DART mission launches to test asteroid deflection

[berkeman]

Um, why are we spending $330M on a mission to (re-)prove that conservation of momentum works in space? What am I missing?

https://www.cnbc.com/2021/11/23/spa...t- spacecraft -to-crash-into-an-asteroid.html

SpaceX is launching a NASA spacecraft that will crash into an asteroid​

“We’re smashing into an asteroid,” NASA’s Launch Services Program senior launch director Omar Baez said during a press conference. “I can’t believe we’re doing that”

 

[hutchphd]

I think the dynamics of the interaction may by quite complicated because no one really knows how solid the surface is. If there is a lot of ejecta then that too must be included in the momentum conservation. Also I guess it is not known how accurately this will be a "head-on" collision because it is partially autonomous. That's what I know. Also its cool.

 

[mfb]

The big question is how much material it ejects at what speed. As energy scales with velocity squared the ejected material can deliver a much larger momentum change than the primary impact because it has so much more mass.

Another question is how accurately we can hit the asteroid when approaching at 6.6 km/s, and what that means for smaller targets. No mission ever had a target that small with that approach velocity.JWST had a mishap in the integration with Ariane 5. Four days delay to check that vibrations didn't exceed specifications, now the launch is planned for December 22.

 

[sophiecentaur]

What am I missing?

For success, almost all of the mass of the target needs to acquire the correct momentum (all that's available from the Dart craft) to get into the right orbit. Serious egg on face (or worse) if some of the asteroid ended up coming our way.

How sure can we be that a target asteroid can be treated as one solid lump an that the impact will not result in a large part of it just continuing nearly on its original course? Have there been any records of asteroids actually colliding with each other? I know there are a number that are clearly formed from two originals but how well stuck together are they?

I'd say it was money well spent.

 

[hutchphd]

For success, almost all of the mass of the target needs to acquire the correct momentum (all that's available from the Dart craft) to get into the right orbit.HIS are many

This is not simple. The technique (as I understand) mostly involves changing orbital speed. So if you slow the asteroid, for instance, it might not intersect. But what if you can split the body and make part go faster (and not hit earth) and part go slower (and not hit earth). This might be much more effctive. That is sort of what a collision with a lot of ejecta might look like. Or perhaps the ejecta (a small fraction of the original mass) will hit Earth (bad) but the major body will not (good). Anyhow that is how I understand the complexities.

\

 

[sophiecentaur]

This is not simple. The technique (as I understand) mostly involves changing orbital speed.

That seems to be a common way of manoeuvering craft in orbit. I imagine that's because time, position and direction of the craft (in this case asteroid) are known accurately and errors in direction of engine impulse have least effect when applied forward or reverse.
Rather like a course to settle a craft into orbit with a planet with minimal fuel use, the courses of planet and craft are arranged to coincide and be more or less parallel and similar speeds. It will take much longer but there's more time to adjust things than going in from the side. Corrections of the asteroid orbit at the apogee are easiest, I understand. But this approach has to involve several years to set it all up. When is Dart's rendezvous planned?

 

[hutchphd]

As I recall Sept 2022 and I think it will be relatively nearby

 

[Rive]

But what if you can split the body and make part go faster (and not hit earth) and part go slower (and not hit earth).

The problem is, that as long as the pieces are around they will orbit each other. So either you completely tear apart the pieces (awful lot of energy to dig them up from their gravitational well) of you just added one more parameter (their orbit phases) to the calculations (what if they are happen to be lining up with Earth when they are close?)...

Usually for long term trajectory calculations it's some kind of cone of probability along the curve, giving chances about a possible collision. As far as I understand, to just shift the cone it is the best if the most possible amount of mass leaves the asteroid, with speed just a bit above the local escape velocity (that's what gives the most effect for the same energy budget). Since 'live' it'll be about (likely a nuclear) explosion, knowing the build of the target is really a must.

BTW maybe this is a bit of an off here, and would worth a split.

 

[berkeman]

The big question is how much material it ejects at what speed. As energy scales with velocity squared the ejected material can deliver a much larger momentum change than the primary impact because it has so much more mass.

Sorry, if conservation of momentum works in inelastic collisions, how does ejected material change anything? The CoM of the system of the asteroid and the interceptor stays the same, right? Or is the objective to eject lots of low-mass stuff one way, and thus push the asteroid the other way?

