If this snippet makes us feel anything, it might be because the contrast between the failed rocket, the bickering team, and Homer and Roy's commitment to keeping everyone going adds emotional weight to the solemnity of the boys putting their hands together.
Notice how restrained the snippet is: it doesn't put us inside any of the characters, and it doesn't directly describe anyone's feelings. The thoughts and emotions are communicated in dialogue, with 'solemnly' the only emotional label.
We watch boys try to boost each other's spirits in the face of adversity, and we feel boosted too because we can see how hard that is to do.