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| Deletions are marked like this. | Additions are marked like this. |
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| $ \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 | $ \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 |
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| $ \Delta v_{launch} = \sqrt{ \Delta {v_p}^2 + {v_{esc} }^2 } $ J: 14.2 S: 15.21 km/s | $ \Delta v_{launch} = \sqrt{ \Delta {v_p}^2 + {v_{esc} }^2 }~~~$ J: 14.2 , S: 15.21 km/s |
| Line 20: | Line 20: |
| Years $ \large = \sqrt{ ( 1 + AU )^3 / 32 } $ J: 2.73 S: 5.21 years | Years $ \large = \sqrt{ ( 1 + AU )^3 / 32 }~~~$ J: 2.73 , S: 5.21 years |
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| $ \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 \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 |
| Line 26: | Line 26: |
| $ \large v_{periapse.planet} = \sqrt{ \Delta {v_a}^2 + {v_{esc} }^2 } $ J: 59.77 S: 35.90 km/s | $ \large v_{periapse.planet} = \sqrt{ \Delta {v_a}^2 + {v_{esc} }^2 }~~~$ J: 59.77 , S: 35.90 km/s |
| Line 28: | Line 28: |
| Moon transfer distance ratio $ b = r_{moon} / r_{planet} $ J: 9.3859 S: 6.2138 | Moon transfer distance ratio $ b = r_{moon} / r_{planet}~~~$ J: 9.3859 , S: 6.2138 |
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| 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 | 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 |
| Line 32: | Line 32: |
| Gee force $ \large = v_{periapse.planet}^2 / ( 9.8 * r_{planet} ) $ J: 5.1 S: 2.2 gees | 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. |
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| Perigee deceleration DV $ \large = v_{periapse.planet} - v_{mp} $ J: 2.2 S: 1.3 km/s | Perigee deceleration DV $ \large = v_{periapse.planet} - v_{mp}~~~$ J: 2.2 , S: 1.3 km/s |
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| 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 | 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 |
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| Landing velocity $ \large = \sqrt{ \Delta {v_{ma}}^2 + {v_{me} }^2 } $ J: 2.423 S: 3.731 km/s | Landing velocity $ \large = \sqrt{ \Delta {v_{ma}}^2 + {v_{me} }^2 }~~~$ J: 2.423 , S: 3.731 km/s ---- The motivation for this page was a claim that an aerobraking at Saturn landing on Titan (see the alleged non-fiction book BeyondEarth) was possible because in the novel '''2010''' by A.C. Clarke, an aerobraking 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. |
Aerobraking to Jupiter/Europa and Saturn/Titan
This is only approximate, it assumes circular planet/moon orbits with zero inclination
|
Dist |
Vcirc |
Mass |
Vesc |
Radius |
Moon |
Dist |
Vorb |
Vmesc |
|
Launch |
Tranf. |
paps |
radial |
DV |
Land |
|
AU |
km/s |
|
km/s |
Mm |
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 |
Luna |
384 |
1.02 |
2.38 |
|
||||||
Jupiter |
5.20 |
13.07 |
317.8 |
59.5 |
71.49 |
Europa |
671 |
13.74 |
2.03 |
|
14.2 |
2.73 |
59.8 |
5.1 |
3.2 |
2.4 |
Saturn |
9.55 |
9.69 |
95.2 |
35.5 |
60.27 |
Titan |
1221 |
5.57 |
2.64 |
|
15.2 |
6.01 |
35.9 |
2.2 |
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 / ( 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
The motivation for this page was a claim that an aerobraking at Saturn landing on Titan (see the alleged non-fiction book BeyondEarth) was possible because in the novel 2010 by A.C. Clarke, an aerobraking 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.