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The Voyagers made a grand tour using the gravity assist of each planet. But Jupiter, with a 12 year orbital period, doesn't always line up to be useful for spacecrafts destined to further planets. Venus is much quicker on its feet, but light.

What have been the altitudes of spacecrafts' perijove and perikrition (a look up word for periapsis at Venus) to date? What kind of delta-V change could one achieve by passing by Venus as close as possible, on the way to say Saturn or Uranus? Could aerobraking at Venus be helpful in optimizing the velocity vector?

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    $\begingroup$ While making these 'as low as safely possible' would yield the strongest gravity assist, it would also thoroughly randomize the ejection angle. The actual altitude choice prioritizes ejecting the probe in the desired direction over maximizing delta-V gains. $\endgroup$
    – SF.
    Nov 29, 2018 at 9:30
  • $\begingroup$ aerobraking is unlikely to help much with an outer planets mission, since it dissipates energy and you are going to need that energy to get out of the Suns gravity well. Could be useful for a Mercury or close solar mission though. $\endgroup$
    – Steve Linton
    Nov 29, 2018 at 12:39
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    $\begingroup$ @SF. I don't understand why a close flyby would fling of a probe randomly. The location of Saturn is said to be determined within one kilometer now. Fantastically. And the distance to a spacecraft within a radio wavelength or so. My impression is that this needle's can be thread. $\endgroup$
    – LocalFluff
    Nov 29, 2018 at 21:42
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    $\begingroup$ @LocalFluff: The periapsis altitude causes change in ejection angle. Yes, you can foresee exactly where the lowest possible periapsis will eject you. The problem is your calculation will most likely result in "in a completely useless direction." $\endgroup$
    – SF.
    Nov 29, 2018 at 22:19
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    $\begingroup$ If you choose a very low periapsis, you get the most acceleration from the planet, but simultaneously your trajectory is curved the most. And you don't want your trajectory to be curved "the most", you want it curved "just the right amount". $\endgroup$
    – SF.
    Dec 1, 2018 at 19:39

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What have been the altitudes of spacecrafts' perijove and perikrition (a look up word for periapsis at Venus) to date?

HORIZONS & Wikipedia (Jupiter & Venus & Hyperbolic orbital mechanics) have most of the information needed to answer the first question. It's pretty straightforward for Jupiter:

Mission: $r_p$ (km, from center of body): $\Delta V$ (km/s):
Pioneer 10 203,300 15.3
Pioneer 11 113,600 16.7
Voyager 2 722,900 11.5
Voyager 1 348,500 16.3
Ulysses 450,500 16.4
Cassini-Huygens 9,794,500 2.2
New Horizons 2,304,500 5.1

Where

$$\Delta V = \frac{2 \cdot v_{\infty}}{1 + \frac{r_p \cdot v_{\infty}^2}{\mu}}$$

(Source)

Venus is a solar system oddity; it's hosted more missions than any other planet, yet most of these came some 50 years ago and/or from the Soviet Union so their archiving leaves a lot to be desired. Consider that NAIF only has trajectory data for Mariner 2 (and not later Mariners at Venus).

Luckily "close approach distance" is a commonly touted parameter (even if of dubious origin). Additionally, knowing mission dates (thus knowing planetary locations) we can determine the Venusian flyby energy, $v_{\infty}$, and thus find the $\Delta V$. Instances where this was done are denoted in the fourth column (indirect):

Mission: $r_p$ (km, from center of body): $\Delta V$ (km/s): Calculation:
Mariner 2 41,000 2.3 direct
Mariner 5 10,000 4.8 indirect
Mariner 10 11,800 4.7 indirect
Venera 11 40,000 2.5 indirect
Venera 12 40,000 2.5 indirect
Venera 13 36,000 2.7 indirect
Venera 14 26,000 3.5 indirect
Vega 1 39,000 2.8 indirect
Vega 2 24,500 3.6 indirect
Galileo 22,200 3.4 direct
Cassini Huygens, x2 6340, 6650 7.1, 6.7 direct
MESSENGER, x2 9040, 6390 5.5, 6.9 direct
Parker Solar Probe, x7! 8480, 9060, 6890, 8440, 9860, 10100, 6440 3.1, 2.9, 3.8, 3.1, 2.7, 2.7, 4.0 direct
BepiColombo, x2 16770, 6600 3.7, 7.0 direct
Solar Orbiter, x8!! 13500, 14050, 12650, 6550, 6830, 6400, 6400, 8710 3.5, 3.4, 2.6, 4.7, 4.5, 4.8, 4.8, 3.6 direct

For reference the radius of Jupiter and Venus are ~70,000 km & ~6050 km, respectively.

What kind of delta-V change could one achieve by passing by Venus as close as possible

This answer from Mark Alder explains the shape of the curve well, there is an optimal $v_{\infty}$ value for maximum $\Delta V$ equal to the orbital velocity at the periapsis height ($\sqrt{\frac{\mu}{r_p}}$). This is also equal to the maximum $\Delta V$ gained in the flyby. For Venus at a height of 250km the maximum $\Delta V$ is 7.18 km/s.

Could aerobraking at Venus be helpful in optimizing the velocity vector?

In theory it could be helpful. It's noted in this answer that Cassini-Huygens's inner solar system deep space maneuver "reduced its heliocentric energy" so the idea of losing energy is not outright bad. However, this adds enormous complexity to a mission and it is not a mission enabling architecture (the same end results can be accomplished by other means).

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