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The DART spacecraft will ultimately be a kinetic energy impactor, using its 500 kg mass at a relative velocity of over 6000 m/s to slightly change its target 65803 Didymos's companion Dimorphos's velocity. The degree of success will be the momentum transfer fraction (actual vs theoretical maximum) as observed from Earth by the slight change in the orbital period of the pair.

Dimorphos (aka "Didymos B", "Didymoon") has a diameter of about 170 meters as measured by delay-doppler radar by Arecibo R.I.P. and careful photometric light curve analysis and modeling of the pair.

Trying to implement a near-direct hit of a 170 meter target for maximum momentum transfer as it wobbles circling every 12 hours around another asteroid while approaching with a relative velocity of >6000 m/s (>21600 kph) is certainly quite a challenge!

Many asteroid missions have established near-osculating intercept orbits, then fallen in to gravitationally bound orbits about the asteroid, then successively lowered those orbits.

This is the opposite of that, you come up on a tiny rock at heliocentric velocity, so fast that it's as wide as the Moon (0.5 degrees) only 3 seconds before impact. This is roughly ABM or ASAT-like performance!

But it's in deep space, millions of kilometers from Earth and by a ion-engine propelled spacecraft.

Question: How (the heck) will DART be able to hit a 170 meter rock dead-center at over 6000 m/s? What technologies will be use and how will they work together?

Here's an attempt to find some previous examples of spaceflight marksmanship or ways of calculating it. Since the target is only 85 meter in radius and the goal would be to hit somewhere near the middle the target B or impact parameter here is probably 10 or 20 meters!

Fig. 21. Definition of target or arrival B-plane coordinates click for larger

Fig. 21. Definition of target or arrival B-plane coordinates

Source Interplanetary mission design handbook. Volume 1, part 2: Earth to Mars ballistic mission opportunities, 1990-2005 page 20, found in @MarkAdler's answer

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  • $\begingroup$ Early Navigators on planet Earth oceans use a compass based magnetic field guidance. In the current context, it may be seemingly possible, at a certain point in this flight, to switch to an analogous magnetic field guidance system (AKA, a compass, assuming a magnetic core in the comet). This could be a path to impact. $\endgroup$
    – AJKOER
    Nov 27 at 21:36
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    $\begingroup$ @AJKOER the reasons that magnetic compasses work for navigators include 1) Earth's powerful dynamo, driven by a rotating liquid+solid metal core, and 2) navigators always remained on the surface of the Earth at a nearly constant 6,000+ km from the Earth's center. Dipole fields, magnetic or otherwise fall off as the inverse cube of distance ($1/r^3$) and so rapidly weaken as you get further away. $\endgroup$
    – uhoh
    Nov 27 at 21:55
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    $\begingroup$ @AJKOER One hour before impact the distance will be about 22,000 km even Earth's field would be only 2% of what it is on Earth's surface, and this tiny ~170 meter diameter asteroid would not be expected to have anything like Earth's magnetic field strength. And while early navigators could map Earth's field's shape (it's quite a lousy dipole 1, 2, 3) nobody knows if Dimorphos has any field,... $\endgroup$
    – uhoh
    Nov 27 at 21:59
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    $\begingroup$ @AJKOER ...and if it did have a tiny one, what shape it would be. So no, I don't think that that would work in any reliable way. But it does suggest a new question: How many solar system bodies have had their magnetic fields directly measured? $\endgroup$
    – uhoh
    Nov 27 at 22:06
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Didymos will be roughly 11 million kilometers (6.8 million miles) from Earth at the time of the DART impact.The round trip time for a radio signal from DART to the control center on Earth will be about 73 seconds. The impact speed to Didymos will be about 6.6 km/s, after the 73 seconds DART will be 484 km closer to its target.

So DART should navigate autonomously during the last hour before impact. The only instrument of DART is the camera DRACO (Didymos Reconnaissance and Asteroid Camera for Optical navigation).