 

[hutchphd]

This is not realistic but if it breaks into a "dumbell" and Earth slips between the two lobes of the "dumbell" then we save the planet. The COM will be largely devoid of mass... you get the idea. Clearly it won't be that simple, but the game may work. I don't think anyone really knows.

 

[mfb]

I split the discussion.

How sure can we be that a target asteroid can be treated as one solid lump an that the impact will not result in a large part of it just continuing nearly on its original course?

The target is very large. Unless DART hits very close to the edge it cannot fly through independent of the composition of the object. Even water with the same volume would stop DART. That part of the momentum change is guaranteed if DART doesn't miss.

Serious egg on face (or worse) if some of the asteroid ended up coming our way.

This is not a risk. It's nowhere close to an Earth-crossing orbit. I mean... some ejected pebbles might, obviously, but that's not a concern.

For an impact scenario that's at least a few orbits in the future the most effective approach is generally a kick in the direction of motion - forward or backward, depending on what's easier in terms of orbital dynamics and predicted path for the impact. That changes the orbital period, so the distance to the undisturbed position keeps increasing over time. A deflection orthogonal to the direction of motion only changes the shape of the orbit but keeps the period unchanged, so the effect of the deflection doesn't increase over time.
If the object makes a close fly-by before a potential collision then we can achieve a much larger deflection, as a small change in the fly-by geometry will lead to a larger change in the orbit afterwards.

But what if you can split the body and make part go faster (and not hit earth) and part go slower (and not hit earth).

Splitting an asteroid deliberately, and doing it with such a precision, is pure science fiction.

That [changing orbital speed] seems to be a common way of manoeuvering craft in orbit. I imagine that's because time, position and direction of the craft (in this case asteroid) are known accurately and errors in direction of engine impulse have least effect when applied forward or reverse.

No, they have the largest effect, just like the propulsion itself. That's why it is done whenever possible - maximal effect for a given amount of fuel.

Rather like a course to settle a craft into orbit with a planet with minimal fuel use, the courses of planet and craft are arranged to coincide and be more or less parallel and similar speeds.

Spacecraft don't do that, it would be a waste of fuel. It's more efficient to have any intersecting trajectory and then slow down (relative to the planet) when the spacecraft is at its closest approach.
Dawn was an exception, it approached Vesta and Ceres slowly because it only had an ion thruster so it couldn't use the conventional approach - but it only flew to asteroids, not planets.

Corrections of the asteroid orbit at the apogee are easiest, I understand.

If you want to change the perigee, yes. If you want to change the apogee you should do it at perigee. Usually you don't want to change either of them in particular, you want to change the orbital period which can be done at any time. Finding a suitable trajectory from Earth is more important. That might take years for some objects, but in this case it's under a single year to the September 2022 impact.

Sorry, if conservation of momentum works in inelastic collisions, how does ejected material change anything? The CoM of the system of the asteroid and the interceptor stays the same, right? Or is the objective to eject lots of low-mass stuff one way, and thus push the asteroid the other way?

The material is ejected from the impact site, so it is directional.

Toy scenario with rounded numbers for simplicity: DART at 500 kg impacts at 6 km/s. A perfect inelastic collision with no debris would transfer 3,000,000 kg m/s momentum to the asteroid. The impact releases 9 GJ of energy. If e.g. 1 GJ of that energy kicks 100 tonnes away from the surface it will leave at a typical velocity of ~150 m/s. About 100 m/s of that will be against DART's flight direction (and ~100 m/s orthogonal to it in random directions), adding another 10,000,000 kg m/s momentum change in the same direction, three times the primary momentum transfer using just ~10% of the energy. Will 10% of the energy go into ejected debris, or is it 1%, or 0.1%, or 30%? Will it be of the order of 100 tonnes, or 10, or 1000, or whatever? Instead of just assuming a typical velocity, what will the distribution be? All these questions matter.

 

[sophiecentaur]

maximal effect for a given amount of fuel.

That makes sense. Changing gravitational potential with a rocket is not good value (efficiency at lift-off is an example) changing KE is better.

If you want to change the perigee, yes. If you want to change the apogee you should do it at perigee. Usually you don't want to change either of them in particular, you want to change the orbital period which can be done at any time

I was rather thinking that asteroids 'visiting' from further out (high apogee) could be taken to a higher perigee and permanently out of harm's way?

Spacecraft don't do that, it would be a waste of fuel. It's more efficient to have any intersecting trajectory and then slow down (relative to the planet) when the spacecraft is at its closest approach.

