“NASA has never had a scientist as administrator; you and I would have had fun,” he said.

Now, nobody knows where NASA’s rockets are going on their biblical smoke pillars. Donald J. Trump’s one mention of the space program during his campaign was to tell a kid that potholes on Earth need fixing first.

But he also campaigned on the promise to “make America great again,” and hardly anything in recent history says that more clearly than the Apollo moon landings. That has some space buffs hoping that a Trump administration will put its weight behind another grand adventure in space, most likely a return for good to the moon.

At the same time, there is no evidence that Congress would give NASA any more money than it is already getting to carry out these adventures. Mr. Trump’s potholes, a military buildup and tax cuts beckon.

Early in December, the first member of Mr. Trump’s transition “landing team,” Christopher Shank, policy director for the House Committee on Science, Space and Technology and a former member of NASA arrived at its headquarters to begin taking stock of the agency. He did not respond to an email request for an interview and none of the other members of the team, which now numbers seven, have commented publicly.

Even NASA insiders are reduced to reading tea leaves and possible smoke signals, clues scattered by Mr. Trump and Republican space and science insiders during the last year. In a recent speech in Washington, Bob Walker, a former congressman who advised the Trump campaign on space, reiterated his desire for NASA to concentrate on basic science and exploration and farm out climate research, which he has referred to as “politicized science,” to other agencies like NOAA. That’s a notion that alarmed climate scientists regard as either naïve or cynical.

Mr. Walker also said that Vice President-elect Mike Pence would be presiding over a reinstated National Space Council, last used during George W. Bush’s administration, to oversee and coordinate civilian and military space efforts. One of its jobs would be to decide how much NASA should depend on commercial space entrepreneurs like Mr. Musk and Jeff Bezos to shoulder the rocket load.

Last summer many of these insiders, including Michael Griffin, a former NASA former administrator, gathered around a television at Mr. Shank’s house to cheer on Eileen Collins, the first woman to command a space shuttle mission, as she spoke at the Republican National Convention. Denouncing what she saw as a lack of American leadership, at least as far as human spaceflight was concerned, she noted that it had been five years since an American was launched into space from American soil.

“We are a nation of explorers,” she declared. “Nations that lead on the frontier lead in the world.”

Ever since John Glenn orbited Earth in 1962, the United States space program has limped through a series of auspicious starts and stops. Americans landed on the moon in 1969 and abandoned it in 1972. We built the space shuttle and then retired it; we embarked on the Constellation program to return to the moon, then canceled it in favor of eventually going to Mars. The International Space Station was supposed to get us ready for deep space travel, but we haven’t gone anywhere.

Mr. Glenn died last week, at age 95. Reflecting on the long arc of his life and the space program, Dr. Grunsfeld asked, “What do we have to show for it?”

Are we in for another outer space pivot back to the moon?

Among the many Trump advisers is Newt Gingrich, who promised a lunar colony by 2020 when he was running for president four years ago, quipping that it could apply for statehood someday.

At the time eyes rolled, but times have changed. Recently Jeb Bush declared it a “cool” idea. Europe, China and Russia are all reportedly eager to establish a base on the moon.

Jim Bridenstine, an Oklahoma congressman rumored to be in the hunt for NASA administrator, said in a recent speech: “This is our Sputnik moment. America must forever be the pre-eminent spacefaring nation, and the moon is our path to being so.”

Among the attractions of a lunar base, its adherents say, would be the ability to mine ice at the moon’s poles to produce rocket fuel. According to recent studies, refueling at the moon, or nearby, would be the cheapest way to go to Mars.

It could be the mother of all infrastructure projects, perhaps a notion attractive to Mr. Trump’s developer instincts, in effect paving a highway to Mars and beyond.

It would also take a lot of money, time and political capital.

“The moon’s a nice place to visit, but you wouldn’t want to live there,” Dr. Grunsfeld said.

But we can go to Mars without breaking NASA’s budget, Dr. Grunsfeld said, reaching for my notebook.

First he drew a line of rockets.

Forget the giant heavy-lift super booster rocket. Assemble a Mars spacecraft in orbit using the kinds of rockets like Atlas or Delta we already have.

Suppose it takes 10 launches to get all the pieces up there, he said. At $350 million a launch, that adds up to $3.5 billion.

Adding in another $500 million to launch the crew brings the total to $4 billion.

If the spaceship segments themselves cost $1 billion apiece, the whole Mars ship is $14 billion.

Make two, just to be on the safe side.

“For $4 billion a year for seven years you get a Martian spaceship including a full spare,” he said.

Where does the money come from?

As it happens, this is the amount of money NASA now spends on the space station every year, money that will be available one day to go someplace.

They could only go around Mars, without landing . But it would still be an epochal voyage, the interplanetary version of Apollo 8’s Christmas voyage around the moon in 1968, setting the stage for what is to come if people are ever going to live off-planet.

Someone should do it. All that money would be spent here — on things we say we care about, like science, technological development and education, things that stimulate the economy and inspire generations.

“Going to Mars would make NASA great again,” Dr. Grunsfeld said.

I asked him how long it would all take. Seven to 10 years, he texted me later. “Whenever someone decides to start.”