. I'd say around 16 km/s from LEO to LMO. – HopDavid Aug 22 '16 at 22:13
• @HopDavid I found this on some pages as well. But how so? E.g. trs-new.jpl.nasa.gov/dspace/bitstream/2014/15789/1/00-1530.pdf gives 5.4 km/s from Earth C3. Getting from LEO to C3 should not be more than 8 km/s (3.2 km/s high thrust) – asdfex Aug 23 '16 at 20:43
• LEO to Earth C3=0 about 7 km/s. Earth heliocentric to Mars heliocentric about 5.5 km/s. Mars C3 = 0 to LMO, about 3.5 km/s. – HopDavid Aug 26 '16 at 0:54
• The PDF I linked says 5.4 from Earth C3=0 to LMO. I don't know who is right here. I don't have enough experience to do a simulation... – asdfex Aug 26 '16 at 15:55
• A rule of thumb for low thrust trajectories is speed of departure orbit minus speed of destination orbit. Earth moves about 29.8 km/s and Mars moves about 24.2 km/s about the sun. 29.8 - 24.2 or about 5.6 km/s. So I'm wondering if Brophy and Rodgers made an error. Or maybe they're relying on the launch vehicle to give the Trans Mars Injection delta V as well as getting out of earth's gravity well. – HopDavid Aug 26 '16 at 23:00