Do you really mean that arrival from a radial direction is better than a near tangential direction? That seems to disagree with point about changing KE rather than GPE. The paths that I have seen to get into orbit round Mars seem to have been as I described.

Toy scenario with rounded numbers for simplicity:

Interesting paragraph. You make the point that, in the light of the masses involved, 'splitting the asteroid in two halves' is not a scenario - just a varying small amount of ejecta.

 

[Rive]

just a varying small amount of ejecta

An important point is that the ejected/split matter needs to leave the asteroid to have any effect (speed above escape velocity). It's easy to do that with just some ejected matter, but certainly will be far more difficult with half the asteroid.
Also, in the future these kind of missions (I mean, if there is real need/danger already) will likely involve nuclear weapons too, so that 'small' can be quite relative, depending on the actual circumstances/material composition.

 

[mfb]

I was rather thinking that asteroids 'visiting' from further out (high apogee) could be taken to a higher perigee and permanently out of harm's way?

That would need a deflection of the order of a kilometer per second (and I don't see a plausible scenario where this would leave the asteroid intact), while asteroid defense scenarios look at millimeters to centimeters per second.

Do you really mean that arrival from a radial direction is better than a near tangential direction?

No. The most common approach for direct flights is a Hohmann transfer, which arrives at the target at significant relative speed along the orbital direction. That relative velocity is reduced around the time of closest approach to enter an orbit, or it's shed in the atmosphere for a direct landing.

 

[sophiecentaur]

a Hohmann transfer, which arrives at the target at significant relative speed along the orbital direction.

That's what I was thinking of.

while asteroid defense scenarios look at millimeters to centimeters per second.

Useful information, thanks. Why would the required velocity change be as high as 1km/s? Would it be because of the need to increase the total orbital energy so much? Sort of makes sense if the original orbit had high eccentricity.
But the total energy needed for a large asteroid would be a fair bit for any manoeuvre, I suppose.
The idea of using two similar ('twin') asteroids for the experiment, with one acting as a control, is also very smart.

 

[mfb]

Asteroids have no reason to have circular orbits or a perihelion extremely close to 1 AU. Both perihelion and aphelion are somewhere random, and changing them by a lot needs a large velocity change. Of the order of 300 km/s (or 0.01 times Earth's orbital velocity) for a 1 million kilometer change (~0.01 AU) - which isn't much on the scale of Earth's orbit.

The idea of using two similar ('twin') asteroids for the experiment, with one acting as a control, is also very smart.

Not a control, but a tool to detect small velocity changes. Measuring the changed orbital period can be done far more precisely than measuring the velocity change itself. There is saying that comes from optics, but it's true almost everywhere: Reduce every measurement to a frequency measurement if you can.

 

[sophiecentaur]

Not a control, but a tool to detect small velocity changes.

That's what I meant; to see the difference that the 'treatment' has achieved. The with and the without cases.

Both perihelion and aphelion are somewhere random,

But more outside Earth's orbit than inside? If perihelion were taken to >1AU the problem would be solved. But you have pointed out that the energy involved to do that would be too much.

Measuring the changed orbital period can be done far more precisely than measuring the velocity change itself.

. . . . going right back to Kepler's Laws, in fact. We can see the 'when' with a telescope much easier than the where or how fast.

 

[mfb]

But more outside Earth's orbit than inside? If perihelion were taken to >1AU the problem would be solved. But you have pointed out that the energy involved to do that would be too much.

Both are somewhat random but only the set of asteroids with perihelion <=1 AU and aphelion >=1 AU can be potentially dangerous obviously (the actual range is slightly larger because of Earth's eccentricity). That's a post-selection.

 

[Galexy]

The big question is how much material it ejects at what speed. As energy scales with velocity squared the ejected material can deliver a much larger momentum change than the primary impact because it has so much more mass.

Another question is how accurately we can hit the asteroid when approaching at 6.6 km/s, and what that means for smaller targets. No mission ever had a target that small with that approach velocity.JWST had a mishap in the integration with Ariane 5. Four days delay to check that vibrations didn't exceed specifications, now the launch is planned for December 22.

I also have a question about DART? If the spacecraft does not hit the target exactly head on (which is likely), some of the collision energy will go into rotational energy of the target moon. A 'glancing blow' would cause most of this energy to become angular momentum of the moon. We will not know the 'angle of attack'(?) for a long time, (if ever) and I don't see how they will be able to determine how much rotational energy the moon has when the second spacecraft arrives.

