At his Psychology Today blog, Michael Chorost delves into a question about exoplanets that I've not really thought much about before — how easy they would be to leave.
Many of the potentially habitable exoplanets that we've found — the ones we call "Earth-like" — are actually a lot bigger than Earth. That fact has an effect — both on how actually habitable those planets would be for us humans and how easily any native civilizations that developed could slip the surly bonds of gravity and make it to outer space.
The good news, says Chorost is that the change in surface gravity wouldn't be as large as you might guess, even for planets much bigger than Earth. The bad news: Even a relatively small increase in surface gravity can mean a big increase in how fast a rocket would have to be going in order to leave the planet. It starts with one equation — SG=M/R^2.
Let’s try it with [exoplanet] HD 40307g, using data from the Habitable Exoplanet Catalog. Mass, 8.2 Earths. Radius, 2.4 times that of Earth. That gets you a surface gravity of 1.42 times Earth.
... it’s amazingly easy to imagine a super-Earth with a comfortable gravity. If a planet had eight Earth masses and 2.83 times the radius, its surface gravity would be exactly 1g. This is the “Fictional Planet” at the bottom of the table. Fictional Planet would be huge by Earth standards, with a circumference of 70,400 miles and an area eight times larger.
Does that mean we could land and take off with exactly the same technology we use here, assuming the atmosphere is similar? Actually, no. Another blogger, who who goes by the moniker SpaceColonizer, pointed out that Fictional Planet has a higher escape velocity than Earth. Put simply, escape velocity is how fast you have to go away from a planet to ensure that gravity can never bring you back. For Earth, escape velocity is about 25,000 miles per hour. Fictional Planet has an escape velocity 68% higher. That’s 42,000 miles per hour.
Thanks to Apollo 18, who also helped with the math for Chorost's post.