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Researching small asteroids up close by use of robotic probes seems like an appealing near-future mission. One option is a sample return mission that goes to one large body, another is a mission where a number of smaller bodies are visited over time. In either case, the thing is to land, then launch again, and ultimately return to Earth with samples, perhaps even drilled core samples. Maybe a little digging could be done, or seismic tests, to see what it is really like to work on the surface of an asteroid.

Dawn visited both Vesta and Ceres by using ion thrusters. How large a body could a probe similar to Dawn - with 3 NSTAR ion engines, the same amount of xenon propellant, and of similar mass - land on and return from in the asteroid belt?

Alternatively, how many smaller bodies could such a craft visit, probe the surface of, and then return from? (I suppose this depends greatly on how the bodies are spaced out, and their relative velocities and orbits, but perhaps it is possible to make a fair estimate of what those would probably be.)

Partly I am curious about the kinds of applications ion thrusters can be used for, partly each time I think through examples of orbital mechanics and propulsion in space, I understand it a little better. (Because so far life has prevented me from taking the time to learn how to work through the formulas myself.)

(Note: OSIRIS-REx is going to use hydrazine thrusters to reach the Near Earth Asteroid Bennu, and will return a sample to Earth. It is the first instance of a mission returning a sizable sample, so perhaps deserves mention. Hayabusa earlier returned a milligram or so from Itokawa)

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Here's how you can work it out.

First, thrust in kilo-Newtons (kN) divided by mass in metric tons yields acceleration in meters-per-second-per-second. Divide by 10 to get acceleration in approximate Earth surface gravities (9.81 is the real factor).

Dawn uses its thrusters only one at a time (they aren't pointed the same direction), and a single NSTAR thruster yields 90 milli-Newtons of thrust, i.e. 0.00009 kN. Dawn massed 1.24 tons fully loaded; 0.425 tons of that is Xenon fuel, so when it's almost empty it masses more like 0.8 tons. 0.00009 divided by 0.8 yields about 0.00011 m/s2 acceleration, which is not very much at all.

When landing, you need somewhat more acceleration from thrusters than the gravity you're fighting, otherwise you won't slow down at all. A factor of 1.5 is reasonably sufficient; the more thrust margin you have, the less fuel you'll spend on the way down.

Ceres has substantial surface gravity - 0.29 m/s2 worth - so landing there is obviously a no-go by a factor of about 4000.

Even comet 67P/Churyumov–Gerasimenko, of Rosetta/Philae fame, has a surface gravity around 0.001 m/s2, 15 times too much for a safe landing (although using collapsible landing gear or similar lithobraking techniques, it could be done).

For bodies of similar density, surface gravity is proportional to radius, so we want a body about 1/15 the size of 67P, or a couple hundred meters across.

Dawn also has chemical thrusters about ten times as powerful as the ion thrusters, though, which it could use to land; with those, a body about one km across would probably be landable.

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