# Help choosing a gravity assist scenario for this problem

The problem stated below is from an assignment I was given. My initial approach involved doing a direct Hohmann Transfer to Saturn. This approach violated the fuel constraints and hence was deemed unfit for a solution.

So, then I considered using a Gravity assist. To start with, I considered Venus. Using NASA Trajectory Browser, I got the launch window in March 12, 2020 and arrival to venus by July 2, 2020 which is 112 day transfer. On analyzing, I found out that the flyby around Venus will be a leading flyby and I wanted a trailing flyby.

I am kind of confused as to what to do now as I need to submit the assignment to my prof by 5th December.

A crew of one former pilot, three scientists, and two robots are launched inside a multi-purpose crew vehicle (MPCV) into a circular orbit of radius 8×104 km about Earth, with 20◦ inclination with respect to Earth’s equatorial plane and 0◦ right ascension of the ascending node. At 00:00 UT on January 1st, 2020 (taken as the mission start time, t0), the MPCV has an anomaly of 30◦ (from the ascending node) and is lagging behind Spaceship Endurance by 90◦, which is also on the same circular orbit.

The crew’s mission is to rendezvous with and enter Endurance, and then travel to an orbit of radius 105 km about Saturn with 0◦ inclination with respect to the plane on which Saturn’s orbit about the Sun lies.

However, time is of the essence, because the ultimate goal of the mission is to enter a wormhole that has been discovered close to Saturn’s orbit, but in order to ensure the wormhole will be there upon arrival, the crew should be in its target Cronian (Saturnian) orbit preferably within 8 years from t0. In addition, as a result of rapid reduction of natural or industrial resources due to crop blight on Earth, the mission cannot exceed a total budget of ∆vtot = 15 km/s. Design the mission architecture.

• @uhoh Any insights into this? Dec 26, 2018 at 2:52
• well, I think your assignment is a bit late now ;-) I am not a "mission planner" but some people here are. Maybe I can help attract some interest with a bounty.
– uhoh
Dec 26, 2018 at 2:53
• The obvious gravity assist for Saturn mission is Jupiter. Is there a reason not to do that? Dec 26, 2018 at 23:38
• I think Hohmann+aerocapture into retrograde orbit would be the optimal approach and the inclination 180 instead of 0 would result in the same orbital plane... and it's not like you perform a rendez-vous with a wormhole, you just dive into it!
– SF.
Dec 27, 2018 at 3:07
• @SteveLinton Jupiter is always the best option! But, I don't think only Jupiter flyby will accomplish the mission. More gravity assists options might have to be considered. Dec 27, 2018 at 4:47

I plugged in the numbers you provided to NASA's Trajectory Browser. They recommend a Feb-22-2019 date, with a Mar-18-2022 arrival date, and a flyby of Jupiter on Jun-16-2020. Total delta-v usage of less then 10 km/s. The scenario can be found at this link.

There are no doubt options that could improve the scenario further, including things like a flyby of Titan to get in to the right orbit, flying by Venus, etc, but it seems like this will get you to where you want to go, with 5 km/s of spare delta-v.

EDIT: Given the launch window opening in 2020, the best opportunity then becomes a launch on March 28, 2020. There are a number of possibilities that range from an EJS approach of anywhere between 4.6-7.5 years, with 7.3- 8.5 km/s of delta-v used. I think I personally would shoot for this one, with 4.6 years and 8.3 km/s of fuel use.

• Oh that is sooo cool!
– uhoh
Jan 2, 2019 at 11:27
• NASA's Trajectory Browser is pretty neat indeed! Jan 2, 2019 at 12:38
• @PearsonArtPhoto But as per the problem, the spacecraft is launched into Earth orbit only in 2020 January. Jan 3, 2019 at 20:22
• Missed that... Sigh. Then the proposal is to launch directly to Saturn, will update. Jan 4, 2019 at 1:58
• I did that. An interplanetary Hohmann transfer to Saturn using Patch Conics violates the fuel constraint. Total fuel required would be around 17.72 km/s Jan 6, 2019 at 3:36