DRACO is a high-resolution imager derived from the New Horizons LORRI camera to support navigation and targeting, to measure the size and shape of the asteroid target, and to determine the impact site and geologic context. DRACO is a narrow-angle telescope with a 208-millimeter aperture and field of view of 0.29 degrees. It has a complementary metal-oxide semiconductor (CMOS) detector and sophisticated onboard image processor to determine the relative location of Dimorphos and support SMART Nav.

As part of guidance, navigation, and control (GNC), the DART team has developed algorithms called SMART Nav (Small-body Maneuvering Autonomous Real Time Navigation). This autonomous optical navigation system will identify and distinguish between the two bodies at Didymos and then, working in concert with the other GNC elements, directs the spacecraft toward the smaller body, Dimorphos, all within roughly an hour of impact. To accurately navigate to the asteroid using onboard systems, the DART team is leveraging decades of missile guidance algorithms developed at APL.

The total mass of the DART spacecraft is approximately 1,345 pounds (610 kilograms) at launch and 1,210 pounds (550 kilograms) at impact. DART carries both hydrazine propellant (about 110 pounds, or 50 kilograms) for spacecraft maneuvers and attitude control, and xenon (about 130 pounds, or 60 kilograms) to operate the ion propulsion technology demonstration engine. The spacecraft will use at most 22 pounds (10 kilograms) of xenon.

So autonomous optical navigation and more than 50 years of experience with missile guidance algorithms will be used during the last hour before impact to hit a 170 meter rock at its center. For fast trajectory and attitude corrections, the hydrazine thrusters may be used.

During the 10 month travel to Didymos the ion engine may be used by ground control to optimize the trajectory.

Source

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I don't work for NASA, so I don't know exactly what algorithm DART will use for its terminal guidance. But I do know that it doesn't need to be particularly complicated.

DART has a high-resolution narrow angle camera that (once it's within a few hours or days of impact) can see both its target, Dimorphos, and background stars. The key observation is that when the center of your target isn't moving relative to the stars, you're on a collision course with it (or flying straight away from it — but that's not a likely mistake under the circumstances).

Of course, the observation above is strictly true only when both you and the target are moving in a straight line at a constant velocity, which isn't quite true in this case. But the orbital period of Dimorphos around Didymos is about 12 hours, so on timescales of less than an hour or so, it might as well be moving in a straight line.

So my guess is that DART will initially follow a precalculated intersect trajectory with Didymos and Dimorphos, which NASA will gradually refine based on observations both from Earth and from the probe itself. It's possible that these non-autonomous course corrections alone might be enough to put DART on a collision course with Dimorphos, since trajectories in space are highly predictable. But I'm also pretty certain that NASA won't rely on that alone.

Instead, once DART is close enough to Dimorphos to see it, they'll turn on the automated guidance algorithm. Of course they'll initially monitor its behavior from Earth, maybe even running it initially in "dry run" mode where it just reports what it sees and what steering corrections it would've made. But eventually, as DART gets closer to impact and lightspeed lag makes guiding it from Earth impractical, they'll just let the algorithm steer it autonomously for the last few hours or so.

It's possible (and quite likely) that DART's guidance algorithm will include a correction term for the curvature of Dimorphos' orbit, but that's just extra polish — a naïve tracking algorithm that just steered the probe to keep the target stationary against the stars should be able to do the job just fine for the last few minutes, maybe using slightly more maneuvering fuel than necessary.

The guidance algorithm itself will likely also make use of Kálmán filters and other similar control theory tools to compensate for noisy input, imprecise steering outputs, etc. This doesn't necessarily need to be particularly complicated either — even a simple old PID loop should do the job — but since this is an expensive device developed by NASA, I'm sure they'll use the best and fanciest algorithms available.

That said, I don't think writing a simple kOS script to perform a comparable guidance task in Kerbal Space Program would take much time — maybe less than writing this answer. I might give it a try, though I don't currently have KSP installed on this computer. The most time-consuming part would in fact probably be restricting the inputs to what's realistically available to DART and adding some noise to the steering outputs for realism.

