Jeff Bezos and Elon Musk spent Thursday exchanging barbs about their respective plans to conquer space.

At an event in Washington, D.C., Bezos unveiled plans to put people on the moon, unveiling a giant lunar-landing vehicle named "Blue Moon."

According to Bloomberg, one of Bezos' slides included a subtle reference to Musk's red planet mission, pointing out the pitfalls of life on Mars.

Musk tweeted that "putting the word 'Blue' on a ball is questionable branding."

Visit Business Insider's homepage for more stories.

It's the intergalactic battle of the billionaires that's taking place right here on Earth. Yes, Jeff Bezos and Elon Musk are exchanging barbs again about their respective plans to conquer space.

The two have a history of clashes over their space race ambitions, and their rivalry came to the fore again on Thursday as Bezos drew back the curtains on his vision to put people on the moon.

Business Insider's Dave Mosher was in the room as Bezos revealed a giant lunar-landing vehicle created by his rocket company Blue Origin. Designed to deliver payloads to the moon's surface, the "Blue Moon" would aim to establish a "sustained human presence" on the moon.

"It's time to go back to the moon, this time to stay," Bezos said.

Jeff Bezos shows off Blue Origin's lunar lander concept, called Blue Moon, in Washington, DC, on May 9, 2019. Dave Mosher/Business Insider

During the Washington DC event, Bezos couldn't resist an indirect swipe at Musk's plans to colonize Mars through his company, SpaceX. According to Bloomberg, one of Bezos' slides included a reference to Musk's red planet mission, suggesting that the moon is the more realistic ambition.

"Round-trip on the order of years," one slide reportedly read, with an image of Mars. "No real-time communication."

Read more: Elon Musk just trolled Jeff Bezos on Twitter, and it could reignite a years-old feud between the billionaires

Musk, as is his tradition, responded on Twitter.

The Tesla and SpaceX CEO posted three times about Bezos' presentation, starting out with an open-minded tone. "Competition is good. Results in a better outcome for all," he said, before turning a little more puerile.

"Putting the word "Blue" on a ball is questionable branding," he added, in a nod to "blue balls," a slang term for male sexual frustration.

He later wrote, "Oh stop teasing, Jeff 😉," with a screenshot of a New York Times article with Bezos pictured in front of his lunar-landing vehicle.

It's not the first time this year that Musk has called out Bezos on Twitter. He branded the Amazon CEO a copy cat over his plan to launch thousands of satellites that would deliver high-speed internet to remote parts of the world. SpaceX has been working on a similar project.

But it's not always so testy between the billionaires — the two have also exchanged pleasantries before. Bezos wished SpaceX the "best of luck" with the Falcon Heavy launch in February last year. Musk thanked him with a kissing emoji, before Bezos responded with "woohoo" and three rocket emojis.