Relativelyquiteimpressiveguy

So, as you may be aware some European scientists recently 'discovered' a new planet (or 'exoplanet', which simply means a planet outside of our solar system), supposedly the most Earth-like to date. It's been all over the news (the official paper was submitted to the journal Astronomy & Astrophysics). You can check it out on Wikipedia, of course (I'm pretty crazy about Wikipedia). The planet orbits the star Gliese 581 (once every 12.9 days) and is aptly named Gliese 581c. Three planets have been detected orbiting the star, Gliese 581b, c, and d (You might think it would be a, b and c, but the star itself actually gets the letter a). The star system is approximately 20 light years away towards the constellation Libra. We can't actually see the planets from Earth (yet), but we detect them by noticing the small but detectable effect of their gravity on the star, which we can see.

So, as you may be aware, the discovery Gliese 581c is special because it is in what is called the Habitable Zone. This is the window of distance from the parent star that a planet can orbit and be at the proper temperature to have water in the liquid phase (It is actually much closer to its sun than we are to ours, but its sun is a red dwarf, much cooler than our sun. So it balances out (see above for an artist's rendition of the sunrise/set on Gliese 581c)). This water thing is a huge deal because liquid water is crucial for life, as far as we know. This made me think, what it there is life on that planet? What if there's a civilization of beings that look just like us but are much more technologically advanced? What if their planet was about to come to an end and no one believed the one scientist who was predicting it? What if that one scientist sent his baby son on a space ship headed towards Earth, the last son of Gliese 581c? What if that child crash-landed in a small town in Middle America and grew up on a farm and discovered he had extraordinary powers? What if this one time these other three people from that planet who had been exiled into the Phantom Zone but were released by a nuclear explosion in space came to Earth and ran amok (is that really how you spell that?) but the last son of Gliese 581c couldn't do anything (because he gave up his powers to become his mild-mannered reporter alter-ego and be in love with some nosy woman reporter) until he managed to trick the three bad-guys into giving up their powers and getting back his own?

[To get straight to the answer and skip the BS, just go to the bottom.]

So, as you may be aware, I'm a pretty big Superman fan. As I was reading about Gliese 581c, I noticed a lot of similarities it has with Krypton: Both have a red sun, unlike our yellow sun; Both have a greater mass than Earth; Both could harbor life; Both are in space; Both are planets. Maybe you can see what I'm getting at. What if someone were to come to Earth from this newly discovered real planet? Would they be like Superman? Well, according to the earliest versions of the Superman tale, Superman was so strong because Krypton had a much stronger gravity than Earth. It would be like us going to the moon. He could leap over tall buildings in a single bound, etc. Sound familiar?

So I've got this book, The Physics of Superheroes. Phenomenal book. Written by a physics professor at the University of Minnesota, James Kakalios. In the first couple chapters Kakalios uses the facts that Superman weighs about 220 pounds and can leap over a tall building (about 660 feet) to figure out how much force Superman needs to exert to jump that high (about 5,600 pounds), what the gravity is like on Krypton (apparently 15 times that of Earth), and how big/dense Krypton has to be (either 15 times denser, 15 times larger, or somewhere in between). My goal? Using this book as I guide I will figure out what kinds of powers someone would have if they came from the planet Gliese 581c rather than Krypton. Also, just for fun, to see how high I could jump on Gliese 581c.

So to start off, I have this information that the brilliant scientists of Earth have been able to deduce: Gliese 581c is about 5 times the mass of Earth, and has a radius about 1.5 times as large. The first thing I need to do is calculate the gravity on 581c. The acceleration due to gravity of a planet at its surface is given by the equation

g = Gm/r²

where g is acceleration due to gravity, G is a the universal gravitational constant (6.67300 × 10^-11 m³ kg^-1 s^-2), and r is the radius of the planet. So I know everything I need to know about earth:

g_e = 9.800 m/s²
r_e = 6.3781 x 10⁶ m
m_e = 5.9742 x 10²⁴ kg

And I know that for Gliese 581c, r_g = 1.5r_e and m_g = 5m_e. So I can just plug those values into the equation to find the gravity on 581c, g_g:

g_g = 5Gm_e/(1.5r_e)² = 21.78 m/s²

So this is about 2.2 times the gravity on earth. I weigh about 143 pounds here, so I'd way about 318 pounds on Gliese 581c (but of course my mass will always be 65 kg).

Now, the important part. How high could I jump on Gliese 581c. According to the guy who wrote this book (who would know a lot more than me) most people can exert a jumping force approximately equal to their weight. Converting my weight to metric/standard units (you've just got to use metric for any kind of serious calculations)... 636 kg∙m/s² or simply 636 N. First on Earth: I will use the fact that I flex my legs for about 0.25 seconds while jumping, gravity on Earth is 9.8 m/s², and the following equations to find my liftoff acceleration, liftoff velocity, and then jump height:

my acceleration = force/mass
= 636 N / 65 kg = 9.8 m/s²
liftoff velocity = acceleration x time
= 9.8 m/s² x 0.25 s = 2.45 m/s
jump height = velocity² / (2 x deceleration of gravity)
= (2.45 m/s)² / (2 x 9.8 m/s²) = 0.31 m

So according to my estimations, I should be able to jump about a foot high on Earth, which is sadly close to the truth. I tried to measure my vertical jump. I was disappointed.

Now on Gliese 581c:

jump height = velocity² / (2 x deceleration of gravity)
= (2.45 m/s)² / (2 x 21.78 m/s²) = 0.14 m

Pretty sad. Let's try someone a little more interesting than myself. Cleveland Cavalier (that's basketball, folks) LeBron James (6' 8", 245 lbs, 111.1 kg) can jump 44" (1.12 m) on Earth. Using the same assumptions as above, we get...

LeBron's liftoff velocity is 4.69 m/s
LeBron's liftoff force is 2082 N (468 lbs!)

That means LeBron can exert almost 2x the force of his own weight when jumping! Bet you can't do that (unless... LeBron, are you reading this?). So on Gliese 581c, that translates to a 20" (0.50 m) vertical (simply multiplying by the gravity ratio)... Still more than I can jump on Earth. Ouch.

Okay, that was fun, BUT what if some guy just like me but from Gliese 581c came to Earth? Well, on Earth he'd way only 143 pounds, even though on his home planet he weighed 318 pounds (but of course his mass will always be 65 kg). If he's like me, which he is because I said so, he could jump with a force equivalent to his weight, 318 lbs = 1415 N. Using the same equations I used to figure out how high I could jump on Earth, I find that Dave from Gliese 581c (SuperDave?) can jump 1.51 m (about 5 ft) on Earth. Not quite Superman, but he could jump clear over some people I know. Maybe... Relativelyquiteimpressiveguy?

What about SuperLeBron? He'd be able to jump 5.53 m. Is that high? Who knows? Let's see... 5.53 x 3.28... Wow! 18 feet! Sounds pretty super to me.

Phew.

[Mistakes/Corrections? I don't care, I'm not changing it. It took me a long time to write all that.]