When using gravity assist from a planet to change a spacecraft's orbit, it is not possible to put the spacecraft into any desired final orbit.
The spacecraft interacts with Jupiter in a manner similar to a small projectile hitting a larger one. The interaction is governed by the conservation of angular momentum and energy and as a result only certain paths are possible. Do the orbits the spacecraft in this example satisfy those restrictions?
As the spacecraft is lifted into a larger orbit, it gains energy and momentum. Those gains should equal to the loses of energy and momentum by Jupiter. Is that in the example here?
|Eccentricity||Energy per mass|
(km/s)2 = MJ/kg
|Angular Momentum per mass|
|Spacecraft Orbit to Jupiter||3.50||0.67||-126.7||8.727|
|Spacecraft Orbit past Jupiter||11.16||0.714||-39.8||14.274|
If we calculate the value of Tisserand's Parameter for the orbits before and after the spacecraft's closest approach to Jupiter we can determine if our example satisfies Tisserand's Criteria.
We see that our example does satisfy the criteria within the accuracy of our calculations. In the example here, we arbitrarily selected a path of closest approach and took whatever resulting solar orbit it produced, since I was only wanted to show the principles of gravity assist. Tisserand's criteria is more useful than testing example orbits; it can be used to predict what approach to the planet is needed to get into a desired final orbit.
For more on the Tisserand Criteria see the Calculation of the Gravity Assist to Neptune