Fifty years ago, on July 20, 1969, Neil Armstrong became the first human to step onto the surface of the moon. I still find that amazing—both the moon landing and the fact that it was half a century ago. In honor of that historic achieve­ment, and mindful of our carbon footprint as plans develop for a return trip, I thought I would estimate how long it might take to get there by bike.

What? Yup. As President John F. Kennedy said, we do such things not because they are easy, but because they are hard. And they bring up some great physics questions! I'll walk you through the basics, and then I'll leave you with some questions for homework.

So let's just get some implementation issues out of the way. We'd need to string a cable between Earth and the moon, obviously. And you, if you chose to accept this mission, would have a nifty white NASA bike with special grippy wheels to ride along the cable. (We'll assume no energy loss to friction.) Oh, and the wheels only roll one way, so you won’t come crashing down if you pause to rest.

Just to be clear, this scheme would not have worked out timewise for the Apollo program. Kennedy vowed to put a man on the moon before the decade was out, and as it was, NASA barely made it. Luckily, it took the Apollo 11 spacecraft just four days to get there. Making the trip by bike would have blown through that deadline. But exactly how late would we have been?

Getting off the ground

For starters, we need some facts to work with. First, how far away is the moon? Since the moon's orbit around Earth isn't perfectly circular, there’s no one answer. But let's go with an average distance of 240,000 miles (386,000 km)—that's the number I think about when my car is getting old. Once I hit 240,000 on the odometer, I know I've gone far enough to reach the moon.

Now, you might think, OK, a human can pedal 15 miles an hour; I can use that to calculate the duration of the trip. Nope. You might be able to do 15 mph on a nice flat road, but in this case, you’d be riding uphill—like, straight up. Then, to really complicate the math, as you get farther away from Earth, the pull of gravity continuously declines. Each day the same effort would take you slightly farther. Eventually you’d get close enough to the moon that it becomes a downhill ride and you could just coast.

So instead of estimating the speed, which would vary, I'm going to estimate the power output of a human. If you are a Tour de France cyclist, you might be able to produce 200 watts for six hours a day. (Check out Ben King’s stage 4 ride on Strava.) Let's use that value for now; you can change it later if you’re not a Tour de France cyclist.

Next, we want to figure out how long it would take to move up just a short distance Δy on your special moon-cable bike. Let's say the gravitational field has a strength g (in newtons per kilogram). The change in gravitational potential energy (U G ) for this short climb would be: