The new car and the campaign is being unveiled today. The campaign makes use of the car manufacturer's global partnership with Richard Branson’s company Virgin Galactic, which was announced in April.
The pair has launched the "galactic discovery" global competition with an online film that features famous adventurers including Ranulph Fiennes and Bear Grylls talking about exploring the unknown.
The film unveils Land Rover's new compact SUV, which drives around Spaceport America in New Mexico, the base for Virgin Galactic's commercial space flights. The film was directed by Oliver Wurffell through Pulse Films.
Those who want to win the prize, which is worth $1 million, will have to upload a film or photo that demonstrates their "spirit of adventure" and link to three people they want to take with them on Facebook.
PR and social media activity will support the competition until the winners are announced on the 2 December.
Dominic Chambers, the global marketing director at Land Rover, said: "This highly-innovative, socially-driven campaign really brings alive the Land Rover mantra 'above and beyond'.
"Our expectation is that in this pre-sales period we will reach out to millions of new people bringing them closer to Land Rover and the new Discovery Sport."
The campaign has been created and developed by The Brooklyn Brothers, who will oversee implementation in 40 countries.
Miranda Mitchell, the head of outreach at The Brooklyn Brothers, said: "A trip to space with your friends really is the ultimate adventure and as a platform it lends itself perfectly to a vast global social and earned media programme.
"We are expecting interest from all ages and all demographics as space has no boundaries."