For Ham, that place was NASA's Johnson Space Center in Houston, where he flew on the zero-G airplane — the climbing and diving 707 known as "the vomit comet." It was there that he began to meet astronauts and seriously consider a career in space.
After more education and training — including U.S. Naval Test Pilot School at Patuxent River — Ham served 12 years as an astronaut and flew two shuttle missions to the International Space Station.
Still on active duty in the Navy, he returned to Annapolis last summer to begin a three-year tour as chairman of the aerospace engineering department, where he is teaching "Introduction to Aeronautics and Elements of Flight Test Engineering."
Reightler, who retired from the Navy as a captain in 1995, holds a three-year appointment to a chair endowed by the family of science fiction writer Robert A. Heinlein, a 1929 academy graduate. He teaches "Space Environment and Human Space Flight."
The other astronauts who have taught at Annapolis are Wendy Lawrence and Pierre Thuot, both academy graduates who flew on the shuttle. Bolden, the current NASA administrator, served as deputy commandant of midshipmen in the 1990s.
Ham described the opportunity to teach and influence midshipmen as a privilege.
"Most of these individuals are going to go be aviators," he said. "Which is what I've done my whole life, and I loved doing it. So passion comes easy.
"They're graduating to go be combat naval aviators. When I can speak at that level, in a mundane, I'm-one-of-you kind of deal, and then occasionally sneak in real-world problems in space flight, show a video, talk about some of these stories — for them, it connects the dots to reality."
Midshipman Brian T. Ma, a member of Reightler's "Human Space Flight" class, said being taught by an astronaut gives students an inside perspective of the space program.
"He was really there in the simulations, in training and in space," said Ma, a fourth-year midshipman from Nacogdoches, Texas. "It's a really interesting class."
Phillips, the academic dean, said it's important to put role models in front of the midshipmen.
"There's something about when you have that kind of individual who's lived it teaching you the material that it's going to stick," he said. "So that if that's what they want to do, they can approach somebody and ask, 'What did it take? Tell me about your time at the Naval Academy. What did you do? What about your time in the Navy? What are my chances?' "
In the 52 years since Soviet cosmonaut Yuri Gagarin piloted Vostok I to an altitude of 200 miles and a single orbit of Earth, fewer than 540 humans have flown in space.
Reightler and Ham both spoke of the experience as life-changing.
"It makes you feel a little bit removed," Reightler said. "You feel detached. You feel not part of this planet that you've been on all your life and where all your friends are and all history has taken place.
"You see pictures of how big the Earth is and how thin the atmosphere is. But when you really see that, I mean, it really strikes home how fragile the planet is."
Ham said his "welcome to space moment" came on his first shuttle flight. He was looking down on Europe at night, admiring "the beauty of city lights from space," when a shooting star passed below.
"I'm convinced the more people in the world that go do this, the more our race will change," he said. "It is that altering of an experience, from looking back on the planet to the physical fragility of the planet, how politics might not really matter that much in the big scheme of things.
"It's just a different perspective that I think it would help us all."