On what does gravity assist depend? (possibly with sources)

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Gravity assist relies on several factors beyond just velocity change, including the angle of approach and the mass ratio between the spacecraft and the planet. The trajectory must be carefully planned, as passing behind the planet increases velocity in the planet's direction, while passing in front decreases it. Understanding hyperbolic orbits is crucial, as they dictate how both the probe and planet interact during the maneuver. The discussion emphasizes the need for a balanced explanation that caters to the audience's educational level. Comprehensive sources that bridge the gap between oversimplification and complex physics are essential for a successful presentation.
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Hey guys, I am preparing for a presentation about gravity assist and I cant find much information about this topic. Ive gone already through wikipedia but wikipedia only talks about the velocity change. What are other factors which could have affects on the gravity assist?

Like I assume the velocity of the probe is important and perhaps even the angle of attack. But I couldnt explain why.

Hope you can help me out! I've searching for valuable sources for the past 6h but couldnt find something between oversimplified and raw physics degree. :(
 
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It is just a velocity change, though, isn't it? Looking at the planet and the probe, they just loop round each other in a hyperbolic orbit, and they both change speed and direction (the probe more than the planet, due to the mass ratio). You just set up the approach to the planet so the exit speed of the probe is faster with respect to the Sun (or slower, whichever you were going for).

What education level are you supposed to be presenting at?
 
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If you read this Wikipedia article, what, specifically, are you asking for?
 
A key aspect to explain is why you need to pass behind the planet to gain velocity in the planet's direction but in front of it to gain velocity the other way.
Can you find an argument for that?
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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