Mutta's current mission is one that he should be capable of specialising in, that being work on improving the lunar buggy, but for now that takes something of a back burner as other elements come to the fore.
Although Mutta does discuss any perceived weaknesses of the buggy with his brother (and everyone seems to have completely overlooked the catastrophic operational and instructional oversight that caused the lunar accident for some reason, Hibito included), his more pressing requirement is actually a photo shoot - a joint effort with Hibito for a Japanese business magazine that depicts the two brothers, complete with spacesuits, on the Moon's surface.
Alongside this, we get a glimpse into an issue that Hibito has previously kept quiet about - but simply, he's suffering from panic attacks whenever he dons a spacesuit in any kind of potentially stressful situation. Given his nightmarish accident and near-death on the Moon, this is hardly surprising, but it's rather a large problem for both Hibito himself and NASA, who have warned him that he can't participate in any lunar missions in his current state.
It might not make for the best television in its own right, but it's actually rather impressive to see Space Brothers give some time and thought to a panic disorder such as this; particularly one inherent from a traumatic experience that goes on to cause real issues in Hibito's work. Having suffered from such a disorder for a while as a result of illness myself (elements of which still come back to bite me on occasion), I'll be interested to see how its handling pans out, but once again it adds real weight to the overall experience of watching the series and the thought that it's put into its scenario.