Could we use the atmospheres of planets like Mars or Jupiter to separate xenon from them to replenish the engines?

Question

Could we use the atmospheres of planets like Mars or Jupiter to separate xenon from them to replenish the engines? I mean, touch the atmosphere of Mars and separate Argon and Xenon for ionic engines, would this be possible? Or the atmosphere would lower us?

Answer 1

Let's see if the physics of collecting ion propellant from atmospheres makes sense first. Using the vis-viva equation and the standard gravitational parameters for the two extreme cases that you've asked about, we can see what those orbital velocities might be for a circular orbit near the atmosphere (I'll use 5% larger than the planet's radius, it doesn't matter much for the speed calculation):

$$v^2 = GM \left( \frac{2}{r} - \frac{1}{a}\right)$$

planet     1.05 R        GM        v_circ      v_esc   
             m         m^3/s^2       m/s         m/s
Mars      3.56E+06    4.28E+13      3,500       4,900
Jupiter   7.34E+07    1.26E+17     42,000      59,000

The escape velocity is the speed at 1.05 $$ when you are just transitioning in a capture or release.

Now let's look at the velocities of ion engine exhaust. Assuming 100 kV acceleration voltage producing a kinetic energy E of 1E-04 GeV for a charge of +1, and using 1 GeV per nucleon for the masses and using $v/c = 2E/mc^2$

atom      mass      v/c          v
           GeV       -          m/s
helium       4     0.0071    2,100,000
argon       40     0.0022      670,000
xenon      131     0.0012      370,000

So even for the largest atom and the largest planet, the exhaust velocity at 100 kV is six times the orbital velocity.

This means that the available thrust can potentially be much larger than the drag you incur by dropping into the atmosphere and collecting it.

However that's if you use all the gas and don't try to separate a tiny amount of useful gas from the rest. If you are doing that you could certainly lose this advantage. For example if the concentration is only 1% then you'll need an exhaust velocity 100x larger than the orbital velocity just to break even!

So it's better to choose an ion engine design that can somehow work with the planet's native atmospheric mixture that occurs at the altitude where you're collecting it.

I have a hunch that this fraction problem has been explained in another answer on this site before, but I can't remember where.

Now, if you are dropping into orbit, then drag is your friend and it will work together with your thrust. For more on that see the aerobraking tag.

To lower your orbit after dropping into it, or to raise your orbit when it's time to go, or to just do a make-up burn to counteract drag and keep your current orbit, you'll do your burn somewhere near the lowest point.