During his Inaugural Address on Monday, President Donald J. Trump again promised to launch American astronauts to Mars.

Seated nearby, Elon Musk, a political benefactor of Mr. Trump who founded SpaceX in the hope that it would one day be able to send colonists to Mars, beamed with enthusiasm and offered two thumbs up. The gargantuan Starship rocket that Mr. Musk’s company is currently developing is meant for that task.

Mr. Trump left a number of specifics unsaid, including what the new initiative would mean for NASA’s existing moon program, when astronauts would get to Mars and what other NASA programs might be cut to pay for it.

What Trump has said about Mars

Mr. Trump has mentioned landing on Mars before. During a campaign rally in Reading, Pa., on Oct. 9, he promised that this would occur during his presidency. “We will lead the world in space and reach Mars before the end of my term,” he said.

He did not specify whether he meant landing American astronauts on Mars by Jan. 20, 2029, his last day in the White House, or whether just sending a prototype of the spacecraft that would take astronauts someday further in the future would suffice.

On Monday, he said that American astronauts would “plant the stars and stripes on the planet Mars,” but left out when.

Separately, Mr. Musk has not been shy in making his own proclamations. In September, he said that SpaceX would launch five Starships to Mars in 2026, albeit with no one aboard, to test their ability to survive re-entry through the thin Martian atmosphere and to arrive on the surface in one piece.

Earth and Mars pass relatively close to each other once every 26 months; the next time they will be in alignment will be in late 2026. If those landers succeeded, the first people would travel at the next opportunity, in 2028, Mr. Musk said.

Mr. Musk’s timeline is thus possible, at least in terms of orbital dynamics. But many other questions remain to be answered.

What happened to the moon?

Mr. Trump did not mention the moon, even though the centerpiece for the space program during his first term was returning astronauts to the moon as part of NASA’s Artemis program. There are already signs that the new administration is planning major changes to Artemis.

One hint involves who is running NASA right now.

During a change of presidential administrations, NASA’s top political appointees typically resign, and a career official, the associate administrator, fills in until a new administrator is confirmed by the Senate. Mr. Trump has nominated Jared Isaacman, a billionaire who has flown two private astronaut missions on SpaceX rockets and who is a close associate of Mr. Musk.

On Monday, Mr. Trump said that Janet Petro, the director of NASA’s Kennedy Space Center in Florida, would serve as acting administrator. In doing that, he bypassed James Free, the third-highest official at NASA.

Mr. Free has been a defender of the current Artemis program.

“Jim Free made it clear that Artemis was perfect and didn’t need to be changed,” said James Muncy, a Republican space policy consultant who was not involved with the NASA transition for Mr. Trump. “Which is disqualifying to a president that wants to change things.”

Crucial parts of the current Artemis program include the Space Launch System, a powerful but expensive NASA rocket, and the Orion capsule where the astronauts would travel between the Earth and the moon.

Many in the space industry expect the incoming Trump administration to cancel S.L.S., and possibly Orion as well.

On Christmas, Mr. Musk wrote on X, “The Artemis architecture is extremely inefficient, as it is a jobs-maximizing program, not a results-maximizing program. Something entirely new is needed.”

The next day, Mr. Musk, who has met repeatedly with Mr. Trump, appeared to call for skipping the moon altogether: “No, we’re going straight to Mars. The Moon is a distraction.”

Mr. Musk downplayed the moon, even though SpaceX holds a $4 billion contract to build a version of Starship to take astronauts from lunar orbit to the surface of the moon.

A cancellation of Artemis would also cancel SpaceX’s contract.

“We will see whether or not there is no money for the moon at all in the budget when it comes out,” said Mr. Muncy, who said he would prefer that NASA continue the moon program using commercial alternatives to S.L.S.

Can American astronauts really get to Mars?

Mr. Musk has a long history of offering unrealistic, overly optimistic schedules for his rocket developments. In 2016, he predicted that the first uncrewed SpaceX missions on Mars would launch in 2022, and that astronauts would be headed there this year.

SpaceX has made technological strides, but they remain far short of what is needed to pull off a Mars journey. Some of the most significant hurdles include quick turnarounds between launches and refueling Starships while in orbit.

The life-support system on Mars-bound versions of Mr. Musk’s Starship would also have to work reliably — scrubbing carbon dioxide from the air, recycling water and performing other tasks to keep the ship habitable — for more than a year.

If the astronauts successfully landed on Mars, the return trip would require more yet-to-be-proven technologies.

For one, the Starship would have to be refueled with methane and oxygen.

The technology for extracting those gases from Martian air is still mostly hypothetical. SpaceX could conceivably send additional Starships with the propellants for the return trip, but that would add complexity.

Then there is the question of who would pay for all this. These Mars flights would occur at a time when NASA would be busy with its Artemis moon missions, presumably with SpaceX fulfilling its contractual obligations to build a moon lander.

At least on paper, it thus might make sense for Mr. Musk for the Artemis moon missions to be canceled and for NASA to pay him instead to aim for Mars.