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Precisely!Filip Larsen said:Math-wise the whole thing can be modeled fine by a sequence of three two-body problems (Sun orbit before, the hyperbolic fly-by, and Sun orbit after) that are then patched together.
Precisely!Filip Larsen said:Math-wise the whole thing can be modeled fine by a sequence of three two-body problems (Sun orbit before, the hyperbolic fly-by, and Sun orbit after) that are then patched together.
The math surrounding the gravity assist requires the small object to be optimally traveling at escape velocity for the primary. It also needs to be traveling at a speed similar to the orbital velocity of the primary. One can see why this needs to be the case, because the gravitational influence of the giant body must exceed the gravitational influence of the primary for a significant portion of the trip. Otherwise we would say the object is "captured" by the primary, and the giant body's influence is comparatively small throughout its entire trajectory. At that point, a 2 body analysis can be close enough, but then again we would not be talking about an interplanetary trip.A.T. said:We are moving around the galactic center at 230 km/s, which is even bigger. Why is it fine to ignore that?
The Sun being a neutron star is irrelevant for this possibility.LesRhorer said:I have not done the math, but if our Sun were a neutron star, it might be possible to get a 200 Km/s gravity assist from it.
The range of velocities is irrelevant for the local approximation. The local approximation merely ignores the gradient of the Sun's gravity. That's is the only reason it might not be accurate enough for some applications. All your arguments based on velocity make no sense.LesRhorer said:all under only local gravitational influence (which means a limited range of velocities).
Irrelevant. We are discussing gravity assists in general, not just the specific case of a gravity assist inside a star system with multiple bodies. And we certainly aren't discussing long range orbital trajectories, just the short-range interactions between bodies during a gravity assist.LesRhorer said:In these cases, however, we can ignore the effect of all the planets on the Sun, since it is so huge, and similarly ignore the effect on each planet on every other since they are relatively much smaller and so far from each other, and totally ignore the effect of a tiny spacecraft on everything. For intra-planetary travel, we can never ignore the Sun and wind up with anything like an accurate prediction. Thus: three bodies.
LesRhorer said:they are unwilling to even listen (or heaven forbid admit they are wrong)
Thanks! I always enjoy spawning a spirited, yet polite, debate.Juanda said:This is a pretty interesting thread.
True, mostly. It is very easy to accidentally make an error in physics that causes one to apply the math incorrectly and wind up with an answer that is physically incorrect.Juanda said:First of all, how are we really defining "Gravity-assisted maneuvers"? As someone said near the beginning of the thread, the important thing is that the math is right so that the orbit of the spacecraft works as intended. Definitions of the concepts are irrelevant to the physical results.
That is specious for a couple of reasons. First of all, it is a bit misleading to say the energy is "shared" between the Earth and the asteroid. While true, in the two body analysis, virtually all the energy is "owned" by the small body. Why? Because the only proper motion of the system is that of the barycenter. Since we restricted the mass of the two bodies so that the mass of the asteroid is essentially insignificant, the barycenter is in essence a fixed point at the very center of the Earth, and the Earth's velocity relative to that point is basically zero. Thus effectively all the energy is invested in the asteroid, and none in the Earth. That single flaw by itself invalidates the entire analysis, because there is a vast amount of gravitationally moderated energy and a vast amount of gravitationally moderated momentum involved with the Earth's path around the Sun. Furthermore, the proper motion of the Earth / asteroid system is not around its own barycenter, but rather around the Earth / asteroid / Sun system, which is effectively the center of the Sun.Juanda said:@Drakkith offered a case in #17 involving only 2 bodies and he obtained a transfer of energy from the Earth to the asteroid. The total energy of that system is shared between the kinetic energy of the two bodies (Earth and the asteroid) and the gravitational energy of the field (similar to a spring connecting them).
When the asteroid reaches the same distance after the flyby the gravitational energy is the same since it is only dependent on the distance. However, the asteroid's kinetic energy is greater after the flyby. Therefore, some of the kinetic energy from Earth was transferred to the asteroid (it could be a spacecraft so the whole maneuverability makes more sense).
If one wishes to change only the direction of a spacecraft's motion but not its speed, nor the inclination of its orbit, then one can do so by sending it around a large object in deep space. That is a simple 2 body problem. If one wished to call it a "gravity assist", then that is OK (ish), too,m because all definitions are arbitrary. It s not what NASA did with Voyager or many other spacecraft, however, andone must then come up with a different term to describe what NASA did. As you yourself pointed out, it is ot the definitions that matter, but the physical results. One cannot obtain the results NASA did with Voyager, Cassini, etc. if only two bodies are involved.Juanda said:How does this fail to be a gravity-assisted maneuver? Posts #24 argues against it and #25 defends it again. So far, I consider this to be a valid gravity-assisted maneuver involving only two bodies.
