Hurrah - Physics Works (Dart Mission)

[saac]

Nice example of momentum in action.  The Dart mission team (experiment to divert the trajectory of asteroid Dimorphos) have reported that they achieved a greater deflection due to the unexpected amount of ejecta created by the impact projectile. Bruce Willis (Armageddon) stand down, Newton has everything under control  

Jim 

https://www.bbc.co.uk/news/science-environment-63995869

[markse68]

I don’t really understand the physics of why it should deflect more with ejecta than with perfect transfer of kinetic energy like a newtons cradle, but doesn’t this mean that should we really need to use this technique we are still in the dark as it’s effect will be totally dependent on the makeup of the asteroid? Which we might not know in time

Mark

Edited December 18, 2022 by markse68

[saac]

33 minutes ago, markse68 said:

I don’t really understand the physics of why it should deflect more with ejecta than with perfect transfer of kinetic energy like a newtons cradle, but doesn’t this mean that should we really need to use this technique we are still in the dark as it’s effect will be totally dependent on the makeup of the asteroid? Which we might not know in time

Mark

Hi mark, it's a consequence of the characteristics of momentum. Unlike Kinetic Energy during any collision the total momentum must be conserved. When the collision results in material being ejected backward this results in a greater change in momentum than had no material been ejected because the velocity component is a vector and so is sensitive in sign (+ or - ) to direction. Having the ejecta thrown backward in the direction the Dart probe impacted imparts a further change in momentum.  All of this translates to a higher impulse (Force x time), and it's the higher Force that resulted in the greater level of deflection than expected.  Impulse (Force x time) itself equating to the change in momentum. So a higher change in momentum results in a larger Impulse. A great example of this in practice is seen in the design of the Pelton water wheel. The convolutes in the Pelton wheel blade cause the water to go through a greater change in direction than would happen with say a flat profile blade. Hence the Pelton wheel is able to extract a greater change in momentum from the water and hence more power. 

Edited December 18, 2022 by saac

[DarkAntimatter]

So if the impactor spaceship could be made to bounce back off the asteroid at the negative of its impact velocity it would impart twice the momentum change on the asteroid than if it just embeds itself?  Assuming nothing is ejected.

[markse68]

That’s the bit i’m not sure about too- if it were a perfect elastic collision then momentum and Ke would be conserved but they call the effect of ejecta production “momentum enhancement” in that the transfer of momentum is higher than the momentum of the projectile alone so presumably it shifts the target more than a perfectly elastic collision would?

https://www.sciencedaily.com/releases/2022/11/221101100742.htm

@saac Jim, I think your water wheel example shows that by scooping the blades the water is deflected backwards transferring more momentum to the wheel than if it were deflected sideways by a flat blade which makes sense but if there were no ejecta at all and the projectile somehow survived the impact and bounced straight back off the target, would that be less efficient than what we see here in deflecting the target? The ejecta has more mass than the projectile but presumably must be moving at lower velocity than the projectile to conserve momentum? 

It’s all very interesting anyhow

Mark

edit: thinking about it some more, is the time factor the key? I could imagine in a perfectly elastic collision the impact would be instantaneous and the bodies would dissipate some energy as their bodies deformed and resonated elastically- a bit like this tennis ball:

 

whereas with the inelastic collision that happened the impact duration is much longer and the energy channelled into the rearward firing ejecta jets leading to more efficient momentum transfer?

 

Edited December 19, 2022 by markse68

[saac]

Here is an overly simplified and very casual analysis showing how ejecta (having opposite vector sign to both projectile and target) have an additive effect to the change in the speed of the target after the collision.  This is really an horrible over simplification as the ejecta does not behave as a homogeneous body nor is it constrained to a single plane however it demonstrates the general effect in conservation of momentum.   

The Pelton blades do exactly that they re direct water back in the direction )partially) of the incident water flow. There is also some lateral displacement of the water and with twin petals as shown the effect here is to cancel the axial loads on the wheel bearings. If you want a very intuitive demonstration as to the effect of the ejecta increasing the change of momentum try this. Set a tea spoon between your thumb and forefinger (held loosely). Using your forefinger to balance the spoon over and your thumb to apply a restraining force to stop it rotating. Now place the spoon in the flow of water from a tap - try it concave face out then reverse. You will notice a far greater torque is applied to the spoon when the water hits the concave face. The water is forced to go through a greater change in direction (effectively ejecta) hence greater change in momentum (remember the mass flow rate is exactly the same for both demonstrations). Another analogy is to consider a cricket ball being caught - catch an incoming ball by pushing your hand toward the ball and then compare to catching by allowing your hand to match the incoming ball speed and direction (pulling back). The first will result is some considerable pain to your hand as a greater change of momentum is experienced with commensurate higher impulse applied to your hand.   The tennis ball in the video is experiencing an inelastic collision during which the momentum will be conserved but the kinetic energy is not conserved (deformation resulting in both ball and  bat). 

 

 

 

 

 

Edited December 19, 2022 by saac
typo

[saac]

Here's another example of an inelastic collision; who would have thought something as rigid as a golf ball could deform in such a way.  I love watching this video  

Jim 

 

[markse68]

But if they return to original form it’s elastic surely? I can imagine a similar thing happens when 2 snooker balls collide or 2 ball bearings in a Newtons cradle (on a much smaller scale obviously)

I understand your point about the water wheel Jim - of course if the ejecta had been ejected sideways instead of backward they wouldn’t have contributed to the momentum transfer and maybe that is what the scientists were surprised by, i’m wondering though if the ejecta caused a greater deflection than had it been a perfectly elastic collision (a ridiculous hypothetical i realise) and how much the elastic deformation analogous to the golf ball affects this?

Mark

Edited December 19, 2022 by markse68

[saac]

Maybe imagine it this way Mark;  treat the ejecta as a completely separate event separate from the impact and absorption of the Dart missile. If you stand on a skateboard and throw a heavy medicine ball forward, the overall change in momentum on you will cause you to move in the opposite direction.  No different from a rocket engine really with the exhaust gases being expelled resulting in an opposite direction on the rocket itself (Newton's 3rd law). Now apply same thought to the asteroid. Add the change in momentum due to material being thrown backward to the change in momentum caused by the impact of the Dart missile itself. Without the ejecta you would have a lesser change in momentum.  I think also what may be confusing  is your use of the term "elastic". An elastic collision is defined by the conservation of Kinetic Energy. If the Kinetic Energy  is conserved then the event is said to be elastic, if the kinetic energy is not conserved it is inelastic. There is a temptation to think of elastic meaning nothing is deformed but this is not the case - the test is conservation of Kinetic Energy. There are practically no true elastic collision in the macro world; the golf ball is  an inelastic collision -  magnetic repulsion may be a close approximation to an elastic collision but only an approximation.  Irrespective of the golf ball returning to its original shape, energy was removed (converted to heat) during the deformation, hence Kinetic Energy was not conserved, only momentum.  There is a paper on the arxiv server which presents on a model for the determination of the momentum transfer; looks in detail at the geometry of expected ejecta plume to determine density/mass and related momentum transfer. Well above my understanding but I fool myself into thinking I can follow parts of it   

https://arxiv.org/abs/2007.15761

chrome-extension://ieepebpjnkhaiioojkepfniodjmjjihl/data/pdf.js/web/viewer.html?file=https%3A%2F%2Farxiv.org%2Fftp%2Farxiv%2Fpapers%2F2007%2F2007.15761.pdf

Jim

Edited December 19, 2022 by saac