Gliese 370b’s surface gravity

It’s happened again. For just the third time in our history, humanity has found an exoplanet that exists in the habitable zone of its star. The previous two, Gliese 581g and Gliese 581d, I have covered previously. I calculated the surface gravity of Gliese 581g here. For both Gliese 581d and Gliese 581g I calculated the size its star would look in the sky. You can view those posts here and here, respectively. But enough about these old planets; time to talk about the newest one discovered just yesterday! Named by most as HD 85512 b, it orbits (predictably) the star HD 85512 b right in the habitable zone where liquid water could theoretically exist. I like to call this planet Gliese 370 b, however, for it’s easier to remember and still technically correct. (HD 85512 and Gliese 370 are the same star, just under different classification systems) And of course, if this planet has water, I’d like to imagine that humans will eventually get there. Once we arrive on Gliese 370 b, what will the gravity be like? Will it crush us, or will it be too light? Time to find out! (NOTE: This is a post only about the surface gravity of Gliese 370 b. If you want a post about how its star will look in its sky, stay tuned; that post will come in a few days.)

To do this calculation, I will be using Newton’s Universal Law of Gravitation, as it applies to the surface gravity of planets. The equation is:

g=G(m/r^2) where:

g is the surface gravity

G is the Newtonian Gravitational Constant

m is the mass of Gliese 370 b

r is the radius of Gliese 370 b

Here is where we run into a problem, however. We measured and know the mass of Gliese 370 b (3.6 Earth masses), but don’t know the radius. There are ways of finding it, however. To do so, I’m going to use the equation for the volume of a sphere, which states:

V=4/3*r^3*π

Of course, we don’t know the volume of Gliese 370b. There is another equation for volume to help us figure it out, however. It says:

V=m/d where:

m is mass

d is density

This is starting to get a bit repetitive, but we don’t know the density of Gliese 370 b, either. However, we can take a reasonable guess. In relation to the size of the star, Gliese 370 b is about the same distance away as Venus is from our own star. If Gliese 370 b is capable of supporting life as we know it (which, for the purpose of this exercise, we assume is), it has to be a terrestrial planet like Venus, Earth, and Mars. As I’ve already stated, it’s in the same position as Venus so it is more than likely a rocky, terrestrial planet. Terrestrial planets have mostly the same composition, so we can assume that Gliese 370 b’s density is virtually the same as Venus’. Therefore, the density of Gliese 370b is 5.24 grams/cubic centimetre. We know the mass of Gliese 370 b is 3.6 Earth masses, or 2.149991496*10^25 kilograms. Therefore, its volume is 4.103*10^27 cubic centimetres. Working backwards in the previous volume equation, we can find the radius, which turns out to be 9.931258873*10^6 metres.

Now that we have the radius, we can plug it into the original surface gravity equation and finally solve it. With all the values plugged in, we get:

g=G(2.149991496*10^25 kilograms/(9.931258873*10^6 metres)^2)

The result comes out to be 14.55 metres/seconds squared. In comparison, it’s 9.81 m/s^2 and on Gliese 581g it’s (probably) 17.98 m/s^2. Therefore, it’s heavier than Earth but lighter than Gliese 581g. The surface gravity of Gliese 370 b is around 1.5 times heavier than it is here on Earth. Whilst that change in gravity is noticeable, it’s nowhere near enough to kill us; in fact, our bodies would naturally adapt to the heavier G environment within months. It is very possible for humans to settle Gliese 370 b, at least as far as gravity is concerned. Now, the only challenge is figuring out how to get there!