Most of the people there are not like those two. A few are, but most are quite reasonable, if nonetheless untrained in physics. As to whether I feel it is worth it... well it is to me. I hate inaccuracy - especially scientific inaccuracy with a seething passion. I have done so for nearly sixty years. It is not liable to change. I also despise charlatans, sand I am fairly sure this guy is one. He is also an insufferable jerk. He even admits to that.Juanda said:@LesRhorer, if the people from that other forum are like you mentioned, is taking part in it really worth it?
Not with me. I make plenty of mistakes, and I am always more than happy to be corrected, whenever I am in fact wrong. If I am ultimately wro9ng in this case, I absolutely want to know about it. I am pretty sure I am not, since not only do I have a fairly decent understanding of the physics involved, but every reputable reference I can find agrees with me. That includes online publications from NASA, Scientific American, and even Wikipedia, not that the latter is by any means always correct. Neil deGrasse Tyson also agrees, although he also does not bat 1000. I have personally caught him in more than a couple of errors and others have caught him also.Juanda said:Discussions to see who is right are pointless more often than not.
In a forum whose principle thrust is debunking pseudo-science? Perhaps not so much?Juanda said:Online discussions are even more so.
Absolutely. Obviously, it stings a bit to find out one was mistaken, but I certainly hope my ego is more than strong enough to take a little jab once in a while. Certainly I will never call anyone here names, which this guy did the moment he "met" me.Juanda said:That attitude differs a lot from what I usually found in this forum by the way. It's not as much about proving who is right but proving what's right and trying to understand the topics that come up in the process.
I am definitely glad to hear you say it. Certainly I consider it well worth my time, even if I am in some way badly mistaken and even if I do not eventually get the assistance I would like. In my case, I earned all this almost 40 years ago, but I still come across it from time to time. Of course that may beg the question of how much I may have forgotten in the nearly four decades since.Juanda said:I didn't encounter celestial mechanics in a while and I'm having a blast.
Juanda said:First of all, how are we really defining "Gravity-assisted maneuvers"?
I note the lack of response to the request for a definition. I have seen multiple walls of text from @LesRhorer. But no definition is forthcoming.LesRhorer said:True, mostly. It is very easy to accidentally make an error in physics that causes one to apply the math incorrectly and wind up with an answer that is physically incorrect.
And that's exactly why we can use the local frame orbiting with the Earth to compute the change in velocity. As explained in the link posted by @Filip Larsen:LesRhorer said:The total change in velocity is always the same for both frames of reference.
All of physics is approximation. Whether it's appropriate depends on the application.LesRhorer said:I hate inaccuracy
It doesn't really make sense to talk about using the Sun alone for gravity assist maneuvers relative to our galaxy if the probe starts out in a bound orbit around the Sun (which all human made probes do). To be considered a gravity assist maneuver the probe would have to make a hyperbolic(1) close fly-by of some massive object that is not the primary relative to which you'd want to gain or loose orbital energy.LesRhorer said:if our Sun were a neutron star, it might be possible to get a 200 Km/s gravity assist from it.
You can hesitate, but as far as the math goes it works.LesRhorer said:First of all, I hesitate to speak of it as a collision. In ordinary usage, a collision tends to connote a very brief, perhaps virtually instantaneous interaction, not something that spans weeks, months, or even years.
This is not true. Please show your calculation for this specific claim so we can help you with the math.LesRhorer said:the fact is in the frame of reference of the barycenter of the two smaller bodies, the interaction is not elastic. Object V either picks up or drops a rather large amount of energy.
Obvious counterexamples are automobile collisions and billiard ball collisions. Friction, gravity, and the normal forces all act on automobiles and billiard balls before, during, and after their collisions.LesRhorer said:Obviously, in a mechanical collision there is not usually any transverse displacement (displacement perpendicular to the initial velocity vector) and there is never any force exerted on the components after the event is completed. Consequently, there is also no acceleration of any component once the event is complete.
Please see the above references. Particularly the last one where it explicitly acknowledges the three body problem while still treating the gravitational assist as an elastic collision.LesRhorer said:No matter how one slices, dices, smashes, or purees it, a gravitational assist (as opposed to a simple orbit) requires at a minimum three bodies
I did respond.jbriggs444 said:I note the lack of response to the request for a definition.
