How much land is on Kepler-22b

[TexasJustice]

I guess I'll post my question as a riddle?  Not sure where I should have posted this.  Feel free to move it elsewhere.

Hi.  I have a question for a novel I'm outlining.

Question: So let's say that Kepler-22b is 31% land, 69% Ocean. (I'm saying this.  Not reality)  Then what is the land mass in sq miles of Kepler-22b?  What is the ocean mass of Kepler-22b?  What as the formula to get there?

Data that I have found to work with:

Earth has a radius of 3,958.8 miles
Kepler-22b is 2.4 times bigger then Earth (Which I guess means Kepler-22b is way bigger then Earth.  Like 36 times the  mass of Earth, according to google? That sounds crazy to me.)
Kepler-22b therefore has a radius of 9,501? (or so google says. I have zero idea.)

Google also says that Earth has supposedly 57,308,738 Sq miles of land on it. Earth's land coverage is approximately 29% of the total 196,900,000 sq Miles worth of total surface area.  I have no idea if this is relevant, or useless info.

I also found this for a reference, but if I knew how to use it, I wouldn't be here.

 Earth's Size:

    Volume: 6.73 x 1011 cubic miles (1.083 x 1012 km3)
    Radius: 3,959 miles (6,371 km)
    Diameter: 7,918 miles (12,742 km)
    Surface Area: 1.97 x108 square miles (5.1 x 108 km2)
    Mass: 5.972 x 1024 kg

[exchemist]

3 hours ago, TexasJustice said:

I guess I'll post my question as a riddle?  Not sure where I should have posted this.  Feel free to move it elsewhere.

Hi.  I have a question for a novel I'm outlining.

Question: So let's say that Kepler-22b is 31% land, 69% Ocean. (I'm saying this.  Not reality)  Then what is the land mass in sq miles of Kepler-22b?  What is the ocean mass of Kepler-22b?  What as the formula to get there?

Data that I have found to work with:

Earth has a radius of 3,958.8 miles
Kepler-22b is 2.4 times bigger then Earth (Which I guess means Kepler-22b is way bigger then Earth.  Like 36 times the  mass of Earth, according to google? That sounds crazy to me.)
Kepler-22b therefore has a radius of 9,501? (or so google says. I have zero idea.)

Google also says that Earth has supposedly 57,308,738 Sq miles of land on it. Earth's land coverage is approximately 29% of the total 196,900,000 sq Miles worth of total surface area.  I have no idea if this is relevant, or useless info.

I also found this for a reference, but if I knew how to use it, I wouldn't be here.

 Earth's Size:

    Volume: 6.73 x 1011 cubic miles (1.083 x 1012 km3)
    Radius: 3,959 miles (6,371 km)
    Diameter: 7,918 miles (12,742 km)
    Surface Area: 1.97 x108 square miles (5.1 x 108 km2)
    Mass: 5.972 x 1024 kg

The surface area of a sphere is 4πr². If the radius of Kepler 22b is 2.4 x that of Earth, that would be  ~9600 miles.

So the surface area will be 4 x π x 9.6² x 10⁶ sq.miles ~1.2 x 10⁹ sq. miles if my arithmetic is right. Or in "ordinary" notation that is  1,200,000,000 sq. miles. So you can divide that between land area and ocean area as you wish. 

If you want ocean mass, however, as opposed to area, you have to calculate the volume of water, which means you need to say how deep you think the ocean is on average. You can then use the formula for the volume of a sphere 4/3 πr³. Since the water is a spherical shell around the planet it will be the volume at full radius, (call it R) minus the volume at the radius at the ocean floor (call it r) :  i.e. 4/3 π(R³ - r³).  You can then apply the density figure you want to use to get the mass. That would be for a planet whose surface is all ocean , so then you would pro-rate for the proportion that you want to be ocean.

 

 

 

 

Edited May 24, 2021 by exchemist

[TexasJustice]

Hi. Thank you so much for your help.  So if I am understanding this, then you are saying that Kepler-22b has a workable area of 1,200,000,000 sq miles in total, and as such, if I was to say that the land is 31% of the "surface" area, and the ocean was 69%, then the land is 372 Million sq miles, and the Ocean is 828 million sq miles, as I am just dividing that by 100, and multiplying accordingly to my literary needs.  Correct?

[exchemist]

1 hour ago, TexasJustice said:

Hi. Thank you so much for your help.  So if I am understanding this, then you are saying that Kepler-22b has a workable area of 1,200,000,000 sq miles in total, and as such, if I was to say that the land is 31% of the "surface" area, and the ocean was 69%, then the land is 372 Million sq miles, and the Ocean is 828 million sq miles, as I am just dividing that by 100, and multiplying accordingly to my literary needs.  Correct?

Yes, exactly.