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As a little project in a course of spacecraft design, I have to plan a mission to Saturn's moon Titan. The recommended trajectory is Hohmann transfer since it's easy to calculate the delta-V and launch windows. My problem is that after a fast calculation, my delta-v is more than 20 km/s just to get a transfer orbit around Saturn. Is it possible to assume that the delta V of departure is entirely given by the launcher wich will reduce it by about 10 km/s?

I inspired myself of documentation of the Cassini mission, and they choose not to use a Hohmann transfer. This decision was motivated by the fact that the most powerfull launcher at that time could not give enough delta V. It was missing about 2 km/s. Is it realist to plan this mission with Hohmann transfer considering newer launcher and lighter spacecraft (Cassini weighted 2,523kg) or is it necessary to use gravity assists?

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    $\begingroup$ For a direct Hohmann to Saturn, I think you'd need a launch vehicle that would provide you with delta-v in excess of 17 km/s for 5+ years long transfer. That's unrealistic to expect of today's launch vehicles without also doing deep space maneuvers and/or gravity assist flybys (at least DSM + Earth flyby, possibly also Jupiter flyby), and you'd still need at a minimum of 3 km/s for post orbit injection. Why can't you use trajectory tools such as, say, NASA's Trajectory Browser? I don't see what's the purpose of sticking with direct Hohmann transfer. $\endgroup$ – TildalWave Oct 23 '15 at 17:05
  • $\begingroup$ The direct Hohmann transfer is just what the professor's preferred method since we can easily build algorithms to compute values. After some readings, I'll forget this advice and go with gravity assists using trajectory tools like you advises me. Thanks for the link. $\endgroup$ – Tonio Oct 23 '15 at 17:35
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I'm quite confident that for the forseeable future, any mission to Saturn, or for that matter anywhere beyond Jupiter, will involve a flyby of Jupiter, because it gives such a tremendous gravity assist.

The best way to figure out a good gravity assist is playing with NASA's trajectory browser. It unfortunately doesn't allow for finding optimal solutions to Moons, but you can find one to Saturn. From there, you have to add the required delta v to do an orbiting mission, given that you are at C3.

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  • $\begingroup$ I played a little with the trajectory browser, but I am not sure to understand somethings. The tool calculates the trajectories from a 200km LEO orbit. Does that mean that I have to add the Delta-V to get in the parking orbit? If I'm right, that signify that from the best results of the Trajectory Browser (6.35km/s), I gain "only" 4 km/s. Is there a way to calculate a transfer with multiple gravity assists? $\endgroup$ – Tonio Oct 24 '15 at 9:20
  • $\begingroup$ Yes, that is correct. Multiple gravity assists are hard... $\endgroup$ – PearsonArtPhoto Oct 24 '15 at 9:22
  • $\begingroup$ "...at C3." -- Which C3? If C3 is negative, that'd be an elliptical orbit. If C3=0, that's a parabolic escape orbit. If C3 > 0, that's a hyperbolic orbit. en.wikipedia.org/wiki/Characteristic_energy. In the case of a helicentric orbit approaching Saturn, the C3 wrt Saturn would be positive (in other words, a hyperbola). $\endgroup$ – HopDavid Oct 25 '15 at 15:16
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It doesn't really make sense to say that "the delta V of departure is entirely given by the launcher which will reduce it by about 10 km/s". Just because a different stage is being used to accomplish the manoeuvre doesn't mean it reduces the delta-V. You will most likely launch to a parking orbit in LEO before inserting to a trans-Saturn orbit. Once you are in that parking orbit it makes no difference to consider the delta-V coming from an upper stage of the launch vehicle or coming from the spacecraft itself -- you are just distributing mass differently.

Of course overall you would want to use the launch vehicle to accomplish as much of the manoeuvre as possible so that you can ditch the empty mass to make future manoeuvres more efficient.

The question of how realistic a Hohmann transfer is for this scenario is really up to you. As mentioned in the comments, any mission to the outer planets is going to require gravity assists based on the current capabilities of human spacecraft. New improvements in rocket motors and propellants may make it possible to use a simpler approach in the future, but the more significant alternative is the use of ion thrusters (or perhaps solar sails) to achieve interplanetary transfer with a low, continuous thrust. Although using that approach completely changes how you look at the trajectory since we can't assume instantaneous velocity changes.

Since this is for a course project, I would suggest this strategy: use a Hohmann transfer anyway but acknowledge the limitations on delta-V and maybe even show sensitivity studies on how the maximum spacecraft mass changes based on different launchers (or maybe just vary the Isp for your propellant), as well as how the required delta-V (and/or Isp) changes based on a given spacecraft mass. Otherwise planning a completely realistic mission to Titan is impossible without gravity assists or a significantly smaller spacecraft.

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