Aerocapture to Jupiter/Europa and Saturn/Titan

This is only approximate, it assumes circular planet/moon orbits with zero inclination.

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 / ( 9.8 * r_{planet})~~~ 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, the optimum total acceleration is probably (WAG) somewhat lower than the radial circular force.

The motivation for this page was a claim that an aerocapture at Saturn landing on Titan (see the alleged non-fiction 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.