Elon Musk knows how to make a splash, and today he outlined his plan to turn humanity into a "multiplanetary species". Getting people to Mars is certainly doable and Musk's company SpaceX is at the forefront of current developments in space technology. But Musk painted a picture of a future where travel to Mars was downright cheap, with tickets costing as little as $200,000, the median price of an American home.
So is this possible? I have no idea, but it makes for a great Fermi question, a problem so fuzzy and incomplete that educated guesswork is the only way forward. (And "educated" is the key word – these puzzlers are part of the legacy of Enrico Fermi who used to test students with problems like "how many piano tuners are there in Chicago?" alongside more technical physics topics.)
The key number is not distance but cost. Musk talks about making a journey to Mars that lasts a few months, but it will take the better part of a year for the Interplanetary Spaceship to make a return trip to Mars, even if most passengers are only travelling one way. Let's compare that to the cost of long-haul plane travel: I might pay $700 for a one-way trans-Pacific flight. This fare entitles me to 1/300th of a very expensive airplane for most of one day and covers my share of the fuel and the crew.
So how does this stack up against Musk's goal for a trip to Mars? His presentation talked about a craft that holds 100-200 passengers. Let's assume that SpaceX can eventually get to the point where Interplanetary Spaceships are about as expensive to build and run as modern airliners. Splitting the difference between 100 and 200, the daily cost of a single seat would be $1,400 a day. And each passenger is effectively using their slice of an Interplanetary Spaceship for one year, so that works out at about $500,000 for the trip.
By the standards that apply to Fermi problems (where you worry about factors of 10 but ignore factors of 2 or 3) that is pretty close to $200,000. But to make this actually happen we will need to build spaceships that are as cheap as airplanes.
And you would still be flying economy class.
Coda: It's a reasonably safe bet that Elon Musk has read his Heinlein.