Aerocapture to Jupiter/Europa or Saturn/Titan
From a Hohmann transfer orbit from Earth
Aerocapture is theoretical, and has not yet been used on a planetary mission, though it was proposed for the Saturn Explorer Mission.
A vehicle arriving at Jupiter or Saturn in a Hohmann from Earth will be travelling faster than escape velocity. If it plunges deeply into the gravity well of the planet to slow down in its atmosphere, it will move faster than planetary escape velocity, and the aerocapture time will be brief. Extending that time requires negative lift to stay within the narrow band of atmosphere with sufficient drag to slow down, and the negative lift requires a high lifttodrag ratio and imposes high radial acceleration gee forces to remain at approximately the right altitude.
Galileo and Juno used rocket thrust to enter Jupiter orbit, not aerocapture. Cassini also used rocket thrust to enter Saturn orbit, though it got a slingshot boost from Jupiter on the way to Saturn, reducing the delta V to 620 m/s. Total time from Earth (including two gravity assists from Venus then another from Earth) to Jupiter, about 6.8 years.
This is only approximate, it assumes circular planet/moon orbits with zero inclination. A better analysis would compute the actual trajectory of entry with a realistic lift and deceleration plan.

Dist 
Vcirc 
Mass 
Vesc 
Radius 
g 

Moon 
Dist 
Vorb 
Vmesc 

Launch 
Tranf. 
paps 
radial 
DV 
Land 

AU 
km/s 

km/s 
Mm 
m/s² 

Dest. 
Mm 
km/s 
km/s 

km/s 
years 
km/s 
gees 
km/s 
km/s 
Earth 
1.00 
29.78 
1.0 
11.2 
6.38 
9.8 

Luna 
384 
1.02 
2.38 


Jupiter 
5.20 
13.07 
317.8 
59.5 
71.49 
24.8 

Europa 
671 
13.74 
2.03 

14.2 
2.73 
59.8 
2.6 
3.2 
2.4 
Saturn 
9.55 
9.69 
95.2 
35.5 
60.27 
10.4 

Titan 
1221 
5.57 
2.64 

15.2 
6.01 
35.9 
1.1 
1.3 
3.7 
Launch Velocity
\large \Delta v_p = v_{ce} { \Large \left( \sqrt{ { 2 r_a } \over { r_e + r_a } } 1 \right)}~~~ J: 8.7896 , S: 10.2896 km/s
\Delta v_{launch} = \sqrt{ \Delta {v_p}^2 + {v_{esc} }^2 }~~~ J: 14.2 , S: 15.21 km/s
Transfer time ( Earth Years)
Years \large = \sqrt{ ( 1 + AU )^3 / 32 }~~~ J: 2.73 , S: 5.21 years
Apogee Delta V, Delta V to moon transfer
\large \Delta v_a = v_{cp}{ \Large \left( 1  \sqrt{ { 2 r_e } \over { r_e + r_a } } \right) }~~~ J: 5.6467 , S: 5.471 km/s
\large v_{periapse.planet} = \sqrt{ \Delta {v_a}^2 + {v_{esc} }^2 }~~~ J: 59.77 , S: 35.90 km/s
Moon transfer distance ratio b = r_{moon} / r_{planet}~~~ J: 9.3859 , S: 6.2138
Moon transfer periapse velocity \large v_{mp} = v_{m} { \Large \sqrt{ { 2 b^2 } \over { 1 + b }}}~~~ J: 56.592 , S: 34.611 km/s
Gee force \large = ( v_{periapse.planet}^2 / r_{planet}  g ) / GEE ~~~ J: 5.1 , S: 2.2 gees
this is very approximate; on the one hand, the trajectory through the planetary atmosphere will curve less, but there will be more gee force from the deceleration itself.
Perigee deceleration DV \large = v_{periapse.planet}  v_{mp}~~~ J: 2.2 , S: 1.3 km/s
Moon Landing delta V
Moon transfer apoapse velocity \large v_{ma} = v_{m} \left( 1 \Large \sqrt{ 2 \over { 1 + b } } \right)~~~ J: 1.323 , S: 2.637 km/s
Landing velocity \large = \sqrt{ \Delta {v_{ma}}^2 + {v_{me} }^2 }~~~ J: 2.423 , S: 3.731 km/s
Estimating Aerocapture Time
Without inward radial acceleration from negative lift, the "deceleration zone" is about half the scale height, and the time to dip into and out of this zone is approximately t \approx 2 \sqrt{ scale / g } , or 66 seconds for Jupiter and 152 seconds for Saturn. The peak deceleration gee forces without lift would be approximately (WAG) $ g_{dec} \approx DV \sqrt{ g / scale } or 10 gees for Jupiter and 1.8 gees for Saturn. Extending the deceleration time would lower the deceleration gee forces but add radial acceleration. Much depends on the achievable lifttodrag; that was 0.4 for Apollo, I've seen claims of 1.0 for the SpaceX Dragon but I don't know how that is limited by velocity and heat transfer.
The motivation for this page was a claim that an aerocapture at Saturn landing on Titan (see the alleged nonfiction book BeyondEarth) was possible because in the novel 2010 by A.C. Clarke, an aerocapture at Jupiter to a landing on Europa was possible. Well ... Saturn/Titan is sorta/kinda easier in some ways, but 2010 does not mention the high radial gees necessary to stay in the very narrow radial deceleration altitude band at Jupiter. The band is about half the atmospheric scale height, which is 27 km for Jupiter and 60 km for Saturn.