Discussion in 'Physics & Math' started by Saint, Aug 7, 2017.
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This is the scenario we have been discussing:
These statements are incorrect.
1] Since the body entered the well from outside, it already has all the energy it needs to exit the well.
2] And gets no more. (because if were to gain energy, it would leave faster than it came in, wrt the central body).
The gravitational-potential energy is converted to kinetic energy on the in-fall, and then converted back to g-potential energy again on the outfall, with no gain or loss in energy.
3] Thus, the object does not "gain sufficient speed to escape". It already had it. It was never in danger of not escaping.
4] Finally, the angle doesn't matter. As long as it does not actually intersect the central mass, it will follow the hyperbolic trajectory , regardless of angle of entry.
Pt#1 may not be correct in general.
There is something called frame dragging, however small, which will make it more interesting for you.
point #1 is correct, unless someone adds a third body into the scenario, which is what we've been saying all along.
The sun alone is unable to capture fly-by objects. That's the job of our planets and their little cohorts.
(It also happens to be why our returning spacecraft cannot go from a trans-lunar trajectory to an Earth orbit without a decel burn. Without the burn, the craft will simply loop around and climb back out of Earth's well.)
Indeed. Frame-dragging might make an interesting addition to the topic.
Why Sun alone cannot capture flyby? You seem to have a very myopic idea on this topic.
Good point: would be it be better, then, to describe it then as a 2 bodies plus a 3rd frame of reference, i.e. producing a gain in velocity in a desired direction, as measured with respect to a 3rd frame of frame of reference?
Find a reputable reference that demonstrates capture (or escape) in a 2 body scenario.
Heck, start with simply describing how you think it could happen?
You're the one who doesn't know why you can't have a capture in a 2-body scenario.
When you have that answered, then we'll start throwing epithets around.
That's why I said myopic, there is no two body motion around in true sense. Sun need not capture anything from solar system, they are all around Sun only with 99% mass with sun. Capturing is not like plucking moon from earth, capturing is like getting into orbital motion with other objects or at the best attracting for collission non solar system object and still remaining otherwise intact.
Now let us start with your pt#1
1]Since the body entered the well from outside, italready has all the energy it needs to exit the well.
How a body entering earths Gravitational well will already have all the energy to exit the well??
This is not true always.
That's why I pointed out that it may not be correct always, but you are hell bent and asserting it again and again without any qualifier.
And then #4 of yours...
Angle does not matter...why?
Depending on the initial speeds etc with respect to central body angle will matter, the angle is very crucial in determining whether it will pass without striking the central mass or not.
See, 2 body solution itself is pretty complex in GR. You know to calculate the precession of mercury we end up considering the same as point mass around static sun.
The discussion I have been involved in has nothing to do with general relativity. It's just Newtonian orbital mechanics.
Since the body enters the the Earth's gravitational well; it must have a relative velocity. If it does not hit the Earth then the body will exit earths gravity well at the same speed it entered.
That is why exchemist said the angle does not matter as long as the object does not hit the central mass.
And for that angle matters. What you are trying is holding your ear from other side.
For an object not to hit the central mass, both the incidence angle and speed are important and matters. If the object has exited (of course without gain of momentum) that means...
1. It entered with a speed sufficient to escape it from the well.
2. It entered at an angle so that the trajectory inside was such that it exited without striking.
Can't you see both angle and speed are important.
Note : Exchemist is posting thoughtfully safe, it's you and DaveC who are getting over enthusiastic in explaining gravity assist to W4U.
Consider the central mass as a sphere of radius R, say the incidence of other body is at height H from the center of this sphere. So if the vertical angle of incidence (velocity vector direction) is less that Arctan(R/H), it will strike irrespective of its speed. For higher angles we will have to consider the Gravitational deflection to see if it flys away without strike.
Perfect. So you acknowledge that, in order to capture a body, more than 2 bodies must be involved.
The explanation is: that is how conservation of energy works.
Remainder is inflammatory rhetoric.
The "angle does not matter" has been, from the start, explicitly qualified several times as "as long as it doesn't actually hit the central mass".
Note that the sun - from near the edge of our Solar system - is a target about one arc minute wide. That's about one part in 11,000 of an arc wherein it is approaching the sun. So, what you are asserting is that, when W4U said "at a certain angle", he meant, give or take, 10,999 parts out of 11,000.
Go back and read post 47, to see the context of what we are discussing.
Context cannot make your statement incorrect, the context could be conditional.
when a body enters from the edge of our solar system, ignoring all other objects except sun, following can happen..
1. It will enter into orbital path with Sun.
2. It will strike the sun.
3. It will exit SS from some other point after following a particular trajectory.
4. It may get destroyed (we can skip this)
For Sr#1 to #3, initial velocity vector (speed and angle) matters. You can take shelter in any context, but that's simple physics.
Any wandering object may come so close to sun that it may get captured, where is the need for third body?
I am afraid you are quite incorrect.
If it were not already in a long-period orbit around the sun, it will not spontaneously be modified to an ellipse.
You have yet to demonstrate otherwise.
It has been stated explicitly every time that impacting the central mass is the exception. Repeating is as if it were otherwise is argumentative.
It is, however, not what "a certain angle" means.
There is a 1.5" target a mile away that I am to fire at. I wish to miss it.
Note that, of 11,000 angles, 10,999 of them will miss.
So, I ask (rhetorically), what is this "certain angle" I would have to aim at, in order to miss the target?
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