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After you've gotten reasonably adept with the lander (able to hover at altitude, at the expense of rhythmic burns), try this on a new start:

(Exploit: exploites the facts that a) Lander refueling is free and unlimited, b) gas giants do very little damage if you hover at the upper edge of the clouds, c) pilot with an intact Pilot Ejector gets saved without harm from an atmospheric hover, c) Lander gets replaced, once, if you lose it while still in the Sol System, d) Daedalus-7 gets fully refueled for free when Lander drops on Mars.)

-Fly initially to Uranus instead of Mars.
-Do repeated hover missions to just the upper edge of the clouds of Uranus.
-Grab a Hydrogen whenever you can without dropping below the upper layer of clouds. Try to stay above the level where the Lander hull is flashing/degrading from pressure.
-Whenever you snag one Hydrogen, return to ship and offload, so you don't lose your new cargo when the Lander eventually gives out.
-Rinse and repeat, until the Lander eventually accumulates complete hull damage, falls apart, and the pilot ejects to orbit.

(For those of you who have been wondering if Malcolm actually DOES anything, this pattern definitely seems to work better / last longer with Malcolm flying.)

- Daedalus-8 will show up, laugh at you, and replace the Lander.
- Proceed to Mars and start the Adventure normally.

A reasonably good Lander pilot should be able to start the interstellar adventure with an extra 3 to 9 Hydrogen in cargo with this method.

Concievably, an excellent, very patient Lander pilot could collect more than that, but if you collect more you are REALLY constraining cargo space that you will need in the first post-jump system. In fact, if you are going to use this starting tactic, it becomes a factor in ship choice. You may want the USS Endurance because it has the greatest cargo space.

Obviously, the above only works if the Pilot Ejector is intact. Restart if the Pilot Ejjector is destroyed before the first lander fails. If the Pilot Ejector is Damaged, you can still try to run the Hydrogen harvest, but you need to recognize that you will lose you Lander pilot 50% of the time. You may want to restart anyway.

BTW, Uranus (or Neptune) is the recommended source planet for this Hydrogen harvest because it has Average gravity, so the Lander will degrade slightly less rapidly if you dip too deep. It is certainly possible for a good Lander pilot to pull the same trick at Saturn. Jupiter does not offer any Resources during the game Introduction, regardless of pilot bravery/insanity.

You could go for some surface resources at Venus or Mercury instead, but I'm not sure ANY pilot, with an unenhanced Lander, could gather enough rewards to make that effort worthwhile before the first Lander burns. Also, more chance that needed specific systems (Pilot Ejector, Injector Nozzle) will fail from heat before you get a worthwhile result.

I'd love to hear how well this works for you. So far I have been able to start the interstellar with as much as 8 total Hydrogen (5 over base start level.)