Also, I suppose the dynamicists are assuming that the moon is tidally locked to Didymos to begin with, but that is not necessarily the case. There is no way of determining if the moon has any residual rotational energy left over from its formation (or from a recent meteoroid hit).

The way I see it, the unknowns associated with the rotational energy of the moon before and after the collision will seriously complicate the experiment. Am I wrong?

 

[etudiant]

I also have a question about DART? If the spacecraft does not hit the target exactly head on (which is likely), some of the collision energy will go into rotational energy of the target moon. A 'glancing blow' would cause most of this energy to become angular momentum of the moon. We will not know the 'angle of attack'(?) for a long time, (if ever) and I don't see how they will be able to determine how much rotational energy the moon has when the second spacecraft arrives.

Also, I suppose the dynamicists are assuming that the moon is tidally locked to Didymos to begin with, but that is not necessarily the case. There is no way of determining if the moon has any residual rotational energy left over from its formation (or from a recent meteoroid hit).

The way I see it, the unknowns associated with the rotational energy of the moon before and after the collision will seriously complicate the experiment. Am I wrong?

You are very much on the mark, the issue with DART is momentum transfer, from the impacter to the body of the target.
Spin and target material composition are both important variables, the former because it really impacts the latter.
Sending DART to hit a dust cloud would be useless, but we don't even know how solid the DART targets are, so it is a speculative mission.
Ideally, the impacter transfers close to 100% of its momentum to the asteroid. If not, back to the drawing board.

 

[mfb]

The rotation of the moon is irrelevant for changing its center of mass motion. The kinetic energy transferred to the moon is negligible compared to the impact energy anyway. It's all about the momentum.

DART will take pictures and a cubesat will watch the impact as well, we should get a pretty good estimate where it will hit.

Ideally, the impacter transfers close to 100% of its momentum to the asteroid.

100% unless it's a really bad hit. The unknown part is the momentum of the ejected debris.

 

[sophiecentaur]

The rotation of the moon is irrelevant for changing its center of mass motion.

Doesn't conservation of momentum apply to net linear and angular momentum? A glancing blow would involve a lot of spin and less linear momentum change. Likewise, if the moon were spinning and a glancing blow reduced the spin then effectively there would be change in linear momentum.
The relative masses and MI would be relevant to the details of the change, of course.

 

[mfb]

Doesn't conservation of momentum apply to net linear and angular momentum?

Yes, and both are independent.

DART will hit it with 6 km/s. A surface velocity of 1 m/s in any direction is completely irrelevant even if the mission fails and delivers a glancing hit only.

 

[sophiecentaur]

Yes, and both are independent.

DART will hit it with 6 km/s. A surface velocity of 1 m/s in any direction is completely irrelevant even if the mission fails and delivers a glancing hit only.

That is non-intuitive as a general principle. It implies on the face of it, that if a moving ball were to hit a bar with a force, normal to the axis and at the end, that the bar would only rotate and with no change in its linear momentum; i.e. the bar would stay where it is. Would that actually be the case? Will the share of linear momentum between bar and ball, after the collision not depend on where the ball strikes.
You say linear and angular momentum are independent - that sounds like a reasonable basic principle but the initial angular momentum depends on the path of the ball and the final angular momentum of the bar will involve the linear velocity of its CM relative to the ball.
Where is the flaw in my argument?

 

[mfb]

I don't know what you call non-intuitive here. It's like proposing you could make a bullet do less damage by rotating a human body. It's just far too slow to make a difference (and bullets are much slower than DART).

It implies on the face of it, that if a moving ball were to hit a bar with a force, normal to the axis and at the end, that the bar would only rotate and with no change in its linear momentum; i.e. the bar would stay where it is.

No, it doesn't imply something that's obviously wrong...

Will the share of linear momentum between bar and ball, after the collision not depend on where the ball strikes.

After the inelastic collision the far heavier bar has essentially 100% of the initial momentum of the ball. Its rotation is irrelevant, the tiny bit of kinetic energy the buried ball ends up with is irrelevant as well. We only care about the center of mass motion.

but the initial angular momentum depends on the path of the ball and the final angular momentum of the bar will involve the linear velocity of its CM relative to the ball.

So what? It's irrelevant.

The rotation of objects can have an influence on their trajectory via interaction with sunlight but that's a higher order effect and not the point of DART.

 

[sophiecentaur]

Ok. It’s in elastic and the numbers make it irrelevant. Thanks for straightening it out.