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I have to complete a project for a university exam. The task is to design an interplanetary trajectory from Earth to Saturn, and to compare it with a Hohmann transfer to the same planet. I also have some specifications for the trajectory, including two planetary fly-bys.
I'm using a Matlab code to do the maths and get my trajectory, it follows the patched-conics method and the rules of the keplerian motion. By setting two swingbys, I got the following result:

Trajectory

I did not understand the topic very well, so I don't understand what do I have to compare it with. Isn't this trajectory (the one showed the picture) already a Hohmann transfer? Should I try another kind of transfer orbit? What's the most frequent transfer orbit in orbital mechanics?

Edit: the whole text is here.

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  • $\begingroup$ Maybe they just mean compare to a simple Hohmann-like transfer from Earth's orbit to Jupiter's orbit without any fly-bys? $\endgroup$
    – uhoh
    Oct 10, 2018 at 19:17
  • $\begingroup$ I don't think so, they ask to compare the two trajectories before talking about the fly-bys, and it's said that the Hohmann transfer has to achieve the same objectives of the first one (?). $\endgroup$
    – Silmaar
    Oct 10, 2018 at 19:30
  • $\begingroup$ okay then I'd recommend you find some way to show what they say here, so that it's easer to help. If the project description is online, then edit again and add the link to the question. Or copy/paste the relevant text in the question, or add a screen shot or even a photo of a printout. It's possible that there's something there that is a really helpful clue that someone else will be able to notice. $\endgroup$
    – uhoh
    Oct 10, 2018 at 20:05
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    $\begingroup$ Here's the full excerpt from my textbook I'm reading, this likely isn't allowed but fudge it, it's only two pages. $\endgroup$
    – Magic Octopus Urn
    Oct 10, 2018 at 22:20
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    $\begingroup$ If the image is from above the North Pole of the sun, and the spacecraft is going from Earth to Saturn, your solar trajectory is retrogade, and thus, quite a bit more expensive than a standard Hohmann, which would be prograde. $\endgroup$
    – notovny
    Oct 11, 2018 at 19:50

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Partial transcription of this screen shot

The objective is to design an interplanetary trajectory from Earth to Saturn, and to compare it with a Hohmann transfer to the same planet. The trajectory should be designed with the patched conics method and Keplerian motion, assuming all plnets on coplanar orbits about the Sun.

The trajectory should be composed by:

  1. …
  2. Departing date: November 1997
  3. …
  4. …
  5. …
  6. …
  7. …
  8. Computation of a direct Hohmann transfer to achieve the same objectives.
  9. Comparison of the two designs with respect to total delta-v and time of flight.

I see

  • design an interplanetary trajectory
  • compare it with a Hohmann transfer

then

  • The trajectory should be designed with & composed by...
  • Comput(e) a direct Hohmann transfer to achieve the same objectives.

finally

  • Comparison of the two designs with respect to total delta-v and time of flight.

So like I mentioned in this comment:

Maybe they just mean compare to a simple Hohmann-like transfer from Earth's orbit to Jupiter's orbit without any fly-bys?

In the particular context of the project statement, there's an interplanetary trajectory, which you design, and there's a Hohmann transfer which is defined and so you don't design it.

To your question:

Should I try another kind of transfer orbit?

I don't think so. I think it means compare your existing design to a single Hohmann transfer between and Earth-like orbit and a Jupiter-like orbit. It says coplanar, and the true orbits of Jupiter and Earth are not perfectly coplanar, (they're not perfect circles either) so I think you can make some tiny approximations, but you'll see that the differences in delta-v and in time are quite large.

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