Untrue. Although I mentioned it previously, I will clarify again right now.The only reference from any knowledgeable sources I have ever seen is the method used by NASA for Voyager, Casini, etc. to increase the speed of a vehicle relative to some very massive body by the amount equal to the orbital speed of a body of intermediate size. This is often termed the "Slingshot Effect". The effect can be used not only to reduce the amount of fuel required to reach escape velocity (or slow down drastically without using any fuel). It can also be used to inflect the trajectory of a spacecraft away the original plane of the trajectory, as was done with Voyager I. I certainly thought all that was perfectly clear, but in light of your post I must suppose not.jbriggs444 said:I have seen multiple walls of text from @LesRhorer. But no definition is forthcoming.
I consider that to be a very serious accusation. I am compelled to demand you support it. Having done so, I will immediately amend whatever actions of mine in any way lack good faith. Failing that, you need to stop it.jbriggs444 said:I stand by the recommendation in #2. We ought not engage. This member is not participating in good faith.
Where the green line is to show the position of the bodies after the flyby. I feel like the kinetic energies of the bodies before (black line) and after (green line) should be exactly the same.
I suspect that this is key. Picking a reference frame. We can all agree that in the case of a two body situation viewed from the reference frame of the combined center of mass, both objects emerge with the same speed that they entered, albeit in new directions.Juanda said:The CoM of the two bodies won't move since there are no external forces involved. Let's use that as a reference frame then.
This is not correct. The aforementioned results can indeed result from a standard elastic collision with only two bodies in any frame of reference other than the center of mass frame. Only the center of mass frame has the symmetry you mentioned.LesRhorer said:no interaction between two bodies is ever capable of achieving the aforementioned results. All two body interactions result in perfectly symmetrical trajectories.
True. This would probably have to be some vehicle coming in from deep space. As you very clearly are aware, the required parameters for a gravity assist are rather narrow. Instituting an actual hyperbolic orbit around a neutron star from only a few million Km away would be tricky, indeed. From a few parsecs, not so much.Filip Larsen said:It doesn't really make sense to talk about using the Sun alone for gravity assist maneuvers relative to our galaxy if the probe starts out in a bound orbit around the Sun (which all human made probes do).
Yes, that is precisely my point, although I labeled the flown-by object as the Primary and the distant object as the third body. I realize this is not traditional,but it made it easier to transition from a two body system in free space to a similar system in orbit about the additional body, labeled by you (and most folks) the Primary. It of course makes no fundamental difference what we label them.Filip Larsen said:To be considered a gravity assist maneuver the probe would have to make a hyperbolic(1) close fly-by of some massive object that is not the primary relative to which you'd want to gain or loose orbital energy.
Precisely.Filip Larsen said:However, you are correct that the more dense the gravity assist mass is the closer the fly-by can be made and thus the greater angle the velocity vector can be turned. In the (unrealistic and degenerate) limit of a point-like mass the assist maneuver could turn the velocity vector almost 180 deg relative to the primary.
A salient point, upon which I touched earlier. Circular and even somewhat extreme elliptical orbits about the middle-sized objects are too near the planet to be affected by the distant giant in anything more than a modest perturbation of the orbit. The craft must come from and leave into regions where the giant body dominates. Only in that case will the usually rather modest centripetal force from the giant object make the sort of difference we see with Voyager, etc. My entire point is in order to see any such modification to what would otherwise be an actual hyperbola, it requires the presence of an additional body.Filip Larsen said:(1) "Hyperbolic fly-by" is a bit of a pleonasm, since a fly-by kind of imply being on a hyperbolic trajectory.
This is simply not true. You do not need an additional body to consider a hyperbolic trajectory from a different frame than the CoM frame.LesRhorer said:My entire point is in order to see any such modification to what would otherwise be an actual hyperbola, it requires the presence of an additional body.
What matters is the gradient of the bigger body gravity, not its magnitude. Even in regions where the Sun's gravity is far greater than planet's gravity, you can still use the planet's local free falling frame, if the variation of the Sun's gravity is sufficiently small in that region.LesRhorer said:The craft must come from and leave into regions where the giant body dominates. Only in that case will the usually rather modest centripetal force from the giant object make the sort of difference we see with Voyager, etc.
I also think you can achieve hyperbolic trajectories with only two bodies if the incoming speeds are high enough. However, before and after flyby conditions/states would be the same, right?Dale said:This is simply not true. You do not need an additional body to consider a hyperbolic trajectory from a different frame than the CoM frame.
Kinetic energy is not an invariant. It is relative to a reference frame. Many people use the term "really" to refer to invariants only.Juanda said:you would not be really stealing energy from one body to pass it to the other
Dale said:This is not correct. The aforementioned results can indeed result from a standard elastic collision with only two bodies in any frame of reference other than the center of mass frame. Only the center of mass frame has the symmetry you mentioned.
