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Size: 2050
Comment:
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Size: 2068
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 14: | Line 14: |
| $ \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 |
| Line 16: | Line 16: |
| $ \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 |
| Line 24: | Line 24: |
| $ \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 |
| Line 30: | Line 30: |
| 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 |
| Line 34: | Line 34: |
| 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 |
| Line 38: | Line 38: |
| 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 |
| Line 40: | Line 40: |
| 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 |
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
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