This is "future in the past"
The story is being told in the past tense. It is a past tense narrative. Then there is an event that is in the future of that past time. For this we use "would" instead of "will".
Compare a present tense narrative
John has a guitar. He practices every day. He will be a famous pop star when he ...
This is "future in the past".
Historically, various modals were originally in pairs, present and past:
will - would
can - could
may - might
shall - should
All the historically past forms have their own separate meanings now, but they are also used as past tense forms in some contexts.
The most common context is reported speech:
He said "I ...
They would both be grammatically correct (but write Moon's surface instead of Moon surface). The first sentence is in the present tense; the second one is in the past tense. There's kind of a nuanced difference that using the present tense might imply he stepped on the Moon recently (as if you're just reacting to it), or it could imply that no one else has ...
Unlike the other European languages I know, the present perfect is not the most common tense to use in English to describe past actions or states. It is used in special circumstances. For a brief introduction to a subtle issue in English grammar, see
William Shakespeare is dead, so the problem is that it speaks about him in the present tense.
It should be:
How many plays did William Shakespeare write?
You could say of a living person:
He has written twelve plays and he is currently working on two more.