“His feeling was that he was not special because he was the first person to walk on the moon, and that he wouldn’t have done it if it weren’t for the thousands of people who worked on the mission,” Mr. Wales said.

By contrast with the astronaut’s sons, Carol Armstrong — his second wife, whom he married in 1994 after a divorce initiated by Janet Armstrong, Rick and Mark’s mother — is not known to have sold anything. Instead she has lent and donated a collection of memorabilia to the Smithsonian’s National Air and Space Museum in Washington; such loans often convert to donations in an arrangement intended to avoid gift taxes. People who know her say she and her adult children, Andrew and Molly, believe her husband would have opposed the commerce in the trappings of his work and life. (Carol and her children declined to comment.)

Mark Armstrong said that the question of what’s best for posterity and what his father might have wanted is not so simple. He said that he and his brother had already donated to museums more than $500,000 in cash and artifacts worth about $1.4 million, and that they had lent items worth several million more.

But he said donations, which offer the donor tax benefits, do not guarantee public access. “Museums can choose to store items out of sight or unilaterally decide to sell them,” he said in an email forwarded by his wife.

As for his father, Mark said, “I think he would judge us not on whether we auctioned items or not, but rather what we do with the proceeds and how we conduct our lives. Dad said that he wanted to leave the world a better place than he found it. I intend to follow his example and teach my children to do the same.”

Mark and his wife, Wendy, said they were using auction proceeds to create an environmental nonprofit in honor of Mark’s parents, called Vantage Earth, that Wendy said would work “to preserve and protect the earth from the damage done to it by its own population — a concern raised by Neil upon looking back at the earth from the moon.”

Tensions are common in any family affected by divorce. When it is the family of the first human being to step onto the moon, with global fame and a large estate, relations get only more complicated.