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4

Just a short supplementary to try and add a more "intuitive" understanding to the two excellent "equation-based" answers. For me the easiest way to think of this is that you have cause and effect reversed in your description of the problem. Consider PSP at aphelion, which is always more or less at Venus distance from the Sun, so that it ...

2

Another way to express the results of the vis-viva equation at apoapsis is $${v_a}^2 = \frac{2\mu}{r_p+r_a}\frac{r_p}{r_a} = \frac{2\mu}{r_a}\frac{r_p}{r_p+r_a}\tag{1}$$ where $v_a$ is the velocity at apoapsis, $\mu$ is the standard gravitational parameter $\mu\equiv GM$, and $r_a$ and $r_p$ are the apoapsis and periapsis distances. On holding the apoapsis ...

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When thinking about the speeds and distances in a Keplerian orbit we turn to our friend the vis-viva equation: $$v^2 = GM \left( \frac{2}{r} - \frac{1}{a} \right)$$ where $v$ is the speed at distance $r$ for an object with a semi-major axis $a$ and $GM$ is the gravitational constant $G$ times the Sun's mass M. We can call that product the standard ...

1

When the bat strikes the ball, the ball will gain velocity equal to twice the bat's velocity times the cosine of strike angle. The gain is independent of the ball's initial velocity. It's only the velocity of the bat and deflection angle that matter. The same physics applies to gravity assists. However, a faster spacecraft must fly closer to the planet to ...

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