The one failure mode you'll want to avoid, of course, is having to make major course corrections at the last minute and running out of fuel (or time) to do so. But that's straightforwardly avoided by just making as small and precise course corrections as possible early on and trusting in the determinism of orbital mechanics.

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  • $\begingroup$ +1 "...so on timescales of less than an hour or so, it might as well be moving in a straight line." Ya it's likely they will choose maximum elongation for the impact, so the relative orbital motion will be pretty-much parallel to the the intercept and have minimal impact on your algorithm during that last hour. $\endgroup$
    – uhoh
    Nov 27 at 0:26
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    $\begingroup$ Good answer. In marine navigation "constant bearing" predicts collision. It even works with currents, variable speeds and non-linear courses. Other algorithms may achieve collision sooner, but not more reliably. Trying to predict where the target will be at a time in the future and heading for that spot has much lower chance of a collision. $\endgroup$
    – Woody
    Nov 27 at 0:39
  • $\begingroup$ IMO, the particular challenge is not (only) hitting, a "sitting-duck" or a moving, target at its center. It's also doing it at the right time so as to maximize the relative velocity at impact. You do have a recurring opportunity every 12 hours (about). But let's not forget that speeding or slowing to optimize the impact velocity will affect as well the impactor orbit around the Sun. I think that to express this concisely and precisely as a mathematical problem is by itself a nice orbital-mechanic problem (solving the problem is the other side of challenge). $\endgroup$
    – Ng Ph
    Nov 27 at 14:53
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    $\begingroup$ @NgPh: Yes, that's an interesting optimization problem in itself. It's non-linear too, so NASA will probably use some kind of an iterative refinement solver for it. (KSP players will be familiar with the manual version of that iterative refinement process, also known as "roughly eyeball it and then fiddle with the maneuver nodes until you get a good encounter".) But that's all strictly part of the initial trajectory planning. By the time DART gets close enough Didymos to need autonomous guidance, it's way too close and going way too fast to change the impact time in any meaningful sense. $\endgroup$ Nov 27 at 15:11
  • $\begingroup$ 1 hour is ~30° of Dimorphus' orbit, marginally 'a straight line' even considering the helpful cosine factor, which means the 'normal plane' motion of the target in the final hour is, at best, greater than the target's radius, perhaps even greater than its diameter. $\endgroup$ Nov 27 at 18:42
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In my mind there are two different questions here. The first one is where to aim, and the other is how accurately can you do it.

Where to aim is similar to when shooting a weapon at a moving target. The aim should not be towards where the target is now, but where it will be when the projectile arrives at the target.

Using ground based observation it is possible to over a long time create exceptionelly precision in the equations describing the movement of the pair of the asteroid and its moon. And again using ground based equipment you can reach a high degree in precision of the movement of the satellite.

Extrapolating in time using the equations it is possible to describe exactly where the movement vector of the satellite should point - and it is not towards where the asteroid is at the current time.

Far from the asteorid I guess you would orient the satellite looking at the direction of "guide stars" tracker, not necessarily pointing even close to the asteroid. Measuring from earth you could then send corrections which the satellite performs.

Close to the asteroid corrections could be done autonomously by the satellite. There will only be delta available to make small corrections at this time -- the satellite has to be smack on target already. My guess would be to measure the angle between the asteroid and a few selected guide stars and perhaps if the small moon can be seen and input these angles togehter with time into the equations to calculate a correction and then using thrusters. This has to be done in time in order to actually have any effect.

Now for the precision part. Ground based measurement can be done very accurately. And the telescope camera on the satellite has a very high resolution allowing it to "see" with enough precision to reach a high probability of actually hitting the moon.

As Dimorphos has a orbit period of 11.9 hours it will move about 30 degrees around Didymos during the last hour of flight of the satellite.

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