# Some planets are harder to leave than others

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.

Read the full story at Psychology Today blogs

Thanks to Apollo 18, who also helped with the math for Chorost's post.

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1. jackbird says:

Other obligatory XKCD: Exoplanets

1. It is kind of trippy that that article is hosted on Psychology Today’s website.

Something else to chew over:

A lot of exoplanets are turning up in orbits close to their stars. Many of these, or course, will be so close that there’s no chance of their being complex organic life. But some are going to be in the “goldilocks zone” of dim stars. As I recall, luminosity is roughly proportional to mass (in stellar masses) ^ 3.3. Which means that to get the same amount of insolation a planet is going to be more than proportionally closer to its sun and thus proportionally deeper in its gravity well. So the velocity required to leave the world’s vicinity is going to be higher. So, interplanetary travel will be more difficult.

2. Ashen Victor says:

Eight times the Earth surface with the same gravity… wow, that´s some serious inspiration for serious sci-fi or fantasy writers.

3. Robert Silverberg wrote a series of books set on Majipoor, a planet with 10 times Earth’s diameter. It even has its own web site! http://www.majipoor.com/majipoor/majipoor_geography.php

4. Is it possible that many of the potentially habitable exoplanets we’ve detected are larger because those have been the easiest for us to detect? Could there be other potentially habitable exoplanets of Earth size or smaller that we haven’t detected yet because they’re hard to detect? Just spit-balling here, I could be way off.

1. ldobe says:

That’s almost certainly true. We didn’t start out finding super earths, they were so small our instruments couldn’t see them at all for a time.

Bigger things are easier to spot, but over the years we’ve been finding smaller and smaller exoplanets and it’s only a matter of time until we find things the same size and smaller than earth.

5. gsilas says:

Maggie, you are the greatest.  THE GREATEST.

Thank you for writing scientifically literate posts that are accessible and interesting to both general public (I assume) and scientists.  Geek out time!  A hearty “thank you” that is long overdue.

1. Thanks, too, Maggie, for drawing attention to my blog entry. I saw the hit count going up and wondered what was going on. As for the person above who said it was trippy that my posting was on Psychology Today, I’m looking for a new home for my blog, because PT obviously isn’t the right venue. (My first two books were about neuroscience, but my interests have changed…obviously!) Anyone here work for a space/tech website that’s looking for a new blogger?

6. planettom says:

I’ve often thought about, imagine we were on the Moon or Mars and send a spaceship to explore Earth.    So you send your astronauts to land somewhere on Earth and then lift off again.    Assuming they can’t build it from what they find, how do you send them with a vehicle that can get them back to Earth orbit and the mothership.    You basically have to have them land with the equivalent of a Soyuz-FG rocket in crates and assemble it.

7. David Lanteigne says:

“Heavy Planet” by Milton A. Rothman, Astounding Science Fiction, 1939.  Creatures who know they are trapped in their gravity well fight over the crashed spaceship (perhaps from earth) that will give them the secret of atomic power–and escape.

8. pjcamp says:

My first car was a 72 Olds Delta 88 — pre oil embargo, GM in the bad days — I think it was probably the biggest car that ever slouched out of Detroit. It could seat 10 comfortably and put all their luggage in the trunk. I used to flip on the cruise and put my feet up on the dashboard while I drove (and I was 6’4″ at the time). Slam the door and it rattled for a good five minutes. Had a 450 cc V-8 and still had the acceleration of a pill bug. 0 to 60 in a day and a half. I got a ticket one time for inability to get out of the way. Gas cap went missing but that had no detectable effect on mileage.

So I guess what I’m saying is I get why “rocket” is in scare quotes. It was a rocket in the same sense that my ass is a doorknob.

9. Thanks for sharing this, Maggie!  It’s a rather interesting problem, and I was a little surprised by the results that I got while figuring out how much fuel it takes to get off of any of these planets we’re discovering.

To add some more math here (yay math!): the interesting thing that Michael points out is that it would take roughly 4X the mass of fuel to launch a Saturn V type rocket from his Fictional Planet into interplanetary space, compared to the amount of fuel it’d take to do the same thing from Earth.  The smaller planet Gliese 581g has a higher surface gravity (1.32 g), but a lower delta-V requirement and therefore a lower fuel requirement – only 2X the mass of fuel required to launch a Saturn V type rocket to interplanetary space.  And it’s the amount of fuel that can be linked to the cost of a rocket launch.

The math is Tsiolkovsky’s rocket equation, V = Isp * g * ln(m0 / m1).  This just says that your change in velocity, V, is a function of the rocket engine’s performance (Isp) and the ratio of the mass of your rocket with fuel (m0) and without fuel (m1).  (“g” is just Earth’s gravity and is thrown in to balance the equation.)  Since there’s a natural log function here, we know that the relationship between delta-V and fuel mass isn’t linear.

But then things get a little tricky.  All successful interplanetary and orbital launches from this planet are made using multi-stage rockets.  That just means that once a particular stage has burned through its fuel allotment, it is jettisoned, getting rid of the “dry mass” of the empty stage and giving a better (m0 / m1) ratio for the rest of the flight.  This also means that the engines of each stage can be optimized for their individual portions of the trajectory – for instance, the first-stage engines typically have worse performance than the upper-stage engines, since they have to operate inside Earth’s atmosphere.  The result is that the amount of fuel required for a multi-stage rocket is less than that for a single-stage rocket, but the math is a little more complicated (to say nothing of the engineering).

10. I could totally see “Some planets are harder to leave than others” being used in a holiday brochure for a super-earth at some point in the future.