Not exactly true. As long as the CoM of the system is not accelerating, we can choose any FoR we like. If it is accelerating, however, it is not the case. A major point here, however, is that an accelerating CoM cannot ever happen with only two objects. One must absolutely infer a third body, and a barycenter for the larger system that is not at all coincident with the CoM of the two bodies. The inference is really quite straightforward, and absolutely concrete.Dale said:The laws of physics do not require us to use the CoM frame.
LesRhorer said:No, it can't.
jbriggs444 said:Kinetic energy is not an invariant. It is relative to a reference frame. Many people use the term "really" to refer to invariants only.
The same interaction can be described in frames where energy goes from one body to the other, from the other body to the one or is not transferred at all.
C´mon, don't be harsh. I actually think we are making progress.weirdoguy said:Yes it can, and this discussion is getting pointless. You are the one who is wrong and unwilling to admit it.
No. That's completely wrong. Energy is frame dependent. That's of fundamental importance.Juanda said:Total kinetic energy depends on the frame of reference. That's for sure. Work however remains constant. Or at least that's how I recall it from the last time I had to derive it for a similar conversation regarding elastic collisions.
If two bodies interact gravitationally with each other, the orbits will be either elliptical or hyperbolic depending of the initial velocities of the bodies. We previously agreed the reference frame at the CoM between the two seems to be very useful so I will keep using that one during the discussion.
View attachment 329334
Before (black line) and after (green) flyby the kinetic energies of the bodies are the same. Do we agree on this? If they are the same, no work has been transferred. No matter the reference frame chosen, that will remain true. Therefore, to "steal" energy from one body and give it to the other, having only 2 bodies interacting with each other is not enough for that to be a possibility.
The system doesn’t gain energy. The system doesn’t even gain kinetic energy. That is built into the elastic collision equations.LesRhorer said:No matter what, an interaction between two solid bodies can never result in the system gaining energy
Changing to a different frame of reference does change the kinetic energy.LesRhorer said:Changing to a different frame of reference never has any effect whatsoever to the internal energy of any system.
100% exactly true. This is the principle of relativity. Are you denying the principle of relativity? It is a bedrock of physics.LesRhorer said:Not exactly true.
In the frame of the probe the planet is indeed gaining and losing KE. KE is ##KE=\frac{1}{2}mv^2##. As ##v^2## changes so does KE.LesRhorer said:Measuring the velocity of the planet, the probe sees it alternately slowing momentarily to a dead stop and then speeding up to a peak of 20 Km/s. The measurements are perfectly correct, but it does not mean the planet is somehow loosing energy and then gaining it back. It is never gaining or losing energy at all.
No. You did not provide a reference for this false claim. Again, treating a gravitational assist as an elastic collision is well established in the professional scientific literature. This claim is closed unless you provide specific peer reviewed literature references to the contraryLesRhorer said:In a gravity assist, the two smaller bodies ARE ineslatic in the FoR of the planetary barycenter
The work done by one object on another is not invariant. It depends on the choice of reference frame.Juanda said:Total kinetic energy depends on the frame of reference. That's for sure. Work however remains constant. Or at least that's how I recall it from the last time I had to derive it for a similar conversation regarding elastic collisions.
The before and after kinetic energies of a given body are identical using the CoM frame. [Assuming some symmetry on where the two measurements are taken within the eccentric elliptical orbits shown in the illustration] Yes. we agree.Juanda said:If two bodies interact gravitationally with each other, the orbits will be either elliptical or hyperbolic depending of the initial velocities of the bodies. We previously agreed the reference frame at the CoM between the two seems to be very useful so I will keep using that one during the discussion.
View attachment 329334
Before (black line) and after (green) flyby the kinetic energies of the bodies are the same. Do we agree on this?
Yes, we agree.Juanda said:If they are the same, no work has been transferred.
No. That is not correct. The work done by one object on another is not an invariant.Juanda said:No matter the reference frame chosen, that will remain true.
Juanda said:Work however remains constant.
Just to put the record straight. The purpose of this forum is to promote mainstream science. Explicitly that means we must determine what is valid and what is bogus. It's not a debating chamber where every view has equal validity.Juanda said:C´mon, don't be harsh. I actually think we are making progress.
Again, I think it is more convenient to focus the conversation on WHAT's right instead of WHO's right.
It's a long thread already so I'll try an unofficial summary of it to help us get back on track. OP, correct me if this doesn't summarize the content discussed so far.
