Home > Uncategorized > Gravity of GJ 667Cc

## Gravity of GJ 667Cc

2012 February 4

A new planet—probably a rocky super-Earth—has been found squarely within its star’s habitable zone, making it one of the best candidates yet to support life, its discoverers say.

The planet, dubbed GJ 667Cc, orbits a red dwarf star 22 light-years from Earth, in the constellation Scorpio. A binary pair of orange dwarf stars are part of the same system. The new planet has a mass 4.5 times that of Earth and orbits its host star every 28 days. …

…That means if the planet has a rocky surface—which is predicted for planets less than ten times Earth’s mass — and an atmosphere, it could support liquid water and maybe life, said co-discoverer Guillem Anglada-Escudé, who conducted the work while at the Carnegie Institution for Science in Washington, D.C. “If it has an atmosphere, it’s probably reddish all the time, because the star is really red,” Anglada-Escudé said. “It would be like being evening all the time.” For any hypothetical observers on the surface, the binary stars in the distance would be “very prominent in the sky, and it would be an exotic thing.”

Anglada-Escudé and colleagues found the new planet using public data from the European Southern Observatory, which hosts telescopes that can measure wobbles in a star’s orbit caused by a planet’s gravitational tug. The new super-Earth was somewhat unexpected, because some planetary-formation models say that metal-poor stars such as GJ 667C shouldn’t have terrestrial planets around them. …

http://news.nationalgeographic.com/news/2012/02/120202-new-planet-super-earth-habitable-zone-life-space-science/

While the National Geographic article states the mass of GJ667Cc is 4.5 times the mass of earth, other articles have stated that it is no less than 4.5. So the mass of GJ 667Cc is between 4.5 and 10 earth mass, more likely on the lower end of the scale.
Therefore: $4.5 M_{\textrm{earth}} \le M_{\textrm{exo}} \le 10 M_{\textrm{earth}}$

This is believed to be a metal-poor system. So the density of the GJ 667Cc is likely to be lower than the density of Earth. Mar’s density is about 0.7 that of Earth. We will use that as our likely density for the exoplanet.

Let D be the density of a planet…
$D_{\textrm{earth}} = M_{\textrm{earth}}/V_{\textrm{earth}}$
$D_{\textrm{exo}} = 0.7 * D_{\textrm{earth}} = 0.7 * M_{\textrm{earth}}/V_{\textrm{earth}} = M_{\textrm{exo}}/V_{\textrm{exo}}$
where: $4.5 M_{\textrm{earth}} \le M_{\textrm{exo}} \le 10 M_{\textrm{earth}}$

Solve for the volume of the exoplanet as a ratio of Earth’s volume:
$V_{\textrm{exo}}/V_{\textrm{earth}} = (1/0.7) * M_{\textrm{exo}}/M_{\textrm{earth}} = ( 1/0.7)*[4.5 ... 10] = [6.43 ... 14.3]$

The volume of a sphere is $V_{\textrm{sphere}} = \frac{4}{3} \pi R^3$

So for earth and exoplanet:
$V_{\textrm{exo}} / V_{\textrm{earth}} = \frac{4}{3} \pi R_{\textrm{exo}}^3 / \frac{4}{3} \pi R_{\textrm{earth}}^3$

Solve for the Radius of the exoplanet as a ratio of Earth’s radius:
$R_{\textrm{exo}} = (V_{\textrm{exo}} / V_{\textrm{earth}})^\frac{1}{3} = ([6.43 ... 14.3])^\frac{1}{3} = [1.86 ... 2.43]$

Gravitational force can be expressed as $g = G*M/R^2$ where G is the gravitational constant, M is the mass and R is the radius of the body. If we want to express this relative to earth gravity then, since G is constant …
$g_{\textrm{exo}} = [4.5 / 1.86^2 ... 10 / 2.43^2] = [1.3 ... 1.7]$

The gravity of GJ 667Cc is likely to be in the range of 1.3 to 1.7 Earth Gs and more likely to be on the lower end of the scale.

That’s a bit high but not bone crushingly high. Similar to a 150 pound man carrying a pack weighing between 45 and 105 pounds. If it’s a bit high for you, exoskeletons will be available. In models ranging from the lightweight one above to the heavyweight one below. 😉

Unfortunately, there is no way to measure or model atmospheric existence or composition at this time. But to be mapping hundreds of planets, many of them earth-sized, in my lifetime. Wow.

And just to repeat an interesting tidbit from the original quote:
“Anglada-Escudé and colleagues found the new planet using public data from the European Southern Observatory, which hosts telescopes that can measure wobbles in a star’s orbit caused by a planet’s gravitational tug.”

1. 2012 February 6 at 12:49 pm

Now if only we can crack the light-barrier…!

Ward Kendall
“Hold Back This Day”
http://www.amazon.com

2. 2012 May 20 at 10:46 am

This is my term paper topic. Why would they call it a Super Earth if the temperature can’t support life? Doesn’t sound like a Super Earth to me…sounds like just another planet.

3. 2012 May 20 at 10:51 am

There are two major types of planets – ‘small and rocky’ and gas giants. Among the rocky planets of Sol, Earth is the biggest. “Super-Earth” is just a way of saying rocky like the Earth, but bigger. Nothing to do with habitable v inhabitable.

1. 2012 February 23 at 11:04 am