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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7494244" data-attributes="member: 16814">That was the same force presented in different ways, not added together.  No double counting involved.The point of the car example was to explore the question of 'does a frame change from solar to Earth change the direction of a push on the asteroid.'  The crosswind in the example is supposed to be the push on the asteroid.  But, since there's now an added mass of static air that resists the motion of the car, and when the frame change to to car is made this force is remained to a 'headwind', the failure of conception is that this is an actual wind like the crosswind instead of an artifact of the frame change renaming forces.  As you point out, you can sum the forces, as they are vectors, and with the confusion on -wind add the 'head'wind to the 'cross'wind to get something you've called the wind, but the actual components of these forces haven't changed.  The 'crosswind' still only pushes the car laterally, even with the frame change (as you note above).  When you switch over to a scenario that lacks the confusion of the static air in the scenario, it should become entirely apparent that my point about forces not changing direction due to a frame change is completely correct.  The 'crosswind' only ever adds lateral movement in the same direction and same magnitude regardless of the frame.  You adding the renamed air resistance as a 'headwind' notwithstanding.Well, it ignores the 90 to 180 side of things as well (ie, it breaks on that side).  I still disagree that your formula works at all, narrowed coordinate regime or no.Yup, bonehead math fail, again.  Going too fast and not paying attention to the setup because I'm working on the rest.  Doesn't change my points, though.Again, not my problem that you have confusion on this because you didn't read the whole thread.  Dunno what to so, man.Turns out we're both not fully right.  It appears there's multiple solutions to the formula -- I found one between 6.2 and 6.3 and another definite at almost 88 degrees and a number of (around 8 or so) where it may solve.  I'm using numerical substitution in excel rather than expensive plotting software, so...81.6 - 81.775.3-75.4 and 75.5-75.6and so one.  A number of points of crossing.I guess it goes to show you shouldn't eyeball trig.  Good point looking at the slope -- nice catch.I'm not sure what this says about either of our assertions.  The generated angle from sin(x)=dp(lat)/p still doesn't work, but it appears a number of other possible angles will with that dp(lat) value.  In thinking about it, there's a definite minimum miss angle along which the asteroid will miss the disc regardless, but that describes a infinite set of possible triangles comprised of the modified parallel and lateral vectors.  I'm back to my (unspoken) thinking that the optimization problem is a differential equation and can't be solved via trig.Don't have time right now, so I will see if I can check these later (though now I'm getting enough "homework" on this that it may have to wait until the weekend or even Monday).While I won't claim to be infallible, I'm pretty confident that, if you get a miss at x=0, you can get a miss at some other small angle x with the same dp.  And I don't care about whether it's a head-on collision or not.  All we need to know is the require angle of deflection to know if we hit the earth or not.But, where is the force applied?  It's not from the WNW, but from due west.  That's the point -- the force applied doesn't change direction.  The approach of the force, whatever it may be, may appear to change direction, but the force does not.  The laser pushes the car eastward irrespective of the framing.</blockquote>

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