We're trying to figure out if it's possible to pass energy from one body to the other during a flyby. For example:
State 1: 5h before flyby.
State 2: Nearest point in the orbits.
State 3: 5h after flyby.
@LesRhorer claims that it is necessary to have a 3rd body if you want to have any energy transfer between the bodies. Otherwise, incoming and outgoing velocities will be the same. Velocities are dependent on the FoR chosen but the point is that there is no work or energy transfer between them which does not depend on the FoR. I do agree with this.
On the other hand, other people claim that no 3rd body is necessary to accomplish the extra kick.
Only one of those things (2 bodies NOT OK - 2 bodies OK) can be true so it's just a matter of time before we figure out which one it is.
I am no moderator or anything like that but I find the topic especially interesting and I wouldn't like the thread to derail into something nasty looking.
The classic example is an elastic collision between two balls of equal mass. In the rest frame of the first mass, the second mass loses all its KE. And vice versa. In COM frame, both balls rebound with equal and opposite velocities.Juanda said:So it seems Work / Energy transfer is also frame dependent. Let me check some calculations because, as you pointed out, my argument relied on that. If work is frame dependent, then I'm longer sure the 3rd body is necessary in order to be able to "steal" energy from one body and put it on the other.
I'll try solving an elastic collision on two different FoR (at whatever point and at the CoM) to better understand what's going on and that might give me some insight related to this orbital problem.
Good idea. These are related concepts:Juanda said:I'll try solving an elastic collision on two different FoR (at whatever point and at the CoM) to better understand what's going on and that might give me some insight related to this orbital problem.
Actually, for the slingshot effect, we stipulate it starts right at or rather near zero, an infinite distance away. Such an orbit is one right at escape velocity.Any faster and it is not quite a hyperbola, and the craft will never return. Any slower, and it isn't quite a hyperbola, either, but rather an extremely eccentric ellipse. It might take nearly an eternity, but barring any other influences it will eventually return. Such an orbit would be ideal for a slingshot maneuver, except of course the silly planet isn't staying still. It is whipping around the central star. What we need to do is at the point where the planet's gravitational field strength begins to exceed the star's, try as closely as possible to replicate one of the ideal orbits detailed above at that point. We also tray as best we can to select a perigee so that the magnitude of the incoming velocity is as close to the orbital speed of the planet. If we manage to get it just right, we can a much as double the speed of the spacecraft and send it in precisely the direction we want. To say it is a tricky maneuver is an incredible understatement.Juanda said:I also think you can achieve hyperbolic trajectories with only two bodies if the incoming speeds are high enough.
In the case of a two body system, yes absolutely. Adding a third sufficiently large body pretty much destroys the symmetry, to our great advantage.Juanda said:However, before and after flyby conditions/states would be the same, right?
There being no other force to change the motion of either body in the 2 body system, no.Juanda said:So, in that case, you would not be really stealing energy from one body to pass it to the other in the way it was done during the Voyager missions to increase the speed of the probes or other similar missions.
It seems so. It all hinges on the fact there is only one force in a two body system, and that force is perfectly symmetrical with respect to both bodies. Adding a third body introduces a second force which destroys the symmetry. If the two bodies remain close together - i.e. an elliptical orbit around each other - then the force from the third body will never exceed that of the force between the two smaller bodies, and so all it does is perturb their orbit somewhat, rather than produce the very large acceleration we see with a slingshot maneuver.Juanda said:Do you think the reasoning is correct?
Well, it is important. Fundamentally, in order to work as advertised, the spacecraft must be able to exceed escape velocity for the planet. The best way (the only way, really) to do that is for the spacecraft to approach the planet at something close to escape velocity - which to first approximation implies a hyperbolic trajectory.Juanda said:In post #48 I claimed a similar thing to what I'm posting here although I was missing the word "hyperbolic" at that time.
This is not correct. There is no requirement that the velocity be right at the escape velocity. In fact, it should be above it.LesRhorer said:Actually, for the slingshot effect, we stipulate it starts right at or rather near zero, an infinite distance away. Such an orbit is one right at escape velocity.
That is also false. A hyperbolic orbit is always faster than escape validity. I don’t know where you are getting all of this incorrect information.LesRhorer said:Any faster and it is not quite a hyperbola
Only in the CoM frame. A third body is not needed. By the principle of relativity we can use any inertial frame we like.LesRhorer said:In the case of a two body system, yes absolutely.
This is not needed.LesRhorer said:It all hinges on the fact there is only one force in a two body system, and that force is perfectly symmetrical with respect to both bodies. Adding a third body introduces a second force which destroys the symmetry.